Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 71 to 33 computations (53.5% saved)

sample1.7s (36.4%)

Results

1.6s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify103.0ms (2.2%)

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

prune10.0ms (0.2%)

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
	0.6b	(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

0.6b

(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)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series36.0ms (0.8%)

Counts

4 → 36

Calls

4 calls:

18.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
11.0ms	(.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 (1.3%)

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:

26.0ms	(.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))

simplify145.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

504×	`associate-/l*_binary64`
471×	`fma-def_binary64`
345×	`associate-/r*_binary64`
331×	`unswap-sqr_binary64`
310×	`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

prune353.0ms (7.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

0.0b

Counts

284 → 3

Alt Table

Status	Error	Program
▶	0.6b	(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))))))
	1.1b	(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))))))

Compiler

Compiled 20381 to 7293 computations (64.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
✓	0.2b	(*.f64 2/3 (pow.f64 x 3))
✓	0.3b	(/.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)))
	1.0b	(sqrt.f64 (PI.f64))

series18.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

11.0ms

(/.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))))

simplify131.0ms (2.8%)

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 → 115

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

prune143.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	131	3	134

Error

Counts

134 → 3

Alt Table

Status	Error	Program
	0.1b	(fabs.f64 (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))))))
✓	0.6b	(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 (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))))) (/.f64 1 (sqrt.f64 (PI.f64)))))

Compiler

Compiled 4223 to 3118 computations (26.2% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
✓	0.1b	(.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))))) (/.f64 1 (sqrt.f64 (PI.f64))))
	0.2b	(*.f64 2/3 (pow.f64 x 3))
	1.0b	(sqrt.f64 (PI.f64))

series9.0ms (0.2%)

Counts

1 → 12

Calls

1 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))))) (/.f64 1 (sqrt.f64 (PI.f64))))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
22×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 49

Calls

1 calls:

8.0ms

(*.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))))) (/.f64 1 (sqrt.f64 (PI.f64))))

simplify111.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

919×	`fma-def_binary64`
409×	`*-commutative_binary64`
362×	`associate-*l/_binary64`
324×	`exp-prod_binary64`
289×	`associate-*r/_binary64`

Counts

61 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	2486
1	215	2267
2	578	2133
3	1732	2022
4	3225	2022
5	4849	2022
6	4932	2022

prune181.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	155	3	158

Error

Counts

158 → 3

Alt Table

Status	Error	Program
▶	0.1b	(fabs.f64 (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))))))
✓	0.6b	(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 (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))))) (/.f64 1 (sqrt.f64 (PI.f64)))))

Compiler

Compiled 4980 to 3721 computations (25.3% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series55.0ms (1.2%)

Counts

4 → 0

Calls

4 calls:

16.0ms	(.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))
14.0ms	(.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3)))
13.0ms	(.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5)))
12.0ms	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))

rewrite42.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
39×	`add-exp-log_binary64`
25×	`sqrt-prod_binary64`
25×	`associate-l_binary64`
24×	`prod-exp_binary64`

Counts

4 → 125

Calls

4 calls:

10.0ms	(.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))
9.0ms	(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))
7.0ms	(.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3)))
7.0ms	(.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5)))

simplify136.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

558×	`unswap-sqr_binary64`
455×	`associate-/l*_binary64`
389×	`log-prod_binary64`
350×	`associate-r_binary64`
307×	`fma-def_binary64`

Counts

125 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2432
1	377	2267
2	1362	2231
3	2191	2231
4	4300	2231
5	4852	2231
6	4906	2231

prune221.0ms (4.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	140	3	143

Error

Counts

143 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fabs.f64 (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))))))
✓	0.6b	(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 (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))))) (/.f64 1 (sqrt.f64 (PI.f64)))))

Compiler

Compiled 7014 to 5647 computations (19.5% saved)

regimes974.0ms (21%)

Accuracy

Total 0.1b remaining (59.6%)

Threshold costs 0.1b (59.6%)

Counts

117 → 1

Compiler

Compiled 32942 to 19496 computations (40.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`fabs-mul_binary64`
1×	`fabs-div_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	36
1	29	36
2	33	36
3	31	36

end110.0ms (2.4%)

Compiler: Compiled 141 to 118 computations (16.3% saved)

Details

analyze6.0ms (0.1%)

sample1.7s (36.4%)

simplify103.0ms (2.2%)

prune10.0ms (0.2%)

localize23.0ms (0.5%)

series36.0ms (0.8%)

rewrite60.0ms (1.3%)

simplify145.0ms (3.1%)

prune353.0ms (7.6%)

localize14.0ms (0.3%)

series18.0ms (0.4%)

rewrite13.0ms (0.3%)

simplify131.0ms (2.8%)

prune143.0ms (3.1%)

localize18.0ms (0.4%)

series9.0ms (0.2%)

rewrite13.0ms (0.3%)

simplify111.0ms (2.4%)

prune181.0ms (3.9%)

localize20.0ms (0.4%)

series55.0ms (1.2%)

rewrite42.0ms (0.9%)

simplify136.0ms (2.9%)

prune221.0ms (4.8%)

regimes974.0ms (21%)

simplify3.0ms (0.1%)

end110.0ms (2.4%)

Profiling