Details

analyze94.0ms (2.2%)

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)

sample2.0s (47.3%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 135 to 97 computations (28.1% saved)

simplify61.0ms (1.5%)

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

prune4.0ms (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
▶	0.1b	(+.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)))
	0.6b	(.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

▶

0.1b

(+.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)))

0.6b

(*.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 (1.8%)

Local error

Found 4 expressions with local error:

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

series29.0ms (0.7%)

Counts

4 → 84

Calls

4 calls:

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

rewrite70.0ms (1.7%)

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:

69.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
69.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
69.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
69.0ms	(.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

simplify31.0ms (0.7%)

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 → 97

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

prune112.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	93	6	99

Error

0.0b

Counts

99 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.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 (/.f32 -1 (sqrt.f32 (.f32 s 3))) (/.f32 r (sqrt.f32 (.f32 s 3)))))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	24.2b	(+.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)))) (log.f32 (+.f32 1 (expm1.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6))))))))
	0.6b	(.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)))
	0.1b	(+.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)))) (exp.f32 (log.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))))))
	17.1b	(+.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)))) (cbrt.f32 (pow.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6))) 3))))
	0.1b	(+.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 (sqrt.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))) 2)))

Compiler

Compiled 3950 to 2482 computations (37.2% saved)

localize97.0ms (2.3%)

Local error

Found 4 expressions with local error:

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

series74.0ms (1.8%)

Counts

1 → 20

Calls

1 calls:

74.0ms

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

rewrite54.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

525×	`log-prod_binary32`
279×	`pow2_binary32`
180×	`pow1/3_binary32`
176×	`expm1-udef_binary32`
176×	`log1p-udef_binary32`

Counts

1 → 61

Calls

1 calls:

53.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	10
1	210	7
2	2561	7
3	5020	7
0	0	0
1	0	0

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

994×	`fma-def_binary32`
735×	`associate-/l*_binary32`
432×	`associate-l_binary32`
431×	`fma-neg_binary32`
410×	`associate-*l/_binary32`

Counts

81 → 63

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	280
1	23	140
2	57	140
3	123	140
4	308	140
5	1012	140
6	3361	140
7	3771	140
8	4219	140
9	5374	140

prune198.0ms (4.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	112	6	118

Error

0.0b

Counts

118 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.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 (/.f32 -1 (sqrt.f32 (.f32 s 3))) (/.f32 r (sqrt.f32 (.f32 s 3)))))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	24.2b	(+.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)))) (log.f32 (+.f32 1 (expm1.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6))))))))
	0.6b	(.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)))
	0.1b	(+.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)))) (exp.f32 (log.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))))))
	17.1b	(+.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)))) (cbrt.f32 (pow.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6))) 3))))
▶	0.1b	(+.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 (sqrt.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))) 2)))

Compiler

Compiled 4949 to 3267 computations (34% saved)

localize85.0ms (2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 r (.f32 s (*.f32 (PI.f32) 6)))
	0.3b	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
	0.3b	(.f32 (.f32 2 (PI.f32)) s)
✓	0.6b	(pow.f32 (sqrt.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))) 2)

series82.0ms (2%)

Counts

2 → 24

Calls

2 calls:

73.0ms	(pow.f32 (sqrt.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))) 2)
8.0ms	(.f32 r (.f32 s (*.f32 (PI.f32) 6)))

rewrite55.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

859×	`log1p-expm1-u_binary32`
859×	`expm1-log1p-u_binary32`
98×	`add-sqr-sqrt_binary32`
96×	`associate-r_binary32`
93×	`add-log-exp_binary32`

Counts

2 → 59

Calls

2 calls:

53.0ms	(.f32 r (.f32 s (*.f32 (PI.f32) 6)))
53.0ms	(pow.f32 (sqrt.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	209	22
2	2276	22
3	5199	22
0	0	0
1	0	0

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

26×	`associate-l_binary32`
20×	`associate-r_binary32`
17×	`*-commutative_binary32`

