Details

analyze89.0ms (2.6%)

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 (55.9%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 100 to 72 computations (28% saved)

preprocess25.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

654×	`associate-/l*_binary32`
635×	`associate-/l/_binary32`
596×	`times-frac_binary32`
556×	`associate-*r/_binary32`
486×	`associate-/r/_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	106
1	117	86
2	446	70
3	1873	64
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify20.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

622×	`associate-l_binary32`
523×	`associate-r_binary32`
423×	`associate-/r*_binary32`
364×	`associate-/l*_binary32`
320×	`associate-/l/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	53
1	66	43
2	244	35
3	1026	32
4	3417	32

Stop Event

1×	node limit

Counts

1 → 2

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

0.1b

Counts

3 → 2

Alt Table

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

Status

Error

Program

1.0b

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

▶

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)))

Compiler

Compiled 169 to 117 computations (30.8% saved)

localize76.0ms (2.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.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)

series31.0ms (0.9%)

Counts

4 → 84

Calls

21 calls:

5.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)	s	0
4.0ms	(/.f32 (neg.f32 r) (*.f32 3 s))	r	-inf
1.0ms	(.f32 (.f32 (*.f32 6 (PI.f32)) s) r)	s	0
1.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)	s	inf
1.0ms	(.f32 (.f32 (*.f32 2 (PI.f32)) s) r)	r	-inf

rewrite63.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

276×	`expm1-udef_binary32`
276×	`log1p-udef_binary32`
166×	`associate-r_binary32`
166×	`add-sqr-sqrt_binary32`
155×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	339	37
2	4453	37

Stop Event

1×	node limit

Counts

4 → 92

simplify28.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

48×	`associate-l_binary32`
34×	`associate-r_binary32`
26×	`*-commutative_binary32`
2×	`associate-/l*_binary32`
1×	`associate-*r/_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	792
1	30	792
2	73	792
3	142	792
4	155	792

Stop Event

1×

saturated

Counts

176 → 98

prune120.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	93	7	100

Error

0.0b

Counts

100 → 7

Alt Table

Status	Error	Program
	1.0b	(*.f32 (/.f32 (/.f32 (/.f32 1/8 s) (PI.f32)) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 r) (/.f32 -1/3 s))))
	19.4b	(+.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 (.f32 r (*.f32 (PI.f32) 6)) s) 3) 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 (.f32 r (*.f32 (PI.f32) 6)) s)))))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (expm1.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))) 2)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	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 -1/3 (/.f32 r s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
▶	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 s) (.f32 r 1/3)))) (.f32 (.f32 (.f32 6 (PI.f32)) s) r)))

Compiler

Compiled 4031 to 2513 computations (37.7% saved)

localize80.0ms (2.3%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.3%)

Counts

2 → 36

Calls

9 calls:

3.0ms	(.f32 (/.f32 -1 s) (.f32 r 1/3))	r	-inf
1.0ms	(.f32 (/.f32 -1 s) (.f32 r 1/3))	r	0
1.0ms	(.f32 (/.f32 -1 s) (.f32 r 1/3))	r	inf
1.0ms	(.f32 (/.f32 -1 s) (.f32 r 1/3))	s	0
1.0ms	(.f32 (/.f32 -1 s) (.f32 r 1/3))	s	inf

rewrite34.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`log1p-expm1-u_binary32`
709×	`expm1-log1p-u_binary32`
143×	`expm1-udef_binary32`
143×	`log1p-udef_binary32`
80×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	164	11
2	1954	11

Stop Event

1×	node limit

Counts

2 → 37

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`
2×	`associate-/l*_binary32`
1×	`associate-*r/_binary32`
1×	`associate-*l/_binary32`
1×	`associate-/r/_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	216
1	12	216
2	16	216
3	20	216
4	21	216

Stop Event

1×

saturated

Counts

73 → 41

prune129.0ms (3.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	75	6	81

Error

0.0b

Counts

81 → 6

Alt Table

Status	Error	Program
	1.0b	(*.f32 (/.f32 (/.f32 (/.f32 1/8 s) (PI.f32)) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 r) (/.f32 -1/3 s))))
	19.4b	(+.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 (.f32 r (*.f32 (PI.f32) 6)) s) 3) 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 (.f32 r (*.f32 (PI.f32) 6)) s)))))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (expm1.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))) 2)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (.f32 3 s)))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
▶	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 -1/3 r) s))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))

Compiler

Compiled 3087 to 2000 computations (35.2% saved)

localize83.0ms (2.4%)

Local error

Found 4 expressions with local error:

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

series2.0ms (0%)

Counts

1 → 0

Calls

3 calls:

