Metrics for sintan (problem 3.4.5)

analyze585.0ms (4.4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.9%	50.1%	0%	0%	0%	0
0%	0%	49.9%	50.1%	0%	0%	0%	1
0%	0%	49.9%	50.1%	0%	0%	0%	2
0%	0%	49.9%	50.1%	0%	0%	0%	3
0%	0%	49.9%	50.1%	0%	0%	0%	4
0%	0%	49.9%	50.1%	0%	0%	0%	5
0%	0%	49.9%	50.1%	0%	0%	0%	6
0%	0%	49.9%	50.1%	0%	0%	0%	7
0%	0%	49.9%	50.1%	0%	0%	0%	8
0%	0%	49.9%	50.1%	0%	0%	0%	9
0%	0%	49.9%	50.1%	0%	0%	0%	10
0%	0%	49.9%	50.1%	0%	0%	0%	11
0%	0%	49.9%	50.1%	0%	0%	0%	12

Compiler

Compiled 17 to 11 computations (35.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 300.0ms

...c/correct-round.rkt:119:19: 127.0ms (42.3% of total)

ival-sub: 46.0ms (15.3% of total)

ival-sin: 38.0ms (12.7% of total)

ival-<=: 33.0ms (11% of total)

ival-tan: 32.0ms (10.7% of total)

ival-div: 13.0ms (4.3% of total)

ival-and: 9.0ms (3% of total)

backward-pass: 2.0ms (0.7% of total)

sample9.8s (74.2%)

Results

6.9s	4210×	2	valid
1.6s	1271×	3	valid
913.0ms	2692×	1	valid
11.0ms	83×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.5s

ival-tan: 4.8s (56.2% of total)

ival-sin: 2.3s (27.2% of total)

backward-pass: 493.0ms (5.8% of total)

ival-sub: 403.0ms (4.8% of total)

...c/correct-round.rkt:119:19: 260.0ms (3.1% of total)

ival-div: 142.0ms (1.7% of total)

ival-<=: 85.0ms (1% of total)

ival-and: 18.0ms (0.2% of total)

Bogosity

preprocess92.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

1280×	`sum5-define`
800×	`sum4-define`
676×	`fnmadd-define`
610×	`fnmadd-define`
594×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	37	30
2	90	27
3	273	27
4	724	27
5	1555	27
6	2749	27
7	2787	27
8	3156	27
9	3172	27
0	6	9
1	13	9
2	23	9
3	42	9
4	81	9
5	190	9
6	513	9
7	1101	9
8	2365	9
9	2557	9
10	2576	9
11	2584	9
0	2584	9

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))

Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Call 2

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps))))
(neg (/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps)))))

Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps))))
(/ (- eps (sin eps)) (- eps (tan eps)))
(neg (/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps)))))
(/ (- eps (sin eps)) (- (tan eps) eps))

Symmetry

(abs eps)

explain1.0s (7.8%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
158	0	-	3	(2.6585254541415395e-108)	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`
100	1	(2.6585254541415395e-108)	0	-	`(-.f64 eps (sin.f64 eps))`
100	1	(2.6585254541415395e-108)	0	-	`(-.f64 eps (tan.f64 eps))`
0	0	-	0	-	`(sin.f64 eps)`
0	0	-	0	-	`eps`
0	0	-	0	-	`(tan.f64 eps)`

Results

495.0ms	190×	1	valid
373.0ms	246×	2	valid
97.0ms	70×	3	valid
1.0ms	6×	0	valid

Compiler

Compiled 58 to 20 computations (65.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 875.0ms

ival-tan: 686.0ms (78.4% of total)

ival-sin: 137.0ms (15.7% of total)

backward-pass: 28.0ms (3.2% of total)

ival-sub: 17.0ms (1.9% of total)

ival-div: 7.0ms (0.8% of total)

const: 1.0ms (0.1% of total)

eval0.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.3%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(-.f64 eps (tan.f64 eps))
✓	cost-diff	(sin.f64 eps)
✓	cost-diff	(-.f64 eps (sin.f64 eps))
✓	cost-diff	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Rules

676×	`fnmadd-define`
450×	`fmsub-define`
440×	`fnmsub-define`
394×	`fmm-def`
368×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
1	13	22
2	23	22
3	42	22
4	81	22
5	190	22
6	513	22
7	1101	22
8	2365	22
9	2557	22
10	2576	22
11	2584	22
0	2584	22