Counts

83 → 49

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	264
1	15	264
2	35	264
3	55	264
4	55	264
5	55	264

prune140.0ms (3.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	81	6	87

Error

0.0b

Counts

87 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.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 (PI.f32) 6) (*.f32 r s))))
	0.6b	(.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)))
✓	0.1b	(+.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 (/.f32 -1 (sqrt.f32 (.f32 s 3))) (/.f32 r (sqrt.f32 (.f32 s 3)))))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	24.2b	(+.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)))) (log.f32 (+.f32 1 (expm1.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6))))))))
	0.1b	(+.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)))) (exp.f32 (log.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))))))
✓	0.1b	(+.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 (sqrt.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))) 2)))

Compiler

Compiled 3497 to 2204 computations (37% saved)

localize78.0ms (1.9%)

Local error

Found 4 expressions with local error:

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

series9.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(*.f32 (*.f32 (PI.f32) 6) (*.f32 r s))

rewrite40.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

710×	`log1p-expm1-u_binary32`
710×	`expm1-log1p-u_binary32`
146×	`expm1-udef_binary32`
146×	`log1p-udef_binary32`
130×	`log-pow_binary32`

Counts

1 → 15

Calls

1 calls:

40.0ms

(*.f32 (*.f32 (PI.f32) 6) (*.f32 r s))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	162	11
2	1879	11
3	4958	11
0	0	0
1	0	0

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

26×	`associate-l_binary32`
20×	`associate-r_binary32`
17×	`*-commutative_binary32`

Counts

39 → 16

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	264
1	15	264
2	35	264
3	55	264
4	55	264
5	55	264

prune156.0ms (3.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	96	6	102

Error

0.0b

Counts

102 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.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 (/.f32 -1 (sqrt.f32 (.f32 s 3))) (/.f32 r (sqrt.f32 (.f32 s 3)))))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	24.2b	(+.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)))) (log.f32 (+.f32 1 (expm1.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6))))))))
	0.6b	(.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)))
	0.1b	(+.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)))) (exp.f32 (log.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))))))
	0.1b	(+.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 (cbrt.f32 (.f32 (.f32 (PI.f32) 6) (*.f32 r s))) 3)))
✓	0.1b	(+.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 (sqrt.f32 (.f32 r (.f32 s (*.f32 (PI.f32) 6)))) 2)))

Compiler

Compiled 3701 to 2211 computations (40.3% saved)

regimes413.0ms (9.9%)

Accuracy

Total 0.1b remaining (38.5%)

Threshold costs 0.1b (38.5%)

Counts

116 → 1

Compiler

Compiled 12868 to 9517 computations (26% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary32`
3×	`+-commutative_binary32`
2×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	56
1	45	56
2	49	56
3	52	56
4	53	56
5	52	56

end143.0ms (3.4%)

Compiler: Compiled 290 to 214 computations (26.2% saved)

Details

analyze94.0ms (2.2%)

sample2.0s (47.3%)

simplify61.0ms (1.5%)

prune4.0ms (0.1%)

localize76.0ms (1.8%)

series29.0ms (0.7%)

rewrite70.0ms (1.7%)

simplify31.0ms (0.7%)

prune112.0ms (2.7%)

localize97.0ms (2.3%)

series74.0ms (1.8%)

rewrite54.0ms (1.3%)

simplify68.0ms (1.6%)

prune198.0ms (4.7%)

localize85.0ms (2%)

series82.0ms (2%)

rewrite55.0ms (1.3%)

simplify14.0ms (0.3%)

prune140.0ms (3.4%)

localize78.0ms (1.9%)

series9.0ms (0.2%)

rewrite40.0ms (1%)

simplify13.0ms (0.3%)

prune156.0ms (3.7%)

regimes413.0ms (9.9%)

simplify3.0ms (0.1%)

end143.0ms (3.4%)

Profiling