Details

analyze91.0ms (2.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	2.1%	97.9%	0
0%	2.1%	97.9%	1
1%	1%	97.9%	2
1%	1%	97.9%	3
1.5%	0.5%	97.9%	4
1.5%	0.5%	97.9%	5
1.8%	0.3%	97.9%	6
1.8%	0.3%	97.9%	7
1.9%	0.1%	97.9%	8
1.9%	0.1%	97.9%	9
2%	0.1%	97.9%	10
2%	0.1%	97.9%	11
2%	0%	97.9%	12
2%	0%	97.9%	13
2%	0%	97.9%	14

Compiler

Compiled 50 to 36 computations (28% saved)

sample1.9s (51.4%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 135 to 97 computations (28.1% saved)

simplify59.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-neg_binary32`
634×	`associate-l_binary32`
530×	`associate-r_binary32`
445×	`associate-/r*_binary32`
406×	`*-commutative_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	53
1	66	43
2	237	35
3	864	32
4	2572	32
5	3890	32
6	4293	32
7	4871	32
8	4870	32

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	1.0b	(.f32 (/.f32 (/.f32 1/8 (.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))

Status

Error

Program

▶

0.3b

(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))

1.0b

(*.f32 (/.f32 (/.f32 1/8 (*.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))

Compiler

Compiled 169 to 117 computations (30.8% saved)

localize76.0ms (2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
✓	0.3b	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
✓	0.3b	(/.f32 (neg.f32 r) (*.f32 3 s))
✓	0.4b	(.f32 (.f32 2 (PI.f32)) s)

series27.0ms (0.7%)

Counts

4 → 84

Calls

4 calls:

9.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
8.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
6.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
3.0ms	(.f32 (.f32 2 (PI.f32)) s)

rewrite69.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

276×	`expm1-udef_binary32`
276×	`log1p-udef_binary32`
239×	`log-pow_binary32`
166×	`associate-r_binary32`
166×	`add-sqr-sqrt_binary32`

Counts

4 → 93

Calls

4 calls:

68.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
68.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
68.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
68.0ms	(.f32 (.f32 2 (PI.f32)) s)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	339	37
2	3871	37
3	4992	37
0	0	0
1	0	0

simplify29.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

51×	`associate-l_binary32`
35×	`associate-r_binary32`
29×	`*-commutative_binary32`
2×	`associate-/l*_binary32`
1×	`associate-*r/_binary32`

Counts

177 → 96

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	792
1	30	792
2	69	792
3	107	792
4	108	792
5	108	792

prune126.0ms (3.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	91	7	98

Error

0.2b

Counts

98 → 7

Alt Table

Status	Error	Program
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (.f32 -1/3 (/.f32 r s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	23.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (-.f32 (exp.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) s))) 1) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	16.7b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (pow.f32 (pow.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6))) 3) 1/3)))
	17.8b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (pow.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) s) 3) 1/3) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
▶	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (.f32 (PI.f32) r)))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (expm1.f32 (log1p.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))))))
	1.0b	(.f32 (/.f32 (/.f32 1/8 (.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))

Compiler

Compiled 3975 to 2505 computations (37% saved)

localize76.0ms (2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 s (.f32 (PI.f32) r))
	0.3b	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
	0.3b	(/.f32 (neg.f32 r) (*.f32 3 s))
✓	0.4b	(*.f32 (PI.f32) r)

series9.0ms (0.2%)

Counts

2 → 0

Calls

2 calls:

7.0ms	(.f32 s (.f32 (PI.f32) r))
2.0ms	(*.f32 (PI.f32) r)

rewrite54.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

532×	`log1p-expm1-u_binary32`
532×	`expm1-log1p-u_binary32`
438×	`unpow-prod-down_binary32`
330×	`log-prod_binary32`
160×	`pow2_binary32`

Counts

2 → 34

Calls

2 calls:

53.0ms	(.f32 s (.f32 (PI.f32) r))
53.0ms	(*.f32 (PI.f32) r)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	119	13
2	1412	13
3	5368	13
0	0	0
1	0	0

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune140.0ms (3.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	99	6	105

Error

0.2b

Counts

105 → 6

Alt Table

Status	Error	Program
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (pow.f32 (cbrt.f32 (.f32 (PI.f32) r)) 3)))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	1.0b	(.f32 (/.f32 (/.f32 1/8 (.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))
	16.7b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (pow.f32 (pow.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6))) 3) 1/3)))
	17.8b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (pow.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) s) 3) 1/3) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (expm1.f32 (log1p.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))))))
▶	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (.f32 (PI.f32) r)))) (/.f32 (.f32 3/4 (exp.f32 (.f32 -1/3 (/.f32 r s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))

Compiler

Compiled 4009 to 2320 computations (42.1% saved)

localize83.0ms (2.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f32 s (.f32 (PI.f32) r))
	0.3b	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
	0.4b	(*.f32 (PI.f32) r)
✓	0.5b	(*.f32 -1/3 (/.f32 r s))

series7.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

6.0ms

(*.f32 -1/3 (/.f32 r s))

rewrite74.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

607×	`log1p-expm1-u_binary32`
607×	`expm1-log1p-u_binary32`
317×	`log-prod_binary32`
116×	`expm1-udef_binary32`
116×	`log1p-udef_binary32`

