Metrics for Hyperbolic secant

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

Precisions

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

Operation ival-div, time spent: 0.0ms, 0.0% of total-time

Operation ival-exp, time spent: 0.0ms, 0.0% of total-time

Operation ival-add, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

Operation ival-neg, time spent: 0.0ms, 0.0% of total-time

sample1.3s (49.3%)

Results

1.2s	8255×	256	valid
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 521.0ms

Operation ival-exp, time spent: 237.0ms, 45.0% of total-time

Operation ival-add, time spent: 168.0ms, 32.0% of total-time

Operation ival-div, time spent: 65.0ms, 12.0% of total-time

Operation ival-neg, time spent: 38.0ms, 7.0% of total-time

Operation const, time spent: 14.0ms, 3.0% of total-time

Bogosity

preprocess166.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

80×	`fma-neg`
80×	`fma-define`
48×	`sub-neg`
28×	`distribute-lft-neg-in`
28×	`cancel-sign-sub-inv`

FPErrors

Click to see full error table

Overpredictions	Example	Example	Subexpression
0	-	-	`x`
1	(129.41237903789028)	-	`(exp.f64 (neg.f64 x))`
0	-	-	`(neg.f64 x)`
0	-	-	`(exp.f64 x)`
0	-	-	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`
0	-	-	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
0	-	-	`2`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`exp.f64`	`(exp.f64 (neg.f64 x))`	sensitivity	1	1

Confusion

	Predicted +	Predicted -
+	0	0
-	1	255

Precision

0.0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	1	1	254

Precision?

0.0

Recall?

0/0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	124
1	35	124
2	67	124
3	113	124
4	170	124
5	231	124
6	286	124
7	302	124
8	309	124
9	320	124
10	332	124
11	334	124

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(neg.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x)))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(neg.f64 (/.f64 2 (+.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 (neg.f64 x))))))
(/.f64 -2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Symmetry

(abs x)

Compiler

Compiled 68 to 32 computations (52.9% saved)

Precisions

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

Operation ival-exp, time spent: 8.0ms, 39.0% of total-time

Operation ival-div, time spent: 6.0ms, 29.0% of total-time

Operation ival-add, time spent: 3.0ms, 14.0% of total-time

Operation ival-neg, time spent: 2.0ms, 10.0% of total-time

Operation const, time spent: 1.0ms, 5.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize37.0ms (1.4%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

Operation ival-exp, time spent: 4.0ms, 43.0% of total-time

Operation ival-div, time spent: 2.0ms, 21.0% of total-time

Operation ival-add, time spent: 2.0ms, 21.0% of total-time

Operation const, time spent: 1.0ms, 11.0% of total-time

Operation ival-neg, time spent: 1.0ms, 11.0% of total-time

series3.0ms (0.1%)

Counts

1 → 8

Calls

Call 1

Inputs
#<alt (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))>

Outputs
#<alt 1>
#<alt (+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))>
#<alt (+.f64 1 (.f64 (pow.f64 x 2) (-.f64 (.f64 5/24 (pow.f64 x 2)) 1/2)))>
#<alt (+.f64 1 (.f64 (pow.f64 x 2) (-.f64 (.f64 (pow.f64 x 2) (+.f64 5/24 (*.f64 -61/720 (pow.f64 x 2)))) 1/2)))>
#<alt (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))>
#<alt (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))>
#<alt (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))>
#<alt (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))>

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ 2 (+ (exp x) (exp (neg x))))
1.0ms	x	@	inf	(/ 2 (+ (exp x) (exp (neg x))))
1.0ms	x	@	0	(/ 2 (+ (exp x) (exp (neg x))))

rewrite140.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

94×	`associate-r`
62×	`add-exp-log`
62×	`add-log-exp`
62×	`log1p-expm1-u`
62×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	144	20
2	2343	20

Stop Event

1×

unsound

Counts

1 → 10

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
-4
-2
-1
0
1/2
1
3/2
2
3
4

simplify469.0ms (18.3%)

Algorithm

1×	egg-herbie

Rules

4772×	`fma-define`
1168×	`fma-neg`
772×	`distribute-lft-in`
528×	`associate-+l-`
500×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	256
1	68	240
2	136	240
3	294	240
4	582	240
5	929	240
6	1108	240
7	1587	240
8	2418	240
9	3827	240
10	4702	240
11	5157	240
12	5232	240
13	5240	240
14	5240	240
15	5372	240
16	5428	240
17	5428	240
18	7311	240
19	7311	240
20	7311	240
21	7311	240
22	7311	240
23	7313	240

