Details

analyze99.0ms (1.8%)

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)

sample2.1s (37.4%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 135 to 97 computations (28.1% saved)

simplify57.0ms (1%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(+.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)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	1.4b	(.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

▶

0.2b

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

1.4b

(*.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)

localize81.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
✓	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)

series28.0ms (0.5%)

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)
8.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))
4.0ms	(.f32 (.f32 2 (PI.f32)) s)

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary32`
32×	`add-exp-log_binary32`
27×	`pow1_binary32`
16×	`cbrt-unprod_binary32`
16×	`prod-exp_binary32`

Counts

4 → 105

Calls

4 calls:

6.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)
5.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)
5.0ms	(.f32 (.f32 2 (PI.f32)) s)
4.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

512×	`associate-/l*_binary32`
418×	`associate-l_binary32`
326×	`associate-/r*_binary32`
318×	`distribute-rgt-neg-out_binary32`
310×	`associate-r_binary32`

Counts

189 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	2248
1	442	1951
2	1885	1945
3	4571	1945
4	4935	1945

prune287.0ms (5.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	145	9	154
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	147	9	156

Error

0.1b

Counts

156 → 9

Alt Table

Status	Error	Program
	0.2b	(+.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)))) (.f32 6 (.f32 s (*.f32 (PI.f32) r)))))
▶	0.2b	(+.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)))) (.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r)) (sqrt.f32 (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))))
	0.2b	(+.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)))) (.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) (*.f32 (cbrt.f32 r) (cbrt.f32 r))) (cbrt.f32 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)))) (exp.f32 (+.f32 (+.f32 (log.f32 (*.f32 6 (PI.f32))) (log.f32 s)) (log.f32 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)))) (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 6) (log.f32 (PI.f32))) (log.f32 s)) (log.f32 r)))))
	19.5b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (cbrt.f32 (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (.f32 2 (PI.f32))) (.f32 2 (PI.f32))) (.f32 (.f32 s s) s))) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.2b	(+.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)))
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (sqrt.f32 (.f32 (.f32 (.f32 2 (PI.f32)) s) r)) (sqrt.f32 (.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)))
	0.2b	(+.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 (.f32 (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s))) (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s)))))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))

Compiler

Compiled 6603 to 3856 computations (41.6% saved)

localize91.0ms (1.7%)

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)
✓	0.5b	(.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r)) (sqrt.f32 (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))

series34.0ms (0.6%)

Counts

1 → 16

Calls

1 calls:

33.0ms

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

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

268×	`pow1_binary32`
174×	`pow-prod-down_binary32`
104×	`sqrt-pow1_binary32`
26×	`pow-prod-up_binary32`
18×	`pow-sqr_binary32`

Counts

1 → 91

Calls

1 calls:

12.0ms

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

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

521×	`associate-/l*_binary32`
490×	`sqr-pow_binary32`
422×	`fma-def_binary32`
324×	`unswap-sqr_binary32`
312×	`associate-/l/_binary32`

Counts

107 → 60

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	1281
1	109	1062
2	390	960
3	807	943
4	1721	913
5	2807	913
6	4890	913
7	4963	913

prune558.0ms (10.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	181	9	190

Error

0.1b

Counts

190 → 9

Alt Table

Status	Error	Program
▶	0.2b	(+.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)))) (.f32 6 (.f32 s (*.f32 (PI.f32) r)))))
✓	0.2b	(+.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)))) (.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r)) (sqrt.f32 (.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)))) (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 6) (log.f32 (PI.f32))) (log.f32 s)) (log.f32 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)))) (.f32 (.f32 (.f32 (cbrt.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r))) (cbrt.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r)))) (.f32 (cbrt.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r))) (cbrt.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r))))) (.f32 (cbrt.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r))) (cbrt.f32 (sqrt.f32 (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))))))
	0.2b	(+.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)))) (.f32 (pow.f32 (sqrt.f32 6) 2) (.f32 s (*.f32 (PI.f32) r)))))
	0.2b	(+.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)))
	0.2b	(+.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 (.f32 (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s))) (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (cbrt.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)))) (exp.f32 (+.f32 (+.f32 (log.f32 (*.f32 6 (PI.f32))) (log.f32 s)) (log.f32 r)))))
	0.2b	(+.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)))) (.f32 (sqrt.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r))) (pow.f32 (sqrt.f32 (sqrt.f32 (.f32 6 (.f32 s (*.f32 (PI.f32) r))))) 3))))

Compiler

Compiled 9304 to 5681 computations (38.9% saved)

localize79.0ms (1.4%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.3%)

Counts

3 → 0

Calls

3 calls:

8.0ms	(.f32 6 (.f32 s (*.f32 (PI.f32) r)))
7.0ms	(.f32 s (.f32 (PI.f32) r))
2.0ms	(*.f32 (PI.f32) r)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary32`
19×	`add-exp-log_binary32`
19×	`pow1_binary32`
10×	`cbrt-unprod_binary32`
10×	`prod-exp_binary32`

Counts

3 → 63

Calls

3 calls:

7.0ms	(.f32 6 (.f32 s (*.f32 (PI.f32) r)))
4.0ms	(.f32 s (.f32 (PI.f32) r))
3.0ms	(*.f32 (PI.f32) r)

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

505×	`log-div_binary32`
477×	`associate-*r/_binary32`
455×	`associate-*l/_binary32`
350×	`*-commutative_binary32`
262×	`associate-/l*_binary32`

