Metrics for Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

ival-sub: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample987.0ms (21%)

Results

766.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 447.0ms

ival-mult: 390.0ms (87.2% of total)

ival-sub: 44.0ms (9.8% of total)

const: 10.0ms (2.2% of total)

backward-pass: 3.0ms (0.7% of total)

Bogosity

preprocess103.0ms (2.2%)

Algorithm

2×	egg-herbie

Rules

1158×	`fnmadd-define`
954×	`fnmsub-define`
954×	`fmsub-define`
850×	`fma-define`
680×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	87
1	116	83
2	308	80
3	809	80
4	1835	80
5	2995	80
6	3656	80
7	3792	80
8	3792	80
0	8	8
1	19	8
2	50	8
3	114	8
4	177	8
5	284	8
6	520	8
7	732	8
8	1035	8
9	1805	8
10	2126	8
11	2172	8
0	2172	8

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (* x x) (* (* y 4) z))

Outputs
(- (* x x) (* (* y 4) z))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))

Call 2

Inputs
(- (* x x) (* (* y 4) z))
(- (* (neg x) (neg x)) (* (* y 4) z))
(- (* x x) (* (* (neg y) 4) z))
(- (* x x) (* (* y 4) (neg z)))
(neg (- (* (neg x) (neg x)) (* (* y 4) z)))
(neg (- (* x x) (* (* (neg y) 4) z)))
(neg (- (* x x) (* (* y 4) (neg z))))
(- (* y y) (* (* x 4) z))
(- (* z z) (* (* y 4) x))
(- (* x x) (* (* z 4) y))

Outputs
(- (* x x) (* (* y 4) z))
(fmsub x x (* y (* 4 z)))
(- (* (neg x) (neg x)) (* (* y 4) z))
(fmsub x x (* y (* 4 z)))
(- (* x x) (* (* (neg y) 4) z))
(fmsub x x (* y (* z -4)))
(- (* x x) (* (* y 4) (neg z)))
(fmsub x x (* y (* z -4)))
(neg (- (* (neg x) (neg x)) (* (* y 4) z)))
(fnmsub x x (* y (* z -4)))
(neg (- (* x x) (* (* (neg y) 4) z)))
(fnmsub x x (* y (* 4 z)))
(neg (- (* x x) (* (* y 4) (neg z))))
(fnmsub x x (* y (* 4 z)))
(- (* y y) (* (* x 4) z))
(fma x (* z -4) (* y y))
(- (* z z) (* (* y 4) x))
(fmsub z z (* y (* x 4)))
(- (* x x) (* (* z 4) y))
(fmsub x x (* y (* 4 z)))

Symmetry

(abs x)

(sort y z)

explain108.0ms (2.3%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
2	-	-	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
0	-	-	`x`
0	-	-	`(*.f64 x x)`
0	-	-	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
0	-	-	`#s(literal 4 binary64)`
0	-	-	`z`
0	-	-	`(*.f64 y #s(literal 4 binary64))`
0	-	-	`y`

Results

47.0ms

512×

valid

Compiler

Compiled 68 to 26 computations (61.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 18.0ms (85.1% of total)

ival-sub: 3.0ms (14.2% of total)

const: 1.0ms (4.7% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify48.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 y #s(literal 4 binary64))
✓	cost-diff	(.f64 (.f64 y #s(literal 4 binary64)) z)
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Rules

680×	`fnmadd-define`
670×	`fma-define`
504×	`sum3-define`
364×	`fma-lowering-fma.f32`
364×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	19	23
2	50	23
3	114	23
4	177	23
5	284	23
6	520	23
7	732	23
8	1035	23
9	1805	23
10	2126	23
11	2172	23
0	2172	23

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (* x x) (* (* y 4) z))
(* x x)
x
(* (* y 4) z)
(* y 4)
y
4
z

Outputs
(- (* x x) (* (* y 4) z))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(* x x)
(*.f64 x x)
x
(* (* y 4) z)
(.f64 #s(literal 4 binary64) (.f64 y z))
(* y 4)
(*.f64 y #s(literal 4 binary64))
y
4
#s(literal 4 binary64)
z

localize30.0ms (0.6%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 y #s(literal 4 binary64)) z)
✓	accuracy	100.0%	(*.f64 y #s(literal 4 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.4%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Results

22.0ms

256×

valid

Compiler

Compiled 28 to 9 computations (67.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 6.0ms (82.4% of total)

ival-sub: 1.0ms (13.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series8.0ms (0.2%)

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (- (* x x) (* (* y 4) z))>
#<alt (* x x)>
#<alt (* (* y 4) z)>
#<alt (* y 4)>

