Details

analyze1.9s (12%)

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
13.1%	74.3%	12.7%	12
16.1%	70.5%	13.5%	13
18.6%	68%	13.5%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample337.0ms (2.1%)

Algorithm

1×

intervals

Results

78.0ms	67×	body	1024	valid
12.0ms	11×	body	2048	valid
11.0ms	126×	body	128	valid
9.0ms	36×	body	512	valid
3.0ms	16×	body	256	valid
2.0ms	43×	body	128	nan
2.0ms	6×	body	1024	nan
2.0ms	6×	body	256	nan
2.0ms	29×	body	128	overflowed
1.0ms	7×	body	512	nan
0.0ms	1×	body	512	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify246.0ms (1.5%)

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

1.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.5b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 z)
✓	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.0b	(*.f64 y (expm1.f64 z))
✓	6.7b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.1s (7%)

Counts

4 → 96

Calls

4 calls:

814.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
298.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
6.0ms	(*.f64 y (expm1.f64 z))
2.0ms	(expm1.f64 z)

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 71

Calls

4 calls:

17.0ms	(*.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)))
0.0ms	(expm1.f64 z)

simplify118.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

394×	`fma-neg_binary64`
350×	`sub-neg_binary64`
296×	`fma-def_binary64`
235×	`associate-+r+_binary64`
231×	`+-commutative_binary64`

Counts

167 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	363	3505
1	1031	3096
2	3824	3090
3	4891	3090
4	5019	3090

prune150.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	153	6	159
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	153	7	160

Error

0.0b

Counts

160 → 7

Alt Table

Status	Error	Program
✓	1.5b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
▶	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	16.0b	(-.f64 x (*.f64 (/.f64 y t) z))
	1.5b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	1.8b	(-.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (cbrt.f64 t))))
	19.8b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	1.8b	(-.f64 x (.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z))))) (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))

Compiler

Compiled 4357 to 2212 computations (49.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 z)
	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
	0.0b	(*.f64 y (expm1.f64 z))
✓	6.8b	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))

series761.0ms (4.8%)

Counts

1 → 36

Calls

1 calls:

761.0ms

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

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 38

Calls

1 calls:

5.0ms

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

simplify108.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

409×	`associate-/l*_binary64`
389×	`fma-def_binary64`
208×	`fma-neg_binary64`
180×	`sub-neg_binary64`
168×	`distribute-rgt-in_binary64`

Counts

74 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	245	2012
1	684	1753
2	2279	1666
3	4893	1664
4	5008	1664

prune184.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	182	7	189

Error

0.0b

Counts

189 → 7

Alt Table

Status	Error	Program
✓	1.5b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	16.0b	(-.f64 x (*.f64 (/.f64 y t) z))
▶	1.5b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	1.8b	(-.f64 x (.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 1 (cbrt.f64 t))))
	19.8b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	1.8b	(-.f64 x (.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z))))) (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))

Compiler

Compiled 4911 to 2619 computations (46.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
	0.0b	(*.f64 y (expm1.f64 z))
✓	0.9b	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
✓	6.5b	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

series1.8s (11.1%)

Counts

2 → 72

Calls

2 calls:

926.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))
846.0ms	(/.f64 1 (/.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:

6.0ms	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
2.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

simplify135.0ms (0.8%)

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

prune309.0ms (1.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	278	7	285

Error

0.0b

Counts

285 → 7

Alt Table

Status	Error	Program
✓	1.5b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	11.9b	(-.f64 x (/.f64 (expm1.f64 z) (/.f64 t y)))
✓	1.5b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	1.8b	(-.f64 x (.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 1 (cbrt.f64 t))))
	19.8b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
▶	1.8b	(-.f64 x (.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z))))) (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))

Compiler

Compiled 9402 to 4639 computations (50.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)
✓	0.5b	(.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))
✓	0.5b	(.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z))))) (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t))
✓	15.9b	(cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))

series4.2s (26.2%)

Counts

4 → 120

Calls

4 calls:

1.7s	(/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)
1.0s	(.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))
758.0ms	(.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z))))) (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t))
658.0ms	(cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
41×	`cbrt-prod_binary64`
41×	`add-cube-cbrt_binary64`
38×	`times-frac_binary64`

Counts

4 → 143

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z))))) (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t))
4.0ms	(/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)
4.0ms	(.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))
1.0ms	(cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))

simplify283.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

436×	`*-commutative_binary64`
307×	`+-commutative_binary64`
256×	`fma-def_binary64`
235×	`associate-+r+_binary64`
167×	`sub-neg_binary64`

Counts

263 → 372

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1235	18589
1	4203	17727
2	5118	17727

prune735.0ms (4.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	486	0	486
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	486	7	493

Error

0.0b

Counts

493 → 7

Alt Table

Status	Error	Program
✓	1.5b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	1.5b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	11.9b	(-.f64 x (/.f64 (expm1.f64 z) (/.f64 t y)))
✓	1.5b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	1.8b	(-.f64 x (.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 1 (cbrt.f64 t))))
	19.8b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
✓	1.8b	(-.f64 x (.f64 (.f64 (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (cbrt.f64 (log1p.f64 (.f64 y (expm1.f64 z))))) (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))

Compiler

Compiled 38979 to 18665 computations (52.1% saved)

regimes574.0ms (3.6%)

Accuracy

Total 0.2b remaining (40.2%)

Threshold costs 0.2b (40.2%)

Counts

61 → 3

Compiler

Compiled 11461 to 7389 computations (35.5% saved)

bsearch52.0ms (0.3%)

Steps

Iters	Range		Point
6	8.393360149884579e-140	4.1917175890103534e-138	2.6222458264973705e-138
1	-3.4018677558772304e-64	-3.6121975261085393e-66	-3.45751945873103e-65

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	28	40
2	40	40
3	48	40
4	54	40
5	56	40
6	56	40

end1.0ms (0%)

Compiler: Compiled 30 to 19 computations (36.7% saved)

sample2.9s (18%)

Algorithm

1×

intervals

Results

875.0ms	1805×	body	1024	valid
396.0ms	1388×	body	512	valid
338.0ms	3746×	body	128	valid
297.0ms	307×	body	2048	valid
135.0ms	754×	body	256	valid
89.0ms	1523×	body	128	nan
66.0ms	216×	body	1024	nan
52.0ms	798×	body	128	overflowed
50.0ms	237×	body	512	nan
18.0ms	143×	body	256	nan
1.0ms	10×	body	128	invalid
0.0ms	2×	body	512	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 178 to 112 computations (37.1% saved)

Details

analyze1.9s (12%)

sample337.0ms (2.1%)

simplify246.0ms (1.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series1.1s (7%)

rewrite23.0ms (0.1%)

simplify118.0ms (0.7%)

prune150.0ms (0.9%)

localize8.0ms (0.1%)

series761.0ms (4.8%)

rewrite8.0ms (0%)

simplify108.0ms (0.7%)

prune184.0ms (1.2%)

localize8.0ms (0.1%)

series1.8s (11.1%)

rewrite16.0ms (0.1%)

simplify135.0ms (0.8%)

prune309.0ms (1.9%)

localize11.0ms (0.1%)

series4.2s (26.2%)

rewrite29.0ms (0.2%)

simplify283.0ms (1.8%)

prune735.0ms (4.6%)

regimes574.0ms (3.6%)

bsearch52.0ms (0.3%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.9s (18%)

Profiling