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(- eps (sin eps))
eps
(sin eps)
(- eps (tan eps))
(tan eps)

Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(- eps (sin eps))
(-.f64 eps (sin.f64 eps))
eps
(sin eps)
(sin.f64 eps)
(- eps (tan eps))
(-.f64 eps (tan.f64 eps))
(tan eps)
(tan.f64 eps)

localize320.0ms (2.4%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	65.0%	(-.f64 eps (tan.f64 eps))
✓	accuracy	65.0%	(-.f64 eps (sin.f64 eps))
✓	accuracy	39.2%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

224.0ms	123×	2	valid
53.0ms	35×	3	valid
30.0ms	95×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 24 to 7 computations (70.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 247.0ms

ival-tan: 133.0ms (53.9% of total)

ival-sin: 63.0ms (25.5% of total)

ival-div: 21.0ms (8.5% of total)

ival-sub: 19.0ms (7.7% of total)

backward-pass: 11.0ms (4.5% of total)

const: 0.0ms (0% of total)

series4.0ms (0%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/ (- eps (sin eps)) (- eps (tan eps)))>
#<alt (- eps (sin eps))>
#<alt (sin eps)>
#<alt (- eps (tan eps))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	-inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	0	(/ (- eps (sin eps)) (- eps (tan eps)))
0.0ms	eps	@	inf	(- eps (tan eps))
0.0ms	eps	@	-inf	(- eps (tan eps))

rewrite284.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2006×	`-lowering-.f32`
2006×	`-lowering-.f64`
1458×	`sum3-define`
1434×	`fnmadd-define`
1382×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	23	19
2	97	19
3	527	19
4	4031	19
0	8304	19

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 321

Calls

Call 1

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(- eps (sin eps))
(sin eps)
(- eps (tan eps))