Outputs
#<alt (* -4 (* y z))>
#<alt (- (pow x 2) (* 4 (* y z)))>
#<alt (- (pow x 2) (* 4 (* y z)))>
#<alt (- (pow x 2) (* 4 (* y z)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (* -4 (* y z))>
#<alt (* y (- (/ (pow x 2) y) (* 4 z)))>
#<alt (* y (- (/ (pow x 2) y) (* 4 z)))>
#<alt (* y (- (/ (pow x 2) y) (* 4 z)))>
#<alt (* -4 (* y z))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))>
#<alt (pow x 2)>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (* -4 (* y z))>
#<alt (* z (- (/ (pow x 2) z) (* 4 y)))>
#<alt (* z (- (/ (pow x 2) z) (* 4 y)))>
#<alt (* z (- (/ (pow x 2) z) (* 4 y)))>
#<alt (* -4 (* y z))>
#<alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))>
#<alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))>
#<alt (* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 (* y z))>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>
#<alt (* 4 y)>

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	z	@	0	(- (* x x) (* (* y 4) z))
1.0ms	y	@	0	(* (* y 4) z)
1.0ms	y	@	inf	(- (* x x) (* (* y 4) z))
1.0ms	x	@	0	(- (* x x) (* (* y 4) z))
0.0ms	y	@	0	(- (* x x) (* (* y 4) z))

rewrite413.0ms (8.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3896×	`-lowering-.f32`
3896×	`-lowering-.f64`
1744×	`fnmadd-define`
1474×	`pow-lowering-pow.f64`
1474×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	40	19
2	288	19
3	3987	19
0	8575	19

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 149

Calls

Call 1

Inputs
(- (* x x) (* (* y 4) z))
(* x x)
(* (* y 4) z)
(* y 4)

Outputs
(+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal -4 binary64))))
(+.f64 (.f64 x x) (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 y (.f64 z #s(literal -4 binary64)))))
(+.f64 (.f64 x x) (neg.f64 (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))))))
(+.f64 (.f64 x x) (+.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z)))))
(+.f64 (.f64 x x) (+.f64 (.f64 y (.f64 z #s(literal -4 binary64))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(+.f64 (.f64 x x) (+.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))))))
(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))))
(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z)))))
(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))
(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))))))
(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))))
(+.f64 (.f64 y (.f64 z #s(literal -4 binary64))) (*.f64 x x))
(+.f64 (.f64 y (.f64 z #s(literal -4 binary64))) (+.f64 (.f64 x x) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))
(+.f64 (.f64 y (.f64 z #s(literal -4 binary64))) (+.f64 (.f64 x x) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(+.f64 (.f64 y (.f64 z #s(literal -4 binary64))) (+.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal -4 binary64))))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (neg.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z))))))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (neg.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))) (+.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(+.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 x x))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal -4 binary64)))))
(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (*.f64 #s(literal 4 binary64) z)))
(+.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 x x)) (.f64 y (.f64 z #s(literal -4 binary64))))
(+.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 x x)) (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 y (*.f64 z #s(literal -4 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))))) #s(literal -1 binary64)))
(-.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z)))
(-.f64 (.f64 x x) (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))
(-.f64 (.f64 x x) (-.f64 (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z)))))
(-.f64 (.f64 x x) (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(-.f64 (.f64 x x) (-.f64 (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z)))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (-.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (-.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (/.f64 (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))) (+.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z)))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (*.f64 x x)))
(-.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64))))) (-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (/.f64 (.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))))
(-.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 x x)) (.f64 y (.f64 #s(literal 4 binary64) z)))
(-.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 x x)) (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z)))))
(-.f64 (+.f64 (.f64 x x) #s(literal 0 binary64)) (.f64 y (*.f64 #s(literal 4 binary64) z)))
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(.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (*.f64 z z)) #s(literal 64 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (*.f64 z z) #s(literal 16 binary64)))))
(.f64 (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z)))))))
(.f64 (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z)))))))
(.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 x x)))))
(.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64)))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (.f64 (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z))))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (-.f64 (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))) (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z))))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z))))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(exp.f64 (log.f64 (.f64 y (.f64 #s(literal 4 binary64) z))))
(exp.f64 (.f64 (log.f64 (.f64 y (*.f64 #s(literal 4 binary64) z))) #s(literal 1 binary64)))
(pow.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) #s(literal 1 binary64))
(.f64 y (.f64 #s(literal 4 binary64) z))
(.f64 #s(literal 4 binary64) (.f64 y z))
(.f64 (.f64 y #s(literal 4 binary64)) z)
(.f64 z (.f64 y #s(literal 4 binary64)))
(.f64 (.f64 #s(literal 4 binary64) z) y)
(.f64 (.f64 y z) #s(literal 4 binary64))
(.f64 (exp.f64 (log.f64 (.f64 y #s(literal 4 binary64)))) (exp.f64 (log.f64 z)))
(.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 (.f64 y #s(literal 4 binary64)))))
(.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 (.f64 #s(literal 4 binary64) z))))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 4 binary64) z))) (exp.f64 (log.f64 y)))
(.f64 (exp.f64 (log.f64 #s(literal 4 binary64))) (exp.f64 (log.f64 (.f64 y z))))
(.f64 (exp.f64 (log.f64 (.f64 y z))) (exp.f64 (log.f64 #s(literal 4 binary64))))
(*.f64 y #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) y)

simplify139.0ms (3%)