0.0ms	(*.f32 -1/3 r)	r	0
0.0ms	(*.f32 -1/3 r)	r	-inf
0.0ms	(*.f32 -1/3 r)	r	inf

rewrite27.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

321×	`log1p-expm1-u_binary32`
321×	`expm1-log1p-u_binary32`
296×	`add-log-exp_binary32`
295×	`add-exp-log_binary32`
285×	`pow1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	80	4
2	880	4

Stop Event

1×	node limit

Counts

1 → 21

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

21 → 21

prune114.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Error

0.0b

Counts

77 → 6

Alt Table

Status	Error	Program
	1.0b	(*.f32 (/.f32 (/.f32 (/.f32 1/8 s) (PI.f32)) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 r) (/.f32 -1/3 s))))
	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 -1/3 r) s))) (exp.f32 (log.f32 (.f32 (.f32 r (*.f32 (PI.f32) 6)) s)))))
	19.4b	(+.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 -1/3 r) s))) (pow.f32 (pow.f32 (.f32 (.f32 r (*.f32 (PI.f32) 6)) s) 3) 1/3)))
▶	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))) 2)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (.f32 -1/3 r) s))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (expm1.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (.f32 -1/3 r) s))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
✓	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 -1/3 r) s))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))

Compiler

Compiled 2887 to 1851 computations (35.9% saved)

localize86.0ms (2.5%)

Local error

Found 4 expressions with local error:

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

series53.0ms (1.5%)

Counts

2 → 24

Calls

12 calls:

9.0ms	(pow.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 s r))) 2)	r	0
9.0ms	(pow.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 s r))) 2)	s	0
8.0ms	(pow.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 s r))) 2)	s	inf
8.0ms	(pow.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 s r))) 2)	r	inf
5.0ms	(pow.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) (*.f32 s r))) 2)	r	-inf

rewrite42.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

790×	`log1p-expm1-u_binary32`
790×	`expm1-log1p-u_binary32`
95×	`associate-r_binary32`
89×	`add-sqr-sqrt_binary32`
84×	`add-log-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	204	22
2	2235	22

Stop Event

1×	node limit

Counts

2 → 59

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	264
1	15	264
2	37	264
3	72	264
4	83	264

Stop Event

1×

saturated

Counts

83 → 50

prune141.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	88	6	94

Error

0.0b

Counts

94 → 6

Alt Table

Status	Error	Program
	1.0b	(*.f32 (/.f32 (/.f32 (/.f32 1/8 s) (PI.f32)) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 r) (/.f32 -1/3 s))))
	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 -1/3 r) s))) (exp.f32 (log.f32 (.f32 (.f32 r (*.f32 (PI.f32) 6)) s)))))
	19.4b	(+.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 -1/3 r) s))) (pow.f32 (pow.f32 (.f32 (.f32 r (*.f32 (PI.f32) 6)) s) 3) 1/3)))
✓	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (sqrt.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))) 2)) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (.f32 -1/3 r) s))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
	0.1b	(+.f32 (/.f32 (.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (expm1.f32 (log1p.f32 (.f32 (.f32 2 (PI.f32)) (.f32 s r))))) (/.f32 (.f32 3/4 (exp.f32 (/.f32 (.f32 -1/3 r) s))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))
✓	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 -1/3 r) s))) (.f32 (.f32 (*.f32 6 (PI.f32)) s) r)))

Compiler

Compiled 3563 to 2163 computations (39.3% saved)

regimes98.0ms (2.8%)

Accuracy

Total 0.0b remaining (33.4%)

Threshold costs 0.0b (33.4%)

Counts

27 → 1

Compiler

Compiled 2968 to 2200 computations (25.9% saved)

simplify4.0ms (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	26	51
1	42	51
2	46	51
3	49	51
4	50	51

Stop Event

1×

saturated

end134.0ms (3.9%)

Stop Event

1×

fuel

Compiler

Compiled 271 to 202 computations (25.5% saved)

Details

analyze89.0ms (2.6%)

sample1.9s (55.9%)

preprocess25.0ms (0.7%)

simplify20.0ms (0.6%)

prune5.0ms (0.1%)

localize76.0ms (2.2%)

series31.0ms (0.9%)

rewrite63.0ms (1.8%)

simplify28.0ms (0.8%)

prune120.0ms (3.5%)

localize80.0ms (2.3%)

series10.0ms (0.3%)

rewrite34.0ms (1%)

simplify14.0ms (0.4%)

prune129.0ms (3.7%)

localize83.0ms (2.4%)

series2.0ms (0%)

rewrite27.0ms (0.8%)

simplify6.0ms (0.2%)

prune114.0ms (3.3%)

localize86.0ms (2.5%)

series53.0ms (1.5%)

rewrite42.0ms (1.2%)

simplify12.0ms (0.4%)

prune141.0ms (4.1%)

regimes98.0ms (2.8%)

simplify4.0ms (0.1%)

end134.0ms (3.9%)

Profiling