Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
74.9%	0%	25.1%	1

Compiler

Compiled 71 to 33 computations (53.5% saved)

sample1.4s (32.7%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify103.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1509×	`associate-/l*_binary64`
766×	`distribute-rgt-out_binary64`
744×	`distribute-lft-out_binary64`
549×	`unswap-sqr_binary64`
497×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	32	75
1	74	59
2	239	41
3	928	37
4	1549	37
5	3195	37
6	3534	37
7	3698	33
8	2289	33
9	2775	33
10	2823	33
11	4807	33
12	5324	33

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
▶	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Status

Error

Program

0.4b

(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))

▶

0.1b

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 272 to 147 computations (46% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
✓	0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	0.3b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
✓	1.0b	(sqrt.f64 (PI.f64))

series34.0ms (0.8%)

Counts

4 → 36

Calls

4 calls:

17.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
10.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite60.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`add-exp-log_binary64`
78×	`add-cbrt-cube_binary64`
75×	`prod-exp_binary64`
53×	`pow1_binary64`
45×	`cbrt-unprod_binary64`

Counts

4 → 153

Calls

4 calls:

25.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
10.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 (PI.f64))

simplify123.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

504×	`associate-/l*_binary64`
471×	`fma-def_binary64`
345×	`associate-/r*_binary64`
331×	`unswap-sqr_binary64`
312×	`associate-r_binary64`

Counts

189 → 194

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	217	2646
1	396	2039
2	1372	1782
3	2977	1752
4	4619	1719
5	4996	1719
6	4891	1719

prune379.0ms (8.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	280	2	282
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	281	3	284

Error

Counts

284 → 3

Alt Table

Status	Error	Program
	0.8b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
▶	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (*.f64 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.4b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))

Compiler

Compiled 20441 to 7332 computations (64.1% saved)

localize31.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
	0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
	0.3b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
	1.0b	(sqrt.f64 (PI.f64))

prune363.0ms (8.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	238	3	241

Error

Counts

241 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (*.f64 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.8b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (*.f64 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
▶	0.4b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))

Compiler

Compiled 16341 to 7630 computations (53.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 2/3 (pow.f64 x 3))
✓	0.2b	(/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64)))
✓	0.2b	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
	1.0b	(sqrt.f64 (PI.f64))

series16.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

9.0ms

(/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64)))

4.0ms

(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))

3.0ms

(*.f64 2/3 (pow.f64 x 3))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
12×	`associate-r_binary64`

Counts

3 → 84

Calls

3 calls:

5.0ms

(*.f64 2/3 (pow.f64 x 3))

3.0ms

(/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64)))

0.0ms

(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))

simplify124.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-l_binary64`
610×	`associate-r_binary64`
285×	`log-prod_binary64`
262×	`fma-def_binary64`
184×	`swap-sqr_binary64`

Counts

108 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	3342
1	305	3139
2	796	3025
3	3438	3025
4	4851	3025
5	4876	3025

prune142.0ms (3.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	133	2	135

Error

Counts

135 → 2

Alt Table

Status	Error	Program
✓	0.4b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
▶	0.1b	(fabs.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3)))) (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))))

Status

Error

Program

✓

0.4b

(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))

▶

0.1b

(fabs.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3)))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5))))))

Compiler

Compiled 4158 to 3063 computations (26.3% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))
✓	0.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3))))
	0.1b	(*.f64 2/3 (pow.f64 x 3))
✓	0.3b	(*.f64 1/5 (pow.f64 x 5))

series24.0ms (0.6%)

Counts

3 → 24

Calls

3 calls:

11.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))
9.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3))))
3.0ms	(*.f64 1/5 (pow.f64 x 5))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
35×	`associate-l_binary64`
32×	`sqrt-prod_binary64`
26×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`

Counts

3 → 105

Calls

3 calls:

9.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3))))
8.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))
4.0ms	(*.f64 1/5 (pow.f64 x 5))

simplify128.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-def_binary64`
459×	`associate-/l*_binary64`
435×	`sqr-pow_binary64`
350×	`*-commutative_binary64`
223×	`exp-prod_binary64`

Counts

129 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	3232
1	306	2800
2	896	2788
3	1648	2788
4	2477	2788
5	4448	2788
6	5098	2788

prune215.0ms (4.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	182	2	184

Error

Counts

184 → 2

Alt Table

Status	Error	Program
✓	0.4b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
✓	0.1b	(fabs.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3)))) (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))))

Status

Error

Program

✓

0.4b

(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))

✓

0.1b

(fabs.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3)))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5))))))

Compiler

Compiled 6908 to 5511 computations (20.2% saved)

regimes999.0ms (22.9%)

Accuracy

Total 0.1b remaining (90.5%)

Threshold costs 0.1b (90.5%)

Counts

117 → 1

Compiler

Compiled 33600 to 21366 computations (36.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	47
1	31	47
2	30	47

end95.0ms (2.2%)

Compiler: Compiled 116 to 97 computations (16.4% saved)

Details

analyze1.0ms (0%)

sample1.4s (32.7%)

simplify103.0ms (2.3%)

prune5.0ms (0.1%)

localize22.0ms (0.5%)

series34.0ms (0.8%)

rewrite60.0ms (1.4%)

simplify123.0ms (2.8%)

prune379.0ms (8.7%)

localize31.0ms (0.7%)

prune363.0ms (8.3%)

localize14.0ms (0.3%)

series16.0ms (0.4%)

rewrite13.0ms (0.3%)

simplify124.0ms (2.9%)

prune142.0ms (3.3%)

localize18.0ms (0.4%)

series24.0ms (0.6%)

rewrite28.0ms (0.6%)

simplify128.0ms (2.9%)

prune215.0ms (4.9%)

regimes999.0ms (22.9%)

simplify3.0ms (0.1%)

end95.0ms (2.2%)

Profiling