Stop Event

1×

saturated

Counts

18 → 23

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (pow.f64 x 2) (-.f64 (.f64 5/24 (pow.f64 x 2)) 1/2)))
(+.f64 1 (.f64 (pow.f64 x 2) (-.f64 (.f64 (pow.f64 x 2) (+.f64 5/24 (*.f64 -61/720 (pow.f64 x 2)))) 1/2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
-4
-2
-1
0
1/2
1
3/2
2
3
4

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(fma.f64 -1/2 (pow.f64 x 2) 1)
(+.f64 1 (.f64 (pow.f64 x 2) (-.f64 (.f64 5/24 (pow.f64 x 2)) 1/2)))
(+.f64 1 (*.f64 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 2) -1/2)))
(fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 5/24 -1/2) 1)
(fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) 1))
(+.f64 1 (.f64 (pow.f64 x 2) (-.f64 (.f64 (pow.f64 x 2) (+.f64 5/24 (*.f64 -61/720 (pow.f64 x 2)))) 1/2)))
(+.f64 1 (.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (+.f64 5/24 (.f64 (pow.f64 x 2) -61/720)) -1/2)))
(fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) -61/720 5/24) -1/2) 1)
(fma.f64 (pow.f64 x 2) (fma.f64 (pow.f64 x 2) 5/24 (fma.f64 -61/720 (pow.f64 x 4) -1/2)) 1)
(fma.f64 -61/720 (pow.f64 x 6) (fma.f64 -1/2 (pow.f64 x 2) (fma.f64 5/24 (pow.f64 x 4) 1)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (*.f64 -1 x))))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
-4
-2
-1
0
1/2
1
3/2
2
3
4

eval5.0ms (0.2%)

Compiler: Compiled 173 to 143 computations (17.3% saved)

prune5.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	19	4	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	5	24

Accuracy

100.0%

Counts

24 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	46.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
▶	47.2%	1
▶	10.4%	1/2
▶	54.2%	0

Compiler

Compiled 23 to 20 computations (13% saved)

localize48.0ms (1.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(*.f64 -1/2 (pow.f64 x 2))

Compiler

Compiled 24 to 20 computations (16.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

Operation ival-mult, time spent: 10.0ms, 54.0% of total-time

Operation ival-pow, time spent: 5.0ms, 27.0% of total-time

Operation ival-add, time spent: 2.0ms, 11.0% of total-time

Operation const, time spent: 2.0ms, 11.0% of total-time

series2.0ms (0.1%)

Counts

1 → 0

Calls

Call 1

Inputs
#<alt (*.f64 -1/2 (pow.f64 x 2))>

Outputs

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* -1/2 (pow x 2))
0.0ms	x	@	inf	(* -1/2 (pow x 2))
0.0ms	x	@	-inf	(* -1/2 (pow x 2))

rewrite166.0ms (6.5%)

Algorithm

1×	batch-egg-rewrite

Rules

842×	`associate-r`
742×	`associate-l`
490×	`unpow-prod-down`
397×	`log1p-expm1-u`
286×	`log-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	69	16
2	713	16
3	7802	16

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(*.f64 -1/2 (pow.f64 x 2))

Outputs
(+.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) -1)
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/2))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)) (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)))
(-.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) 3) 1) (+.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1)) (+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1)) 1) (+.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) 1))
(pow.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 -1/2 (pow.f64 x 2))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) -1/8) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(pow.f64 (E.f64) (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(fabs.f64 (*.f64 -1/2 (pow.f64 x 2)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/2))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (pow.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (pow.f64 x 2))))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 -1/2 (pow.f64 x 2)))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) -1/8)) 1/3))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 -1/2))) 2))

simplify67.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

2242×	`fma-neg`
630×	`distribute-lft-out`
540×	`associate-+l-`
532×	`associate-+r-`
444×	`associate--l+`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	512
1	164	512
2	410	512
3	1721	227
4	5158	227
5	5983	227
6	7472	227