Outputs
(+.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))) (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))))
(+.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))) (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))))
(+.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))) (*.f64 (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))) #s(literal 1 binary64)))
(+.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))) (+.f64 (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))) (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))))
(+.f64 #s(literal 0 binary64) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))))
(+.f64 (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))))
(+.f64 (/.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (neg.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)))))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) #s(literal 0 binary64)) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))))
(+.f64 (-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 0 binary64)) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(exp.f64 (log.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))) #s(literal 1 binary64)))
(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (-.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 eps) eps))))
(-.f64 (/.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (-.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))))
(-.f64 (/.f64 (/.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 eps (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))) (/.f64 (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)) (sin.f64 eps))) (/.f64 (-.f64 eps (tan.f64 eps)) (/.f64 (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)) (sin.f64 eps))))
(-.f64 (/.f64 (-.f64 eps (tan.f64 eps)) (/.f64 (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)) eps)) (/.f64 (*.f64 (sin.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 eps) eps))) (/.f64 (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)) eps)))
(-.f64 (/.f64 (/.f64 (-.f64 eps (tan.f64 eps)) (sin.f64 eps)) (/.f64 (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)) (.f64 eps (sin.f64 eps)))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 eps) eps)) (/.f64 (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)) (.f64 eps (sin.f64 eps)))))
(-.f64 (/.f64 (-.f64 (tan.f64 eps) eps) (neg.f64 (/.f64 (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)) eps))) (/.f64 (neg.f64 (*.f64 (sin.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 eps) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)) eps))))
(-.f64 (/.f64 (/.f64 (*.f64 eps (-.f64 (tan.f64 eps) eps)) (sin.f64 eps)) (/.f64 (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))) (/.f64 (-.f64 (tan.f64 eps) eps) (/.f64 (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))))
(-.f64 (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 0 binary64)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
(fma.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(fma.f64 eps (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (neg.f64 (-.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))))))
(fma.f64 eps (/.f64 (-.f64 eps (tan.f64 eps)) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (neg.f64 (/.f64 (*.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64)))))
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(-.f64 eps (sin.f64 eps))
(-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (-.f64 #s(literal 0 binary64) eps))
(-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (/.f64 eps #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 (sin.f64 eps) eps))
(-.f64 (/.f64 (sin.f64 eps) #s(literal -1 binary64)) (/.f64 eps #s(literal -1 binary64)))
(fma.f64 eps #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) #s(literal -1 binary64) eps)
(fma.f64 #s(literal 1 binary64) eps (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 eps)) eps)
(fma.f64 #s(literal -1 binary64) (sin.f64 eps) eps)
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(fma.f64 #s(literal -1 binary64) (/.f64 eps #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(fma.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(neg.f64 (-.f64 (sin.f64 eps) eps))
(/.f64 (-.f64 eps (sin.f64 eps)) #s(literal 1 binary64))
(/.f64 (-.f64 (sin.f64 eps) eps) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps))))
(pow.f64 (-.f64 eps (sin.f64 eps)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps))) #s(literal -1 binary64))
(*.f64 (-.f64 eps (sin.f64 eps)) #s(literal 1 binary64))
(*.f64 (-.f64 (sin.f64 eps) eps) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps)))
(*.f64 #s(literal -1 binary64) (-.f64 (sin.f64 eps) eps))
(+.f64 #s(literal 0 binary64) (sin.f64 eps))
(+.f64 (.f64 (sin.f64 eps) (cos.f64 #s(literal 0 binary64))) (.f64 (cos.f64 eps) (sin.f64 #s(literal 0 binary64))))
(+.f64 (.f64 (sin.f64 #s(literal 0 binary64)) (cos.f64 eps)) (.f64 (cos.f64 #s(literal 0 binary64)) (sin.f64 eps)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (sin.f64 eps))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 eps) #s(literal -1 binary64)))
(-.f64 (.f64 (sin.f64 #s(literal 0 binary64)) (cos.f64 eps)) (.f64 (cos.f64 #s(literal 0 binary64)) (sin.f64 (-.f64 #s(literal 0 binary64) eps))))
(-.f64 (.f64 (sin.f64 #s(literal 0 binary64)) (cos.f64 eps)) (.f64 (cos.f64 #s(literal 0 binary64)) (sin.f64 (/.f64 eps #s(literal -1 binary64)))))
(sin.f64 eps)
(neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal 1 binary64)))
(neg.f64 (/.f64 (sin.f64 eps) #s(literal -1 binary64)))
(neg.f64 (sin.f64 (-.f64 #s(literal 0 binary64) eps)))
(neg.f64 (sin.f64 (/.f64 eps #s(literal -1 binary64))))
(/.f64 (sin.f64 eps) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 eps)))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal -1 binary64))
(pow.f64 (sin.f64 eps) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 eps)) #s(literal -1 binary64))
(*.f64 (sin.f64 eps) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sin.f64 eps))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) #s(literal -1 binary64)))
(+.f64 eps (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(+.f64 eps (*.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) #s(literal 1 binary64)))
(+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) eps)
(+.f64 #s(literal 0 binary64) (-.f64 eps (tan.f64 eps)))
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) #s(literal 1 binary64)) eps)
(+.f64 (-.f64 eps #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(exp.f64 (log.f64 (-.f64 eps (tan.f64 eps))))
(exp.f64 (*.f64 (log.f64 (-.f64 eps (tan.f64 eps))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps)))) #s(literal -1 binary64)))
(-.f64 eps (tan.f64 eps))
(-.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) eps))
(-.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) (/.f64 eps #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 (tan.f64 eps) eps))
(-.f64 (/.f64 (tan.f64 eps) #s(literal -1 binary64)) (/.f64 eps #s(literal -1 binary64)))
(fma.f64 eps #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(fma.f64 (sin.f64 eps) (/.f64 #s(literal -1 binary64) (cos.f64 eps)) eps)
(fma.f64 (tan.f64 eps) #s(literal -1 binary64) eps)
(fma.f64 #s(literal 1 binary64) eps (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 eps)) eps)
(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) eps)
(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (*.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal -1 binary64)) eps)
(fma.f64 #s(literal -1 binary64) (tan.f64 eps) eps)
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(fma.f64 #s(literal -1 binary64) (/.f64 eps #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(fma.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps)) (-.f64 #s(literal 0 binary64) (sin.f64 eps)) eps)
(fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps) eps)
(fma.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) eps)
(neg.f64 (-.f64 (tan.f64 eps) eps))
(/.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(/.f64 (-.f64 (tan.f64 eps) eps) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)))
(pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) #s(literal -1 binary64))
(*.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(*.f64 (-.f64 (tan.f64 eps) eps) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps)))
(*.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps))

simplify262.0ms (2%)

