Details

analyze1.6s (9.1%)

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)

sample6.7s (38.1%)

Results

2.2s	1492×	body	8192	exit
1.7s	1870×	body	1024	valid
718.0ms	3850×	body	128	valid
682.0ms	1420×	body	512	valid
471.0ms	356×	body	2048	valid
248.0ms	760×	body	256	valid
237.0ms	1589×	body	128	invalid
122.0ms	217×	body	1024	invalid
97.0ms	246×	body	512	invalid
46.0ms	153×	body	256	invalid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify244.0ms (1.4%)

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

1.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.2b	(-.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 y (expm1.f64 z))
✓	0.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.7b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.2s (6.9%)

Counts

4 → 132

Calls

4 calls:

603.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
371.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
228.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
6.0ms	(*.f64 y (expm1.f64 z))

rewrite23.0ms (0.1%)

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:

9.0ms	(-.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)))

simplify160.0ms (0.9%)

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

prune250.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	250	7	257
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	250	8	258

Error

0.3b

Counts

258 → 8

Alt Table

Status	Error	Program
	23.0b	(-.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))))
	30.8b	(-.f64 x (-.f64 (+.f64 (/.f64 (.f64 y z) t) (+.f64 (.f64 1/2 (/.f64 (.f64 y (pow.f64 z 2)) t)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 y 3) (pow.f64 z 4)) t)) (+.f64 (.f64 1/24 (/.f64 (.f64 y (pow.f64 z 4)) t)) (+.f64 (.f64 1/3 (/.f64 (.f64 (pow.f64 y 3) (pow.f64 z 3)) t)) (.f64 1/6 (/.f64 (.f64 y (pow.f64 z 3)) t))))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 z 3)) t)) (+.f64 (.f64 7/24 (/.f64 (.f64 (pow.f64 y 2) (pow.f64 z 4)) t)) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 y 4) (pow.f64 z 4)) t)) (.f64 1/2 (/.f64 (*.f64 (pow.f64 y 2) (pow.f64 z 2)) t)))))))
	1.4b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))
	15.9b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	1.2b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	1.5b	(+.f64 x (neg.f64 (pow.f64 (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) (cbrt.f64 t)) 3)))
▶	1.2b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	1.2b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))

Compiler

Compiled 8711 to 3267 computations (62.5% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (expm1.f64 z))
✓	0.0b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.8b	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))

series986.0ms (5.6%)

Counts

2 → 84

Calls

2 calls:

590.0ms	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))
396.0ms	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

rewrite59.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`times-frac_binary64`

Counts

2 → 58

Calls

2 calls:

5.0ms	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))
3.0ms	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

simplify131.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
324×	`sub-neg_binary64`
278×	`fma-neg_binary64`
249×	`cancel-sign-sub-inv_binary64`
186×	`+-commutative_binary64`

Counts

142 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	3778
1	913	3303
2	3086	3202
3	4958	3202
4	5009	3202

prune288.0ms (1.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	229	8	237

Error

0.3b

Counts

237 → 8

Alt Table

Status	Error	Program
	1.4b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))
	15.9b	(-.f64 x (*.f64 (/.f64 y t) z))
	16.9b	(-.f64 x (.f64 (log1p.f64 (fma.f64 1/24 (.f64 y (pow.f64 z 4)) (fma.f64 y z (fma.f64 1/2 (.f64 y (.f64 z z)) (.f64 1/6 (.f64 y (pow.f64 z 3))))))) (/.f64 1 t)))
▶	1.2b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
✓	1.2b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	23.0b	(-.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))))
	1.5b	(+.f64 x (neg.f64 (pow.f64 (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) (cbrt.f64 t)) 3)))
✓	1.2b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

Compiler

Compiled 6405 to 3256 computations (49.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.7b	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
✓	4.5b	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

series1.7s (9.7%)

Counts

3 → 120

Calls

3 calls:

662.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))
621.0ms	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
414.0ms	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))

rewrite68.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`times-frac_binary64`
252×	`add-sqr-sqrt_binary64`
243×	`*-un-lft-identity_binary64`
238×	`add-cube-cbrt_binary64`
132×	`prod-diff_binary64`

Counts

3 → 306

Calls

3 calls:

17.0ms	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
4.0ms	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
2.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

simplify369.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

346×	`fma-def_binary64`
316×	`associate-/l*_binary64`
295×	`associate-/r*_binary64`
267×	`times-frac_binary64`
204×	`associate-/r/_binary64`