Stop Event

1×	node limit

Counts

25 → 27

Calls

Call 1

Inputs
(+.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) -1)
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/2))))
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)) (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)))
(-.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) 3) 1) (+.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1)) (+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1)) 1) (+.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) 1))
(pow.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 -1/2 (pow.f64 x 2))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(pow.f64 (*.f64 (pow.f64 x 6) -1/8) 1/3)
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(pow.f64 (E.f64) (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(fabs.f64 (*.f64 -1/2 (pow.f64 x 2)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/2))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (pow.f64 x 2))))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (pow.f64 x 2))))
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 -1/2 (pow.f64 x 2)))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) -1/8)) 1/3))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 -1/2))) 2))

Outputs
(+.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) -1)
(*.f64 -1/2 (pow.f64 x 2))
0
(+.f64 0 (*.f64 -1/2 (pow.f64 x 2)))
(*.f64 -1/2 (pow.f64 x 2))
0
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/2))))
(*.f64 -1/2 (pow.f64 x 2))
0
(+.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)) (log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/4)))
(*.f64 -1/2 (pow.f64 x 2))
0
(-.f64 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1) 1)
(*.f64 -1/2 (pow.f64 x 2))
0
(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) 3) 1) (+.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1)) (+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) 1))))
(*.f64 -1/2 (pow.f64 x 2))
0
(/.f64 (-.f64 (.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1)) 1) (+.f64 (+.f64 (.f64 -1/2 (pow.f64 x 2)) 1) 1))
(*.f64 -1/2 (pow.f64 x 2))
0
(pow.f64 (*.f64 -1/2 (pow.f64 x 2)) 1)
(*.f64 -1/2 (pow.f64 x 2))
0
(pow.f64 (cbrt.f64 (*.f64 -1/2 (pow.f64 x 2))) 3)
(*.f64 -1/2 (pow.f64 x 2))
0
(pow.f64 (*.f64 (pow.f64 x 4) 1/4) 1/2)
(*.f64 -1/2 (pow.f64 x 2))
0
(pow.f64 (*.f64 (pow.f64 x 6) -1/8) 1/3)
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(pow.f64 (*.f64 x (sqrt.f64 -1/2)) 2)
(*.f64 -1/2 (pow.f64 x 2))
0
(pow.f64 (E.f64) (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))) 2)) (cbrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(pow.f64 (exp.f64 (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))) (sqrt.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2))))
(sqrt.f64 (*.f64 (pow.f64 x 4) 1/4))
(*.f64 -1/2 (pow.f64 x 2))
0
(fabs.f64 (*.f64 -1/2 (pow.f64 x 2)))
(*.f64 -1/2 (pow.f64 x 2))
0
(log.f64 (pow.f64 (exp.f64 (pow.f64 x 2)) -1/2))
(*.f64 -1/2 (pow.f64 x 2))
0
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (pow.f64 x 2))))
(*.f64 -1/2 (pow.f64 x 2))
0
(log1p.f64 (expm1.f64 (*.f64 -1/2 (pow.f64 x 2))))
(*.f64 -1/2 (pow.f64 x 2))
0
(exp.f64 (fma.f64 2 (log.f64 x) (log.f64 -1/2)))
(*.f64 -1/2 (pow.f64 x 2))
0
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 -1/2 (pow.f64 x 2)))) 3))
(*.f64 -1/2 (pow.f64 x 2))
0
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 x 6) -1/8)) 1/3))
(cbrt.f64 (*.f64 (pow.f64 x 6) -1/8))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 -1/2))) 2))
(*.f64 -1/2 (pow.f64 x 2))
0

eval8.0ms (0.3%)

Compiler: Compiled 332 to 292 computations (12% saved)

prune7.0ms (0.3%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	27	5	32

Accuracy

100.0%

Counts

32 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	46.5%	(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
✓	47.2%	1
✓	10.4%	1/2
✓	54.2%	0

Compiler

Compiled 42 to 36 computations (14.3% saved)

regimes9.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

Inputs
0
1/2
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Calls

3 calls:

4.0ms	x
2.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))`
100.0%	1	`(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes15.0ms (0.6%)

Counts

4 → 2

Calls

Call 1

Inputs
0
1/2
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))

Outputs
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
0

Calls

1 calls:

15.0ms

Results

Accuracy	Segments	Branch
98.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.3%)

Counts

3 → 2

Calls

Call 1

Inputs
0
1/2
1

Outputs
1
0

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
98.2%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0.3%)

Counts

2 → 2

Calls

Call 1

Inputs
0
1/2

Outputs
1/2
0

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
61.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
0