Algorithm

1×	egg-herbie

Rules

4708×	`-lowering-.f32`
4708×	`-lowering-.f64`
1320×	`+-lowering-+.f64`
1320×	`+-lowering-+.f32`
1274×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	547
1	457	472
2	1539	434
3	6919	432
0	8080	432

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
1
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) eps) (/.f64 #s(literal -1 binary64) eps))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
(+.f64 #s(literal 1 binary64) (+.f64 (.f64 (sin.f64 eps) (+.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (.f64 (sin.f64 eps) (/.f64 (.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 eps eps))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) eps) (/.f64 #s(literal -1 binary64) eps)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sin.f64 eps) (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (.f64 (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) eps)) #s(literal 1 binary64)))) eps))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) (+.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) eps) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) eps) (*.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) eps))
(* 1/6 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal 1/6 binary64))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (*.f64 eps eps) #s(literal -1/120 binary64)))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/120 binary64) (.f64 (*.f64 eps eps) #s(literal 1/5040 binary64)))))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64)))))))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 eps eps) #s(literal -1/5040 binary64))))))))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(* -1/3 (pow eps 3))
(.f64 eps (.f64 (*.f64 eps eps) #s(literal -1/3 binary64)))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/3 binary64) (.f64 (*.f64 eps eps) #s(literal -2/15 binary64)))))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -2/15 binary64) (.f64 (*.f64 eps eps) #s(literal -17/315 binary64))))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -2/15 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -17/315 binary64) (.f64 (*.f64 eps eps) #s(literal -62/2835 binary64))))))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))

eval31.0ms (0.2%)

Compiler: Compiled 7408 to 859 computations (88.4% saved)

prune50.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	366	3	369
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	367	3	370

Accuracy

100.0%

Counts

370 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
▶	99.8%	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
▶	99.2%	#s(literal -1/2 binary64)

Status

Accuracy

Program

▶

100.0%

(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))

▶

99.8%

(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))

▶

99.2%

#s(literal -1/2 binary64)

Compiler

Compiled 24 to 18 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
✓	cost-diff	(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
✓	cost-diff	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
✓	cost-diff	(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
✓	cost-diff	(*.f64 eps eps)
✓	cost-diff	(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
✓	cost-diff	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))

Rules

140×	`fma-define`
104×	`fma-lowering-fma.f32`
104×	`fma-lowering-fma.f64`
76×	`-lowering-.f32`
76×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	59
1	32	54
2	78	54
3	146	54
4	188	54
5	191	54
0	191	54

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
-1/2
(+ (* 9/40 (* eps eps)) -1/2)
(* 9/40 (* eps eps))
9/40
(* eps eps)
eps
-1/2
(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
eps
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
(+ 9/40 (* (* eps eps) -27/2800))
9/40
(* (* eps eps) -27/2800)
(* eps eps)
-27/2800
-1/2

Outputs
-1/2
#s(literal -1/2 binary64)
(+ (* 9/40 (* eps eps)) -1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(* 9/40 (* eps eps))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
9/40
#s(literal 9/40 binary64)
(* eps eps)
(*.f64 eps eps)
eps
-1/2
#s(literal -1/2 binary64)
(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
eps
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(+ 9/40 (* (* eps eps) -27/2800))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
9/40
#s(literal 9/40 binary64)
(* (* eps eps) -27/2800)
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* eps eps)
(*.f64 eps eps)
-27/2800
#s(literal -27/2800 binary64)
-1/2
#s(literal -1/2 binary64)

localize113.0ms (0.9%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
✓	accuracy	99.8%	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
✓	accuracy	99.7%	(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	99.8%	(.f64 #s(literal 9/40 binary64) (.f64 eps eps))

Results

61.0ms	230×	0	valid
10.0ms	11×	3	valid
6.0ms	6×	2	valid
6.0ms	9×	1	valid

Compiler

Compiled 73 to 13 computations (82.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 14.0ms (42.5% of total)

...c/correct-round.rkt:119:19: 10.0ms (30.4% of total)

ival-add: 6.0ms (18.2% of total)

backward-pass: 2.0ms (6.1% of total)

const: 0.0ms (0% of total)

series13.0ms (0.1%)

