Details

analyze101.0ms (2.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0.1%	0.1%	99.8%	3
0.1%	0.1%	99.8%	4
0.1%	0%	99.8%	5
0.1%	0%	99.8%	6
0.1%	0%	99.8%	7
0.1%	0%	99.8%	8
0.2%	0%	99.8%	9
0.2%	0%	99.8%	10
0.2%	0%	99.8%	11
0.2%	0%	99.8%	12
0.2%	0%	99.8%	13
0.2%	0%	99.8%	14

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample272.0ms (6.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify34.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

566×	`fma-def_binary32`
230×	`fma-neg_binary32`
88×	`cancel-sign-sub-inv_binary32`
79×	`distribute-rgt-in_binary32`
67×	`distribute-lft-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
	13.4b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))

Compiler

Compiled 61 to 42 computations (31.1% saved)

localize22.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.4b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))

series228.0ms (5.4%)

Counts

2 → 36

Calls

2 calls:

225.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
3.0ms	(log1p.f32 (neg.f32 u0))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary32`
7×	`add-exp-log_binary32`
7×	`pow1_binary32`
3×	`associate-r_binary32`
3×	`*-un-lft-identity_binary32`

Counts

2 → 32

Calls

2 calls:

4.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
0.0ms	(log1p.f32 (neg.f32 u0))

simplify61.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

588×	`fma-neg_binary32`
526×	`fma-def_binary32`
217×	`times-frac_binary32`
213×	`distribute-rgt-neg-out_binary32`
204×	`distribute-lft-neg-out_binary32`

Counts

68 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	1211
1	390	1075
2	1418	1024
3	4435	1014
4	4952	1014

prune61.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Error

0.0b

Counts

94 → 9

Alt Table

Status	Error	Program
	0.4b	(neg.f32 (.f32 (.f32 alpha alpha) (log1p.f32 (neg.f32 u0))))
	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	3.0b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 (neg.f32 alpha) (neg.f32 alpha)) (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 (.f32 (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	2.1b	(.f32 (.f32 alpha alpha) (+.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))))
	2.1b	(+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (.f32 (pow.f32 u0 2) (pow.f32 alpha 2))) (+.f32 (.f32 1/4 (.f32 (pow.f32 u0 4) (pow.f32 alpha 2))) (*.f32 u0 (pow.f32 alpha 2)))))
	0.9b	(.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))
▶	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 1852 to 885 computations (52.2% saved)

localize21.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.2b	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

series460.0ms (11%)

Counts

2 → 48

Calls

2 calls:

241.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
219.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`associate-l_binary32`
9×	`add-sqr-sqrt_binary32`
9×	`add-cbrt-cube_binary32`
9×	`add-exp-log_binary32`
9×	`pow1_binary32`

Counts

2 → 49

Calls

2 calls:

4.0ms	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
3.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))

simplify74.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary32`
338×	`fma-neg_binary32`
288×	`distribute-rgt-neg-out_binary32`
249×	`distribute-lft-neg-out_binary32`
230×	`times-frac_binary32`

Counts

97 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1675
1	436	1509
2	1377	1427
3	4367	1415
4	4977	1415

prune113.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	155	6	161
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	159	11	170

Error

Counts

170 → 11

Alt Table

Status	Error	Program
	3.0b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 (neg.f32 alpha) (neg.f32 alpha)) (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 alpha (.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (neg.f32 (cbrt.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))
	0.8b	(.f32 alpha (.f32 (.f32 (neg.f32 alpha) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0)))))
	2.9b	(cbrt.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))
	2.9b	(.f32 alpha (+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) alpha)) (+.f32 (.f32 u0 alpha) (.f32 1/2 (.f32 (pow.f32 u0 2) alpha)))))
	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	2.1b	(.f32 (.f32 alpha alpha) (+.f32 (fma.f32 1/4 (pow.f32 u0 4) u0) (.f32 (.f32 u0 u0) (+.f32 1/2 (*.f32 1/3 u0)))))
▶	0.4b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	0.6b	(.f32 (sqrt.f32 alpha) (.f32 (sqrt.f32 alpha) (*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 2869 to 1325 computations (53.8% saved)

localize30.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.3b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
✓	0.3b	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

series178.0ms (4.2%)

Counts

2 → 32

Calls

2 calls:

155.0ms	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
22.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`associate-r_binary32`
12×	`add-sqr-sqrt_binary32`
10×	`*-un-lft-identity_binary32`
10×	`add-cube-cbrt_binary32`
9×	`associate-l_binary32`

Counts

2 → 60

Calls

2 calls:

7.0ms	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
5.0ms	(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))

simplify115.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-def_binary32`
490×	`*-commutative_binary32`
235×	`fma-neg_binary32`
222×	`associate-r_binary32`
220×	`distribute-rgt-neg-out_binary32`