Algorithm

1×	egg-herbie

Rules

2808×	`-lowering-.f32`
2808×	`-lowering-.f64`
1948×	`fnmadd-define`
1514×	`fnmsub-define`
1292×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	445
1	101	445
2	281	445
3	1169	445
4	4112	445
0	8465	445

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(* -4 (* y z))
(- (pow x 2) (* 4 (* y z)))
(- (pow x 2) (* 4 (* y z)))
(- (pow x 2) (* 4 (* y z)))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* -4 (* y z))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* y (- (/ (pow x 2) y) (* 4 z)))
(* -4 (* y z))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* -4 (* y z))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* -4 (* y z))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 (* y z))
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)
(* 4 y)

Outputs
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(- (pow x 2) (* 4 (* y z)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(- (pow x 2) (* 4 (* y z)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(- (pow x 2) (* 4 (* y z)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* y (- (/ (pow x 2) y) (* 4 z)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* y (- (/ (pow x 2) y) (* 4 z)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* y (- (/ (pow x 2) y) (* 4 z)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* z (- (/ (pow x 2) z) (* 4 y)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* z (- (/ (pow x 2) z) (* 4 y)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* z (- (/ (pow x 2) z) (* 4 y)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 (* y z))
(.f64 (.f64 y z) #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))
(* 4 y)
(*.f64 y #s(literal 4 binary64))

eval50.0ms (1.1%)

Compiler: Compiled 7763 to 423 computations (94.6% saved)

prune23.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	231	2	233
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	231	3	234

Accuracy

100.0%

Counts

234 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
▶	57.7%	(*.f64 x x)
▶	49.1%	(.f64 #s(literal -4 binary64) (.f64 y z))

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(*.f64 y z)
✓	cost-diff	(.f64 #s(literal -4 binary64) (.f64 y z))

Rules

26×	`-lowering-.f32`
26×	`-lowering-.f64`
10×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	11	15
2	18	15
3	20	15
0	20	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* -4 (* y z))
-4
(* y z)
y
z
(* x x)
x

Outputs
(* -4 (* y z))
(.f64 z (.f64 #s(literal -4 binary64) y))
-4
#s(literal -4 binary64)
(* y z)
(*.f64 y z)
y
z
(* x x)
(*.f64 x x)
x

localize63.0ms (1.4%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 y z)
✓	accuracy	100.0%	(.f64 #s(literal -4 binary64) (.f64 y z))

Results

17.0ms

256×

valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 6.0ms (99.6% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series2.0ms (0%)

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (* -4 (* y z))>
#<alt (* y z)>
#<alt (* x x)>

Outputs
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(* -4 (* y z))
0.0ms	y	@	-inf	(* y z)
0.0ms	z	@	0	(* -4 (* y z))
0.0ms	z	@	-inf	(* y z)
0.0ms	y	@	inf	(* -4 (* y z))

rewrite160.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1432×	`prod-exp`
1328×	`-lowering-.f32`
1328×	`-lowering-.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	27	11
3	45	11
4	93	11
5	250	9
6	1727	9
7	1756	9
8	1886	9
9	3183	9
0	8549	9

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 10

Calls

Call 1

Inputs
(* -4 (* y z))
(* y z)
(* x x)

Outputs
(.f64 #s(literal -4 binary64) (.f64 y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(.f64 z (.f64 #s(literal -4 binary64) y))
(.f64 (.f64 y z) #s(literal -4 binary64))
(.f64 (.f64 #s(literal -4 binary64) y) z)
(.f64 (.f64 #s(literal -4 binary64) z) y)
(*.f64 y z)
(*.f64 z y)
#s(literal 1 binary64)
x

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

26×	`-lowering-.f32`
26×	`-lowering-.f64`
10×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	228
1	13	228
2	20	228
3	22	228
0	22	228

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

Inputs
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* -4 (* y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval7.0ms (0.2%)

Compiler: Compiled 321 to 17 computations (94.7% saved)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	68	5	73

Accuracy

100.0%

Counts

73 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
✓	57.7%	(*.f64 x x)
✓	49.1%	(.f64 #s(literal -4 binary64) (.f64 y z))
▶	5.4%	x
▶	3.7%	#s(literal 1 binary64)

