Details

analyze1.6s (11.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
12.9%	79.1%	8%	12
15.8%	76.2%	8%	13
18.4%	73.6%	8%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample6.2s (42.7%)

Results

2.0s	1581×	body	8192	exit
1.5s	1844×	body	1024	valid
700.0ms	3922×	body	128	valid
691.0ms	1358×	body	512	valid
408.0ms	315×	body	2048	valid
264.0ms	817×	body	256	valid
239.0ms	1678×	body	128	invalid
120.0ms	222×	body	1024	invalid
104.0ms	274×	body	512	invalid
46.0ms	182×	body	256	invalid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify244.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

3540×	`fma-neg_binary64`
744×	`div-sub_binary64`
658×	`sub-neg_binary64`
627×	`fma-def_binary64`
613×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	23	18
2	48	17
3	86	17
4	177	14
5	318	14
6	465	14
7	536	14
8	618	14
9	723	14
10	1083	14
11	1710	14
12	1873	14
13	2250	14
14	2803	14
15	3186	14
16	3529	14
17	3735	14
18	3809	14
19	4125	14
20	4337	14
21	3179	14
22	3171	14
23	3183	14
24	3183	14
25	4223	14
26	7145	14

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

1.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.1b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.0b	(*.f64 y (expm1.f64 z))
✓	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	3.6b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.2s (8%)

Counts

4 → 132

Calls

4 calls:

565.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
385.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
217.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
6.0ms	(*.f64 y (expm1.f64 z))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64`
56×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

4 → 131

Calls

4 calls:

6.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
3.0ms	(*.f64 y (expm1.f64 z))
2.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
0.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))

simplify157.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

360×	`fma-def_binary64`
345×	`fma-neg_binary64`
243×	`associate-r_binary64`
238×	`associate-+l+_binary64`
236×	`associate-l_binary64`

Counts

263 → 257

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	527	9322
1	1512	6066
2	4776	6064
3	5068	6064

prune218.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	249	8	257
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	249	9	258

Error

0.0b

Counts

258 → 9

Alt Table

Status	Error	Program
▶	1.1b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	15.9b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	1.1b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	23.6b	(-.f64 x (.f64 (sqrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (sqrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	23.9b	(-.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (log1p.f64 (.f64 y (expm1.f64 z)))) (log1p.f64 (.f64 y (expm1.f64 z)))) (.f64 (*.f64 t t) t))))
	18.0b	x
	1.1b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	32.1b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
	25.1b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))

Compiler

Compiled 8555 to 3131 computations (63.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (expm1.f64 z))
	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.9b	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
✓	3.2b	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

series1.4s (9.5%)

Counts

2 → 72

Calls

2 calls:

702.0ms	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
690.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
2.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

simplify174.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

389×	`associate-r_binary64`
291×	`associate-/r*_binary64`
278×	`associate-/l*_binary64`
265×	`times-frac_binary64`
260×	`associate-l_binary64`

Counts

179 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	501	6217
1	1447	5548
2	4978	5546
3	5092	5546

prune426.0ms (2.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	278	9	287

Error

0.0b

Counts

287 → 9

Alt Table

Status	Error	Program
✓	1.1b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	15.9b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	1.1b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	23.9b	(-.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (log1p.f64 (.f64 y (expm1.f64 z)))) (log1p.f64 (.f64 y (expm1.f64 z)))) (.f64 (*.f64 t t) t))))
	18.0b	x
▶	1.1b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	32.1b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
	25.1b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
	7.6b	(-.f64 x (/.f64 (expm1.f64 z) (/.f64 t y)))

Compiler

Compiled 9440 to 4667 computations (50.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
✓	0.2b	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))
	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	3.6b	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)

series1.3s (9.2%)

Counts

3 → 84

Calls

3 calls:

626.0ms	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)
467.0ms	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
243.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 52

Calls

3 calls:

2.0ms	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)
0.0ms	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
0.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-def_binary64`
313×	`associate-r_binary64`
272×	`associate-+l+_binary64`
271×	`associate-l_binary64`
177×	`associate-/r*_binary64`