Counts

1 → 26

Calls

1 calls:

74.0ms

(*.f32 -1/3 (/.f32 r s))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	127	7
2	1574	7
3	4952	7
4	5102	7
0	0	0
1	0	0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune134.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	75	7	82

Error

0.2b

Counts

82 → 7

Alt Table

Status	Error	Program
	16.7b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (pow.f32 (pow.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6))) 3) 1/3)))
	17.8b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (pow.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) s) 3) 1/3) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (.f32 (PI.f32) r)))) (/.f32 (.f32 3/4 (exp.f32 (.f32 -1/3 (/.f32 r s)))) (pow.f32 (sqrt.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))) 2)))
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (.f32 (PI.f32) r)))) (/.f32 (.f32 3/4 (exp.f32 (.f32 -1/3 (/.f32 r s)))) (expm1.f32 (log1p.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))))))
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (.f32 (PI.f32) r)))) (/.f32 (.f32 3/4 (exp.f32 (.f32 -1/3 (/.f32 r s)))) (exp.f32 (log.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))))))
	1.0b	(.f32 (/.f32 (/.f32 1/8 (.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))
▶	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (pow.f32 (sqrt.f32 (.f32 (PI.f32) r)) 2)))) (/.f32 (.f32 3/4 (exp.f32 (.f32 -1/3 (/.f32 r s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))

Compiler

Compiled 3204 to 1845 computations (42.4% saved)

localize85.0ms (2.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
	0.4b	(*.f32 (PI.f32) r)
	0.5b	(*.f32 -1/3 (/.f32 r s))
✓	0.5b	(pow.f32 (sqrt.f32 (*.f32 (PI.f32) r)) 2)

series15.0ms (0.4%)

Counts

1 → 0

Calls

1 calls:

15.0ms

(pow.f32 (sqrt.f32 (*.f32 (PI.f32) r)) 2)

rewrite78.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

906×	`log1p-udef_binary32`
479×	`log1p-expm1-u_binary32`
479×	`expm1-log1p-u_binary32`
417×	`unpow-prod-down_binary32`
263×	`log-prod_binary32`

Counts

1 → 65

Calls

1 calls:

77.0ms

(pow.f32 (sqrt.f32 (*.f32 (PI.f32) r)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	5
1	125	5
2	1282	5
3	4995	5
4	6501	5
0	0	0
1	0	0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune240.0ms (6.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	124	7	131

Error

0.2b

Counts

131 → 7

Alt Table

Status	Error	Program
	16.7b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (pow.f32 (pow.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6))) 3) 1/3)))
	17.8b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (pow.f32 (pow.f32 (.f32 (.f32 2 (PI.f32)) s) 3) 1/3) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (.f32 (PI.f32) r)))) (/.f32 (.f32 3/4 (exp.f32 (.f32 -1/3 (/.f32 r s)))) (pow.f32 (sqrt.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))) 2)))
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (.f32 (PI.f32) r)))) (/.f32 (.f32 3/4 (exp.f32 (.f32 -1/3 (/.f32 r s)))) (expm1.f32 (log1p.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))))))
	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (.f32 (PI.f32) r)))) (/.f32 (.f32 3/4 (exp.f32 (.f32 -1/3 (/.f32 r s)))) (exp.f32 (log.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))))))
	1.0b	(.f32 (/.f32 (/.f32 1/8 (.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))
✓	0.3b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 2 (.f32 s (pow.f32 (sqrt.f32 (.f32 (PI.f32) r)) 2)))) (/.f32 (.f32 3/4 (exp.f32 (.f32 -1/3 (/.f32 r s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))

Compiler

Compiled 5081 to 2866 computations (43.6% saved)

regimes172.0ms (4.6%)

Accuracy

Total 0.1b remaining (42.4%)

Threshold costs 0.1b (42.4%)

Counts

47 → 1

Compiler

Compiled 5236 to 3874 computations (26% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary32`
4×	`+-commutative_binary32`
3×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	58
1	46	58
2	52	58
3	57	58
4	59	58
5	59	58

end157.0ms (4.2%)

Compiler: Compiled 322 to 240 computations (25.5% saved)

Details

analyze91.0ms (2.4%)

sample1.9s (51.4%)

simplify59.0ms (1.6%)

prune5.0ms (0.1%)

localize76.0ms (2%)

series27.0ms (0.7%)

rewrite69.0ms (1.8%)

simplify29.0ms (0.8%)

prune126.0ms (3.3%)

localize76.0ms (2%)

series9.0ms (0.2%)

rewrite54.0ms (1.4%)

simplify7.0ms (0.2%)

prune140.0ms (3.7%)

localize83.0ms (2.2%)

series7.0ms (0.2%)

rewrite74.0ms (2%)

simplify6.0ms (0.2%)

prune134.0ms (3.6%)

localize85.0ms (2.3%)

series15.0ms (0.4%)

rewrite78.0ms (2.1%)

simplify6.0ms (0.2%)

prune240.0ms (6.4%)

regimes172.0ms (4.6%)

simplify5.0ms (0.1%)

end157.0ms (4.2%)

Profiling