Compiler

Compiled 34 to 25 computations (26.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	2
1	4	2
0	4	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
1
x

Outputs
1
#s(literal 1 binary64)
x

localize11.0ms (0.2%)

Results

7.0ms

256×

valid

Compiler

Compiled 6 to 5 computations (16.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite9.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	3	3
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
✓	57.7%	(*.f64 x x)
✓	49.1%	(.f64 #s(literal -4 binary64) (.f64 y z))
✓	5.4%	x
✓	3.7%	#s(literal 1 binary64)

Compiler

Compiled 56 to 37 computations (33.9% saved)

regimes22.0ms (0.5%)

Counts

5 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(*.f64 x x)
(.f64 #s(literal -4 binary64) (.f64 y z))
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Outputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Calls

7 calls:

5.0ms	(.f64 (.f64 y #s(literal 4 binary64)) z)
3.0ms	(*.f64 x x)
3.0ms	(*.f64 y #s(literal 4 binary64))
3.0ms	z
3.0ms	y

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`y`
99.2%	1	`z`
99.2%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
99.2%	1	`(*.f64 x x)`
99.2%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
99.2%	1	`(*.f64 y #s(literal 4 binary64))`

Compiler

Compiled 44 to 32 computations (27.3% saved)

regimes11.0ms (0.2%)

Counts

4 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(*.f64 x x)
(.f64 #s(literal -4 binary64) (.f64 y z))

Outputs
(.f64 #s(literal -4 binary64) (.f64 y z))
(*.f64 x x)

Calls

4 calls:

3.0ms	y
2.0ms	x
2.0ms	z
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
87.2%	2	`x`
73.2%	3	`y`
70.7%	3	`z`
87.2%	2	`(*.f64 x x)`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes8.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(*.f64 x x)

Outputs
(*.f64 x x)

Calls

4 calls:

2.0ms	z
2.0ms	y
2.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
57.7%	1	`z`
57.7%	1	`y`
57.7%	1	`x`
57.7%	1	`(*.f64 x x)`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes7.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x

Outputs
x

Calls

3 calls:

3.0ms	z
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
5.4%	1	`y`
5.4%	1	`z`
5.4%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

3 calls:

1.0ms	z
1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
3.7%	1	`x`
3.7%	1	`y`
3.7%	1	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.657494682706855e-38	1.180133494521189e-32

Compiler

Compiled 18 to 13 computations (27.8% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	27	28
2	44	28
3	54	28
4	62	28
5	65	28

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
(if (<=.f64 (.f64 x x) #s(literal 4789048565205903/95780971304118053647396689196894323976171195136475136 binary64)) (.f64 #s(literal -4 binary64) (.f64 y z)) (.f64 x x))
(*.f64 x x)
x
#s(literal 1 binary64)

Outputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
(if (<=.f64 (.f64 x x) #s(literal 4789048565205903/95780971304118053647396689196894323976171195136475136 binary64)) (.f64 #s(literal -4 binary64) (.f64 y z)) (.f64 x x))
(*.f64 x x)
x
#s(literal 1 binary64)

soundness2.4s (51%)

Rules

2808×	`-lowering-.f32`
2808×	`-lowering-.f64`
2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1948×	`fnmadd-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	27	11
3	45	11
4	93	11
5	250	9
6	1727	9
7	1756	9
8	1886	9
9	3183	9
0	8549	9
0	36	445
1	101	445
2	281	445
3	1169	445
4	4112	445
0	8465	445

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 66 to 40 computations (39.4% saved)

preprocess48.0ms (1%)

Remove

(sort y z)

(abs x)

Compiler

Compiled 182 to 110 computations (39.6% saved)

Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1

analyze0.0ms (0%)

sample987.0ms (21%)

preprocess103.0ms (2.2%)

explain108.0ms (2.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify48.0ms (1%)

localize30.0ms (0.6%)

series8.0ms (0.2%)

rewrite413.0ms (8.8%)

simplify139.0ms (3%)

eval50.0ms (1.1%)

prune23.0ms (0.5%)

simplify6.0ms (0.1%)

localize63.0ms (1.4%)

series2.0ms (0%)

rewrite160.0ms (3.4%)

simplify8.0ms (0.2%)

eval7.0ms (0.2%)

prune3.0ms (0.1%)

simplify4.0ms (0.1%)

localize11.0ms (0.2%)

series0.0ms (0%)

rewrite9.0ms (0.2%)

simplify3.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes22.0ms (0.5%)

regimes11.0ms (0.2%)

regimes8.0ms (0.2%)

regimes7.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify9.0ms (0.2%)

soundness2.4s (51%)

preprocess48.0ms (1%)

end0.0ms (0%)

Profiling