Counts

8 → 96

Calls

Call 1

Inputs
#<alt (+ (* 9/40 (* eps eps)) -1/2)>
#<alt (* 9/40 (* eps eps))>
#<alt (* eps eps)>
#<alt (+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)>
#<alt (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))>
#<alt (* eps (+ 9/40 (* (* eps eps) -27/2800)))>
#<alt (+ 9/40 (* (* eps eps) -27/2800))>
#<alt (* (* eps eps) -27/2800)>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* 9/40 eps)>
#<alt (* eps (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* eps (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* eps (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* -27/2800 (pow eps 3))>
#<alt (* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))>
#<alt 9/40>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>

Calls

24 calls:

Time	Variable		Point	Expression
8.0ms	eps	@	inf	(* 9/40 (* eps eps))
1.0ms	eps	@	0	(+ (* 9/40 (* eps eps)) -1/2)
0.0ms	eps	@	inf	(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
0.0ms	eps	@	inf	(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
0.0ms	eps	@	inf	(* eps (+ 9/40 (* (* eps eps) -27/2800)))

rewrite24.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

154×	`fma-define`
116×	`fma-lowering-fma.f32`
116×	`fma-lowering-fma.f64`
94×	`-lowering-.f32`
94×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	34	44
2	80	44
3	154	44
4	216	44
5	255	44
6	295	44
7	301	44
8	309	44
0	309	44

Stop Event

1×	iter limit
1×	saturated

Counts

8 → 76

Calls

Call 1

Inputs
(+ (* 9/40 (* eps eps)) -1/2)
(* 9/40 (* eps eps))
(* eps eps)
(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
(+ 9/40 (* (* eps eps) -27/2800))
(* (* eps eps) -27/2800)

Outputs
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 #s(literal 9/40 binary64) eps) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 9/40 binary64) eps) eps #s(literal -1/2 binary64))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(.f64 eps (.f64 #s(literal 9/40 binary64) eps))
(.f64 (.f64 eps eps) #s(literal 9/40 binary64))
(.f64 (.f64 #s(literal 9/40 binary64) eps) eps)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 eps)))
(pow.f64 eps #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 eps))
(*.f64 eps eps)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
(+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))))
(+.f64 (+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) (+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64)))
(+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(fma.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))) #s(literal -1/2 binary64))
(fma.f64 eps (.f64 #s(literal 9/40 binary64) eps) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) (+.f64 (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps eps) #s(literal 9/40 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)) (+.f64 (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))) #s(literal -1/2 binary64))
(fma.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)) (.f64 eps eps) (+.f64 (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(fma.f64 (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))) eps #s(literal -1/2 binary64))
(fma.f64 (.f64 #s(literal 9/40 binary64) eps) eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))
(fma.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) eps (+.f64 (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps #s(literal -27/2800 binary64)) (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -27/2800 binary64)) (+.f64 (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal -27/2800 binary64) (+.f64 (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64)))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(fma.f64 eps (.f64 #s(literal 9/40 binary64) eps) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
(fma.f64 (.f64 eps eps) #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
(fma.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
(fma.f64 (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)) (.f64 eps eps) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
(fma.f64 (.f64 #s(literal 9/40 binary64) eps) eps (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(fma.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) eps (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
(fma.f64 (.f64 eps #s(literal -27/2800 binary64)) (.f64 eps (.f64 eps eps)) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
(fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -27/2800 binary64)) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
(fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal -27/2800 binary64) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps)))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(.f64 (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) (.f64 eps eps))
(.f64 (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))) eps)
(+.f64 (.f64 #s(literal 9/40 binary64) eps) (.f64 eps (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(+.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) (.f64 #s(literal 9/40 binary64) eps))
(fma.f64 #s(literal 9/40 binary64) eps (.f64 eps (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(fma.f64 eps #s(literal 9/40 binary64) (.f64 eps (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)) (*.f64 #s(literal 9/40 binary64) eps))
(fma.f64 (.f64 eps eps) (.f64 eps #s(literal -27/2800 binary64)) (*.f64 #s(literal 9/40 binary64) eps))
(fma.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps eps)) (*.f64 #s(literal 9/40 binary64) eps))
(fma.f64 (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)) eps (*.f64 #s(literal 9/40 binary64) eps))
(fma.f64 (.f64 eps #s(literal -27/2800 binary64)) (.f64 eps eps) (*.f64 #s(literal 9/40 binary64) eps))
(fma.f64 (.f64 eps (.f64 eps eps)) #s(literal -27/2800 binary64) (*.f64 #s(literal 9/40 binary64) eps))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(.f64 (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))) eps)
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(+.f64 (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -27/2800 binary64) #s(literal 9/40 binary64))
(fma.f64 #s(literal -27/2800 binary64) (*.f64 eps eps) #s(literal 9/40 binary64))
(fma.f64 (*.f64 eps #s(literal -27/2800 binary64)) eps #s(literal 9/40 binary64))
(.f64 eps (.f64 eps #s(literal -27/2800 binary64)))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(.f64 #s(literal -27/2800 binary64) (.f64 eps eps))
(.f64 (.f64 eps #s(literal -27/2800 binary64)) eps)