Outputs
0

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
54.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch19.0ms (0.7%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	0.04567134099382958	15.898964531535068

Results

16.0ms	127×	256	valid
0.0ms	1×	256	valid

Compiler

Compiled 109 to 98 computations (10.1% saved)

Precisions

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

Operation ival-exp, time spent: 3.0ms, 45.0% of total-time

Operation ival-div, time spent: 1.0ms, 15.0% of total-time

Operation ival-add, time spent: 1.0ms, 15.0% of total-time

Operation ival-neg, time spent: 1.0ms, 15.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

bsearch15.0ms (0.6%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	129.41237903789028	18869.977601217626

Results

13.0ms	111×	256	valid
0.0ms	1×	256	valid

Compiler

Compiled 55 to 52 computations (5.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

Operation ival-exp, time spent: 3.0ms, 60.0% of total-time

Operation ival-div, time spent: 1.0ms, 20.0% of total-time

Operation ival-add, time spent: 1.0ms, 20.0% of total-time

Operation ival-neg, time spent: 1.0ms, 20.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

bsearch19.0ms (0.7%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
19.0ms	129.41237903789028	18869.977601217626

Results

17.0ms	111×	256	valid
0.0ms	1×	256	valid

Compiler

Compiled 55 to 52 computations (5.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

Operation ival-exp, time spent: 3.0ms, 60.0% of total-time

Operation ival-div, time spent: 1.0ms, 20.0% of total-time

Operation ival-add, time spent: 1.0ms, 20.0% of total-time

Operation ival-neg, time spent: 1.0ms, 20.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative`
4×	`*-commutative`
3×	`1-exp`
2×	`sub-neg`
2×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	95
1	39	95
2	41	95
3	42	95

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 3152519739159347/2251799813685248) (+.f64 1 (*.f64 -1/2 (pow.f64 x 2))) 0)
(if (<=.f64 x 350) 1 0)
(if (<=.f64 x 350) 1/2 0)
0

Outputs
(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
(if (<=.f64 x 3152519739159347/2251799813685248) (+.f64 1 (*.f64 -1/2 (pow.f64 x 2))) 0)
(if (<=.f64 x 350) 1 0)
(if (<=.f64 x 350) 1/2 0)
0

Compiler

Compiled 38 to 32 computations (15.8% saved)

soundness32.0ms (1.2%)

Rules

94×	`associate-r`
62×	`add-exp-log`
62×	`add-log-exp`
62×	`log1p-expm1-u`
62×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	144	20
2	2343	20

Stop Event

1×

unsound

end0.0ms (0%)

preprocess48.0ms (1.9%)

Remove: (abs x)
Compiler: Compiled 140 to 112 computations (20% saved)

Iter	Nodes	Cost
0	17	124
1	35	124
2	67	124
3	113	124
4	170	124
5	231	124
6	286	124
7	302	124
8	309	124
9	320	124
10	332	124
11	334	124

Iter	Nodes	Cost
0	17	124
1	35	124
2	67	124
3	113	124
4	170	124
5	231	124
6	286	124
7	302	124
8	309	124
9	320	124
10	332	124
11	334	124

analyze0.0ms (0%)

sample1.3s (49.3%)

preprocess166.0ms (6.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize37.0ms (1.4%)

series3.0ms (0.1%)

rewrite140.0ms (5.4%)

simplify469.0ms (18.3%)

eval5.0ms (0.2%)

prune5.0ms (0.2%)

localize48.0ms (1.9%)

series2.0ms (0.1%)

rewrite166.0ms (6.5%)

simplify67.0ms (2.6%)

eval8.0ms (0.3%)

prune7.0ms (0.3%)

regimes9.0ms (0.3%)

regimes15.0ms (0.6%)

regimes7.0ms (0.3%)

regimes8.0ms (0.3%)

regimes3.0ms (0.1%)

bsearch19.0ms (0.7%)

bsearch15.0ms (0.6%)

bsearch19.0ms (0.7%)

simplify5.0ms (0.2%)

soundness32.0ms (1.2%)

end0.0ms (0%)

preprocess48.0ms (1.9%)

Profiling

Iter	Nodes	Cost
0	17	124
1	35	124
2	67	124
3	113	124
4	170	124
5	231	124
6	286	124
7	302	124
8	309	124
9	320	124
10	332	124
11	334	124