Counts

63 → 81

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	83	786
1	172	633
2	591	633
3	943	633
4	1255	633
5	1830	633
6	4193	633
7	4877	633
8	5132	633

prune286.0ms (5.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	107	11	118

Error

0.1b

Counts

118 → 11

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)))) (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 6) (log.f32 (PI.f32))) (log.f32 s)) (log.f32 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)))) (.f32 6 (exp.f32 (+.f32 (log.f32 s) (log.f32 (.f32 (PI.f32) 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)))) (.f32 6 (exp.f32 (log.f32 (.f32 (*.f32 (PI.f32) r) s))))))
	0.2b	(+.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)))) (.f32 6 (.f32 s (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (*.f32 (cbrt.f32 (PI.f32)) r))))))
▶	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 6 (.f32 s (.f32 (PI.f32) r)))))
✓	0.2b	(+.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)))) (.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r)) (sqrt.f32 (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))))
	0.2b	(+.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)))) (.f32 6 (.f32 s (.f32 (.f32 (cbrt.f32 (.f32 (PI.f32) r)) (cbrt.f32 (.f32 (PI.f32) r))) (cbrt.f32 (*.f32 (PI.f32) 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)))) (.f32 6 (.f32 s (exp.f32 (log.f32 (*.f32 (PI.f32) 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)))) (exp.f32 (+.f32 (log.f32 6) (+.f32 (log.f32 s) (log.f32 (*.f32 (PI.f32) r)))))))
	0.2b	(+.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 (.f32 (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s))) (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s)))))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.2b	(+.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)))) (.f32 (sqrt.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r))) (pow.f32 (sqrt.f32 (sqrt.f32 (.f32 6 (.f32 s (*.f32 (PI.f32) r))))) 3))))

Compiler

Compiled 5036 to 2811 computations (44.2% saved)

localize87.0ms (1.6%)

Local error

Found 4 expressions with local error:

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

series15.0ms (0.3%)

Counts

2 → 8

Calls

2 calls:

9.0ms	(.f32 (.f32 2 (PI.f32)) (sqrt.f32 s))
6.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary32`
16×	`add-exp-log_binary32`
16×	`pow1_binary32`
12×	`associate-r_binary32`
9×	`cbrt-unprod_binary32`

Counts

2 → 49

Calls

2 calls:

12.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s))
5.0ms	(.f32 (.f32 2 (PI.f32)) (sqrt.f32 s))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary32`
682×	`associate-*l/_binary32`
376×	`*-commutative_binary32`
255×	`log-div_binary32`
228×	`distribute-rgt-in_binary32`

Counts

57 → 57

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	71	704
1	171	615
2	615	615
3	885	615
4	1123	615
5	1501	615
6	3981	615
7	4985	615

prune318.0ms (5.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	110	10	120

Error

0.1b

Counts

120 → 10

Alt Table

Status	Error	Program
	0.2b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 (.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 6 (.f32 s (exp.f32 (log.f32 (.f32 (PI.f32) r)))))))
	0.2b	(+.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)))) (.f32 6 (.f32 s (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (*.f32 (cbrt.f32 (PI.f32)) 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)))) (exp.f32 (+.f32 (+.f32 (+.f32 (log.f32 6) (log.f32 (PI.f32))) (log.f32 s)) (log.f32 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)))) (.f32 6 (exp.f32 (+.f32 (log.f32 s) (log.f32 (.f32 (PI.f32) 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)))) (.f32 6 (exp.f32 (log.f32 (.f32 (*.f32 (PI.f32) r) s))))))
✓	0.2b	(+.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)))) (.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r)) (sqrt.f32 (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))))
	0.2b	(+.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)))) (.f32 6 (.f32 s (.f32 (.f32 (cbrt.f32 (.f32 (PI.f32) r)) (cbrt.f32 (.f32 (PI.f32) r))) (cbrt.f32 (*.f32 (PI.f32) 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)))) (exp.f32 (+.f32 (log.f32 6) (+.f32 (log.f32 s) (log.f32 (*.f32 (PI.f32) r)))))))
	0.2b	(+.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 (.f32 (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s))) (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (cbrt.f32 (/.f32 (neg.f32 r) (.f32 3 s)))))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.2b	(+.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)))) (.f32 (sqrt.f32 (sqrt.f32 (.f32 (.f32 (.f32 6 (PI.f32)) s) r))) (pow.f32 (sqrt.f32 (sqrt.f32 (.f32 6 (.f32 s (*.f32 (PI.f32) r))))) 3))))

Compiler

Compiled 5043 to 2632 computations (47.8% saved)

regimes752.0ms (13.6%)

Accuracy

Total 0.1b remaining (40.4%)

Threshold costs 0.1b (40.4%)

Counts

198 → 1

Compiler

Compiled 24184 to 17269 computations (28.6% saved)

simplify3.0ms (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	30	58
1	49	58
2	55	58
3	60	58
4	62	58
5	60	58

end229.0ms (4.2%)

Compiler: Compiled 505 to 359 computations (28.9% saved)

Details

analyze99.0ms (1.8%)

sample2.1s (37.4%)

simplify57.0ms (1%)

prune4.0ms (0.1%)

localize81.0ms (1.5%)

series28.0ms (0.5%)

rewrite24.0ms (0.4%)

simplify93.0ms (1.7%)

prune287.0ms (5.2%)

localize91.0ms (1.7%)

series34.0ms (0.6%)

rewrite30.0ms (0.5%)

simplify89.0ms (1.6%)

prune558.0ms (10.1%)

localize79.0ms (1.4%)

series17.0ms (0.3%)

rewrite16.0ms (0.3%)

simplify83.0ms (1.5%)

prune286.0ms (5.2%)

localize87.0ms (1.6%)

series15.0ms (0.3%)

rewrite20.0ms (0.4%)

simplify70.0ms (1.3%)

prune318.0ms (5.8%)

regimes752.0ms (13.6%)

simplify3.0ms (0.1%)

end229.0ms (4.2%)

Profiling