simplify159.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1696×	`fma-lowering-fma.f32`
1696×	`fma-lowering-fma.f64`
1526×	`-lowering-.f32`
1526×	`-lowering-.f64`
1132×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	634
1	107	526
2	272	522
3	787	522
4	2410	500
5	6788	500
0	8244	500

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* 9/40 eps)
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(* -27/2800 (pow eps 3))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 3))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
9/40
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))) #s(literal -1/2 binary64))
(* -27/2800 (pow eps 4))
(.f64 eps (.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 eps eps))))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 eps eps))))))
(* -27/2800 (pow eps 4))
(.f64 eps (.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 eps eps))))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 eps eps))))))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* -27/2800 (pow eps 4))
(.f64 eps (.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* -27/2800 (pow eps 4))
(.f64 eps (.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* 9/40 eps)
(*.f64 #s(literal 9/40 binary64) eps)
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* -27/2800 (pow eps 3))
(.f64 #s(literal -27/2800 binary64) (.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* -27/2800 (pow eps 3))
(.f64 #s(literal -27/2800 binary64) (.f64 eps (*.f64 eps eps)))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
9/40
#s(literal 9/40 binary64)
(+ 9/40 (* -27/2800 (pow eps 2)))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))

eval30.0ms (0.2%)

Compiler: Compiled 2227 to 194 computations (91.3% saved)

prune11.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	188	3	191

Accuracy

100.0%

Counts

191 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))

✓

99.8%

(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))

✓

99.2%

#s(literal -1/2 binary64)

Compiler

Compiled 55 to 35 computations (36.4% saved)

regimes5.0ms (0%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Outputs
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))

Calls

2 calls:

2.0ms	eps
2.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
100.0%	1	`eps`
100.0%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))

Outputs
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))

Calls

1 calls:

1.0ms

eps

Results

Accuracy	Segments	Branch
99.8%	1	`eps`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)

Outputs
#s(literal -1/2 binary64)

Calls

1 calls:

1.0ms

eps

Results

Accuracy	Segments	Branch
99.2%	1	`eps`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	19	21

Stop Event

1×

saturated

Calls

Call 1

Inputs

(+.f64 (*.f64 eps (*.f64 eps (+.f64 #s(literal 9/40 binary64) (*.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))

(+.f64 (*.f64 #s(literal 9/40 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64))

#s(literal -1/2 binary64)

Outputs
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
#s(literal -1/2 binary64)

soundness294.0ms (2.2%)

Rules

4708×	`-lowering-.f32`
4708×	`-lowering-.f64`
1320×	`+-lowering-+.f64`
1320×	`+-lowering-+.f32`
1274×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	547
1	457	472
2	1539	434
3	6919	432
0	8080	432

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 46 to 30 computations (34.8% saved)

preprocess40.0ms (0.3%)

Remove: (abs eps)
Compiler: Compiled 196 to 120 computations (38.8% saved)

sintan (problem 3.4.5)

analyze585.0ms (4.4%)

sample9.8s (74.2%)

preprocess92.0ms (0.7%)

explain1.0s (7.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify51.0ms (0.4%)

localize320.0ms (2.4%)

series4.0ms (0%)

rewrite284.0ms (2.1%)

simplify262.0ms (2%)

eval31.0ms (0.2%)

prune50.0ms (0.4%)

simplify9.0ms (0.1%)

localize113.0ms (0.9%)

series13.0ms (0.1%)

rewrite24.0ms (0.2%)

simplify159.0ms (1.2%)

eval30.0ms (0.2%)

prune11.0ms (0.1%)

regimes5.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify7.0ms (0.1%)

soundness294.0ms (2.2%)

preprocess40.0ms (0.3%)

end0.0ms (0%)

Profiling