Details

analyze341.0ms (6.7%)

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)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify36.0ms (0.7%)

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

prune7.0ms (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
▶	0.3b	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
	13.9b	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))

Compiler

Compiled 61 to 42 computations (31.1% saved)

localize21.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series244.0ms (4.8%)

Counts

2 → 36

Calls

2 calls:

241.0ms	(.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:

5.0ms	(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
0.0ms	(log1p.f32 (neg.f32 u0))

simplify68.0ms (1.3%)

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

prune68.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	87	7	94

Error

0.0b

Counts

94 → 7

Alt Table

Status	Error	Program
	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)))))
	2.5b	(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)))))
▶	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	2.2b	(+.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)))))
	8.3b	(*.f32 u0 (pow.f32 alpha 2))
	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)))))
	2.2b	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))

Compiler

Compiled 1742 to 831 computations (52.3% saved)

localize21.0ms (0.4%)

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))))

series517.0ms (10.1%)

Counts

2 → 48

Calls

2 calls:

278.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
238.0ms	(.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))))
4.0ms	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))

simplify74.0ms (1.4%)

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

prune105.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	159	9	168

Error

0.0b

Counts

168 → 9

Alt Table

Status	Error	Program
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	2.2b	(+.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)))))
	0.8b	(.f32 alpha (.f32 (.f32 (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))
▶	0.3b	(.f32 1 (.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha))))
	8.3b	(*.f32 u0 (pow.f32 alpha 2))
	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)))))
	2.2b	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (cbrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
	2.5b	(cbrt.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.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))))))

Compiler

Compiled 2793 to 1287 computations (53.9% saved)

localize26.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

series235.0ms (4.6%)

Counts

1 → 24

Calls

1 calls:

235.0ms

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary32`
6×	`add-exp-log_binary32`
6×	`pow1_binary32`
3×	`associate-l_binary32`
3×	`cbrt-unprod_binary32`

Counts

1 → 21

Calls

1 calls:

4.0ms

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

simplify99.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

940×	`unsub-neg_binary32`
356×	`fma-def_binary32`
298×	`fma-neg_binary32`
290×	`neg-sub0_binary32`
285×	`neg-mul-1_binary32`

Counts

45 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	905
1	265	801
2	943	748
3	3086	738
4	4940	738
5	4995	738
6	4988	738
7	4932	738

prune65.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	89	9	98

Error

0.0b

Counts

98 → 9

Alt Table

Status	Error	Program
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	2.2b	(+.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)))))
	0.8b	(.f32 alpha (.f32 (.f32 (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))) (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))) (cbrt.f32 (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))
✓	0.3b	(.f32 1 (.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha))))
	8.3b	(*.f32 u0 (pow.f32 alpha 2))
	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)))))
	2.2b	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))
▶	0.8b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (cbrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
	2.5b	(cbrt.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.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))))))

Compiler

Compiled 1925 to 1034 computations (46.3% saved)

localize38.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))
✓	0.4b	(.f32 (cbrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
✓	0.4b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (.f32 (cbrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
✓	0.5b	(*.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))

series567.0ms (11.1%)

Counts

3 → 60

Calls

3 calls:

281.0ms

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

248.0ms

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

37.0ms

(*.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary32`
31×	`add-exp-log_binary32`
21×	`add-sqr-sqrt_binary32`
20×	`pow-prod-down_binary32`
19×	`cbrt-prod_binary32`

Counts

3 → 97

Calls

3 calls:

12.0ms

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

6.0ms

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

5.0ms

(*.f32 (cbrt.f32 alpha) (cbrt.f32 alpha))

simplify108.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

950×	`fma-def_binary32`
598×	`times-frac_binary32`
389×	`associate-r_binary32`
348×	`associate-l_binary32`
240×	`fma-neg_binary32`

Counts

157 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2862
1	532	2377
2	2216	2311
3	4779	2311
4	5095	2311

prune157.0ms (3.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	247	5	252
Fresh	4	2	6
Picked	1	0	1
Done	0	2	2
Total	252	9	261

Error

Counts

261 → 9

Alt Table

Status	Error	Program
	0.8b	(.f32 (cbrt.f32 alpha) (.f32 (cbrt.f32 alpha) (.f32 (cbrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))))
	2.5b	(cbrt.f32 (.f32 (.f32 (.f32 alpha alpha) alpha) (.f32 (.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))))))
	0.9b	(.f32 (.f32 (.f32 (cbrt.f32 (cbrt.f32 (.f32 alpha alpha))) (cbrt.f32 (cbrt.f32 (.f32 alpha alpha)))) (cbrt.f32 (cbrt.f32 (.f32 alpha alpha)))) (.f32 (cbrt.f32 alpha) (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
✓	0.3b	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
	0.7b	(.f32 (.f32 (cbrt.f32 (sqrt.f32 alpha)) (.f32 (cbrt.f32 (sqrt.f32 alpha)) (cbrt.f32 alpha))) (.f32 (cbrt.f32 alpha) (*.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0)))))
✓	0.3b	(.f32 1 (.f32 (log1p.f32 (neg.f32 u0)) (*.f32 alpha (neg.f32 alpha))))
	0.7b	(.f32 (.f32 (cbrt.f32 alpha) (cbrt.f32 alpha)) (*.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (cbrt.f32 (pow.f32 alpha 4)))))
	2.1b	(fma.f32 (.f32 alpha alpha) (fma.f32 1/3 (pow.f32 u0 3) (.f32 1/2 (.f32 u0 u0))) (.f32 (*.f32 alpha alpha) (fma.f32 1/4 (pow.f32 u0 4) u0)))
	2.2b	(exp.f32 (log.f32 (.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha (neg.f32 alpha)))))

Compiler

Compiled 5607 to 1789 computations (68.1% saved)

regimes872.0ms (17%)

Accuracy

Total 0.3b remaining (92.4%)

Threshold costs 0.3b (92.4%)

Counts

148 → 1

Compiler

Compiled 16572 to 10386 computations (37.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	28	13
3	36	13
4	41	13
5	44	13
6	45	13
7	45	13

end0.0ms (0%)

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

sample1.4s (26.5%)

Algorithm

1×

intervals

Results

603.0ms	8000×	body	128	valid
194.0ms	8000×	pre	128	true

Compiler

Compiled 212 to 132 computations (37.7% 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

analyze341.0ms (6.7%)

sample41.0ms (0.8%)

simplify36.0ms (0.7%)

prune7.0ms (0.1%)

localize21.0ms (0.4%)

series244.0ms (4.8%)

rewrite6.0ms (0.1%)

simplify68.0ms (1.3%)

prune68.0ms (1.3%)

localize21.0ms (0.4%)

series517.0ms (10.1%)

rewrite10.0ms (0.2%)

simplify74.0ms (1.4%)

prune105.0ms (2.1%)

localize26.0ms (0.5%)

series235.0ms (4.6%)

rewrite5.0ms (0.1%)

simplify99.0ms (1.9%)

prune65.0ms (1.3%)

localize38.0ms (0.7%)

series567.0ms (11.1%)

rewrite29.0ms (0.6%)

simplify108.0ms (2.1%)

prune157.0ms (3.1%)

regimes872.0ms (17%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (26.5%)

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