Counts

426 → 468

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	702	23281
1	2004	16368
2	4985	16368
3	4996	16368

prune579.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	511	2	513
Fresh	0	5	5
Picked	1	0	1
Done	1	1	2
Total	513	8	521

Error

0.2b

Counts

521 → 8

Alt Table

Status	Error	Program
	1.5b	(+.f64 x (neg.f64 (pow.f64 (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) (cbrt.f64 t)) 3)))
▶	1.2b	(-.f64 x (/.f64 1 (/.f64 1 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	1.4b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))
	15.9b	(-.f64 x (*.f64 (/.f64 y t) z))
	23.0b	(-.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))))
	1.4b	(-.f64 x (/.f64 1 (.f64 t (/.f64 1 (log1p.f64 (.f64 y (expm1.f64 z)))))))
✓	1.2b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	16.9b	(-.f64 x (.f64 (log1p.f64 (fma.f64 1/24 (.f64 y (pow.f64 z 4)) (fma.f64 y z (fma.f64 1/2 (.f64 y (.f64 z z)) (.f64 1/6 (.f64 y (pow.f64 z 3))))))) (/.f64 1 t)))

Compiler

Compiled 23071 to 9435 computations (59.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	0.2b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.7b	(/.f64 1 (/.f64 1 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))
	4.7b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.3s (7.2%)

Counts

2 → 72

Calls

2 calls:

656.0ms	(/.f64 1 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
607.0ms	(/.f64 1 (/.f64 1 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))

rewrite53.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

471×	`times-frac_binary64`
229×	`*-un-lft-identity_binary64`
229×	`add-sqr-sqrt_binary64`
229×	`add-cube-cbrt_binary64`
57×	`associate-/r*_binary64`

Counts

2 → 299

Calls

2 calls:

11.0ms	(/.f64 1 (/.f64 1 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))
4.0ms	(/.f64 1 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

simplify256.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

413×	`associate-r_binary64`
385×	`times-frac_binary64`
356×	`associate-/r*_binary64`
323×	`associate-/l*_binary64`
276×	`associate-l_binary64`

Counts

371 → 447

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	540	10695
1	1502	9769
2	5190	9769

prune683.0ms (3.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	558	0	558
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	558	8	566

Error

0.2b

Counts

566 → 8

Alt Table

Status	Error	Program
	1.5b	(+.f64 x (neg.f64 (pow.f64 (/.f64 (cbrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) (cbrt.f64 t)) 3)))
✓	1.2b	(-.f64 x (/.f64 1 (/.f64 1 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	1.4b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))
	15.9b	(-.f64 x (*.f64 (/.f64 y t) z))
	23.0b	(-.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))))
	1.4b	(-.f64 x (/.f64 1 (.f64 t (/.f64 1 (log1p.f64 (.f64 y (expm1.f64 z)))))))
✓	1.2b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	16.9b	(-.f64 x (.f64 (log1p.f64 (fma.f64 1/24 (.f64 y (pow.f64 z 4)) (fma.f64 y z (fma.f64 1/2 (.f64 y (.f64 z z)) (.f64 1/6 (.f64 y (pow.f64 z 3))))))) (/.f64 1 t)))

Compiler

Compiled 18266 to 8717 computations (52.3% saved)

regimes800.0ms (4.6%)

Accuracy

Total 1.1b remaining (89.4%)

Threshold costs 0b (0%)

Counts

93 → 1

Compiler

Compiled 22399 to 15006 computations (33% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	14
1	23	14
2	29	14
3	32	14
4	35	14
5	36	14
6	33	14

end125.0ms (0.7%)

Compiler: Compiled 182 to 123 computations (32.4% saved)

Details

analyze1.6s (9.1%)

sample6.7s (38.1%)

simplify244.0ms (1.4%)

prune3.0ms (0%)

localize7.0ms (0%)

series1.2s (6.9%)

rewrite23.0ms (0.1%)

simplify160.0ms (0.9%)

prune250.0ms (1.4%)

localize8.0ms (0%)

series986.0ms (5.6%)

rewrite59.0ms (0.3%)

simplify131.0ms (0.7%)

prune288.0ms (1.6%)

localize9.0ms (0.1%)

series1.7s (9.7%)

rewrite68.0ms (0.4%)

simplify369.0ms (2.1%)

prune579.0ms (3.3%)

localize10.0ms (0.1%)

series1.3s (7.2%)

rewrite53.0ms (0.3%)

simplify256.0ms (1.5%)

prune683.0ms (3.9%)

regimes800.0ms (4.6%)

simplify2.0ms (0%)

end125.0ms (0.7%)

Profiling