Counts

136 → 175

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	464	4678
1	1404	4129
2	5039	4129

prune230.0ms (1.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	220	9	229

Error

0.0b

Counts

229 → 9

Alt Table

Status	Error	Program
✓	1.1b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	15.9b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	1.1b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	23.9b	(-.f64 x (cbrt.f64 (/.f64 (.f64 (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (log1p.f64 (.f64 y (expm1.f64 z)))) (log1p.f64 (.f64 y (expm1.f64 z)))) (.f64 (*.f64 t t) t))))
	18.0b	x
✓	1.1b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	32.1b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
	25.1b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
▶	7.6b	(-.f64 x (/.f64 (expm1.f64 z) (/.f64 t y)))

Compiler

Compiled 7756 to 4158 computations (46.4% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (expm1.f64 z) (/.f64 t y)))
✓	1.6b	(/.f64 (expm1.f64 z) (/.f64 t y))

series37.0ms (0.3%)

Counts

2 → 84

Calls

2 calls:

20.0ms	(-.f64 x (/.f64 (expm1.f64 z) (/.f64 t y)))
17.0ms	(/.f64 (expm1.f64 z) (/.f64 t y))

rewrite61.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

342×	`times-frac_binary64`
238×	`add-sqr-sqrt_binary64`
231×	`*-un-lft-identity_binary64`
229×	`add-cube-cbrt_binary64`
132×	`prod-diff_binary64`

Counts

2 → 270

Calls

2 calls:

17.0ms	(-.f64 x (/.f64 (expm1.f64 z) (/.f64 t y)))
4.0ms	(/.f64 (expm1.f64 z) (/.f64 t y))

simplify361.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-def_binary64`
424×	`associate-*r/_binary64`
358×	`associate-*l/_binary64`
277×	`associate-/r/_binary64`
221×	`associate-/l*_binary64`

Counts

354 → 375

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	588	18553
1	1629	9422
2	4251	9416
3	4966	9416
4	5000	9416
5	4982	9416

prune257.0ms (1.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	373	2	375
Fresh	3	2	5
Picked	1	0	1
Done	0	3	3
Total	377	7	384

Error

Counts

384 → 7

Alt Table

Status	Error	Program
	6.4b	(-.f64 x (/.f64 (/.f64 (expm1.f64 z) t) (/.f64 1 y)))
✓	1.1b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	7.6b	(-.f64 x (.f64 (expm1.f64 z) (.f64 (/.f64 1 t) y)))
	18.0b	x
✓	1.1b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	25.1b	(-.f64 x (/.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 t (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))))))
✓	1.1b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))

Compiler

Compiled 12803 to 2625 computations (79.5% saved)

regimes404.0ms (2.8%)

Accuracy

Total 1.0b remaining (86.8%)

Threshold costs 1.0b (86.8%)

Counts

48 → 1

Compiler

Compiled 8890 to 5731 computations (35.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
2	20	14
3	24	14
4	27	14
5	28	14
6	28	14

end84.0ms (0.6%)

Compiler: Compiled 123 to 84 computations (31.7% saved)

Details

analyze1.6s (11.2%)

sample6.2s (42.7%)

simplify244.0ms (1.7%)

prune3.0ms (0%)

localize7.0ms (0%)

series1.2s (8%)

rewrite23.0ms (0.2%)

simplify157.0ms (1.1%)

prune218.0ms (1.5%)

localize8.0ms (0.1%)

series1.4s (9.5%)

rewrite16.0ms (0.1%)

simplify174.0ms (1.2%)

prune426.0ms (2.9%)

localize11.0ms (0.1%)

series1.3s (9.2%)

rewrite6.0ms (0%)

simplify84.0ms (0.6%)

prune230.0ms (1.6%)

localize6.0ms (0%)

series37.0ms (0.3%)

rewrite61.0ms (0.4%)

simplify361.0ms (2.5%)

prune257.0ms (1.8%)

regimes404.0ms (2.8%)

simplify2.0ms (0%)

end84.0ms (0.6%)

Profiling