Counts

92 → 129

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	1990
1	520	1770
2	1695	1627
3	4473	1546
4	4873	1546
5	5000	1546
6	4944	1546

prune130.0ms (3.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	167	10	177

Error

Counts

177 → 10

Alt Table

Status	Error	Program
	0.6b	(.f32 (sqrt.f32 (sqrt.f32 alpha)) (.f32 (sqrt.f32 (sqrt.f32 alpha)) (*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))))
	2.9b	(.f32 alpha (+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) alpha)) (+.f32 (.f32 u0 alpha) (.f32 1/2 (.f32 (pow.f32 u0 2) alpha)))))
	3.0b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 (neg.f32 alpha) (neg.f32 alpha)) (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 alpha (.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (neg.f32 (cbrt.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
▶	0.4b	(.f32 1 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (*.f32 alpha alpha))))
✓	0.4b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.5b	(.f32 (.f32 (sqrt.f32 alpha) (log1p.f32 (neg.f32 u0))) (neg.f32 (pow.f32 alpha 3/2)))
	0.8b	(.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 3406 to 1975 computations (42% saved)

localize25.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(log1p.f32 (neg.f32 u0))
✓	0.4b	(.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (.f32 alpha alpha)))

series220.0ms (5.3%)

Counts

1 → 24

Calls

1 calls:

220.0ms

(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (*.f32 alpha alpha)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`associate-r_binary32`
5×	`add-sqr-sqrt_binary32`
3×	`associate-l_binary32`
3×	`*-un-lft-identity_binary32`
3×	`add-cube-cbrt_binary32`

Counts

1 → 24

Calls

1 calls:

3.0ms

(*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (*.f32 alpha alpha)))

simplify69.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

707×	`unsub-neg_binary32`
322×	`times-frac_binary32`
298×	`fma-def_binary32`
284×	`fma-neg_binary32`
259×	`neg-sub0_binary32`

Counts

48 → 58

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	934
1	260	853
2	845	800
3	2196	786
4	4179	784
5	5230	784

prune65.0ms (1.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	95	10	105

Error

Counts

105 → 10

Alt Table

Status	Error	Program
	0.6b	(.f32 (sqrt.f32 (sqrt.f32 alpha)) (.f32 (sqrt.f32 (sqrt.f32 alpha)) (*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2)))))
	2.9b	(.f32 alpha (+.f32 (.f32 1/3 (.f32 (pow.f32 u0 3) alpha)) (+.f32 (.f32 u0 alpha) (.f32 1/2 (.f32 (pow.f32 u0 2) alpha)))))
	3.0b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.f32 (neg.f32 alpha) (neg.f32 alpha)) (neg.f32 alpha))) (.f32 (.f32 (log1p.f32 (neg.f32 u0)) (log1p.f32 (neg.f32 u0))) (log1p.f32 (neg.f32 u0)))))
	0.8b	(.f32 alpha (.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (neg.f32 (cbrt.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
✓	0.4b	(.f32 1 (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (*.f32 alpha alpha))))
✓	0.4b	(.f32 (sqrt.f32 alpha) (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (pow.f32 alpha 3/2))))
	0.6b	(.f32 (sqrt.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))) (sqrt.f32 (.f32 (*.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))))
	0.5b	(.f32 (.f32 (sqrt.f32 alpha) (log1p.f32 (neg.f32 u0))) (neg.f32 (pow.f32 alpha 3/2)))
	0.8b	(.f32 (.f32 (.f32 alpha (neg.f32 alpha)) (.f32 (cbrt.f32 (log1p.f32 (neg.f32 u0))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (log1p.f32 (neg.f32 u0))))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 1828 to 983 computations (46.2% saved)

regimes542.0ms (12.9%)

Accuracy

Total 0.3b remaining (95.6%)

Threshold costs 0.3b (95.6%)

Counts

91 → 1

Compiler

Compiled 9055 to 5948 computations (34.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`
5×	`+-commutative_binary32`
5×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	31	13
3	41	13
4	46	13
5	48	13
6	48	13

end0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

sample1.3s (31.7%)

Algorithm

1×

intervals

Results

581.0ms	8000×	body	128	valid
189.0ms	8000×	pre	128	true

Compiler

Compiled 215 to 135 computations (37.2% saved)

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13

Details

analyze101.0ms (2.4%)

sample272.0ms (6.5%)

simplify34.0ms (0.8%)

prune4.0ms (0.1%)

localize22.0ms (0.5%)

series228.0ms (5.4%)

rewrite6.0ms (0.1%)

simplify61.0ms (1.5%)

prune61.0ms (1.4%)

localize21.0ms (0.5%)

series460.0ms (11%)

rewrite10.0ms (0.2%)

simplify74.0ms (1.8%)

prune113.0ms (2.7%)

localize30.0ms (0.7%)

series178.0ms (4.2%)

rewrite15.0ms (0.4%)

simplify115.0ms (2.7%)

prune130.0ms (3.1%)

localize25.0ms (0.6%)

series220.0ms (5.3%)

rewrite4.0ms (0.1%)

simplify69.0ms (1.6%)

prune65.0ms (1.6%)

regimes542.0ms (12.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (31.7%)

Profiling

Iter	Nodes	Cost
0	9	14
1	22	13
2	43	13
3	77	13
4	93	13
5	131	13
6	170	13
7	217	13
8	340	13
9	471	13
10	481	13
11	557	13
12	569	13
13	676	13
14	699	13
15	700	13
16	645	13