Details

analyze2.3s (10.8%)

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)

sample173.0ms (0.8%)

Algorithm

1×

intervals

Results

60.0ms	59×	body	1024	valid
26.0ms	48×	body	512	valid
18.0ms	119×	body	128	valid
18.0ms	9×	body	2048	valid
6.0ms	21×	body	256	valid
6.0ms	11×	body	512	nan
5.0ms	43×	body	128	nan
2.0ms	19×	body	128	overflowed
1.0ms	2×	body	1024	nan
0.0ms	2×	body	256	nan

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify272.0ms (1.3%)

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

prune7.0ms (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

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	3.7b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.8s (8.6%)

Counts

3 → 108

Calls

3 calls:

956.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
525.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
336.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

8.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
2.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
0.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))

simplify187.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

350×	`fma-def_binary64`
308×	`fma-neg_binary64`
277×	`associate-+r+_binary64`
238×	`associate-+l+_binary64`
202×	`associate-r_binary64`

Counts

219 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	500	8918
1	1470	5721
2	4900	5719
3	5158	5719

prune241.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	219	9	228
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	220	9	229

Error

Counts

229 → 9

Alt Table

Status	Error	Program
▶	0.6b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	0.6b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	6.4b	(-.f64 x (/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t))
	31.7b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (sqrt.f64 t))))
	0.9b	(-.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (cbrt.f64 t))))
	17.7b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	0.9b	(-.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)))
	34.6b	(.f64 (sqrt.f64 (-.f64 x (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (sqrt.f64 (-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	16.9b	(-.f64 x (*.f64 (/.f64 y t) z))

Compiler

Compiled 8162 to 2974 computations (63.6% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	3.7b	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))

series1.5s (6.9%)

Counts

2 → 84

Calls

2 calls:

975.0ms	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))
486.0ms	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

rewrite13.0ms (0.1%)

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)))

simplify116.0ms (0.5%)

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

prune229.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	200	9	209

Error

Counts

209 → 9

Alt Table

Status	Error	Program
✓	0.6b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
▶	0.6b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
	6.4b	(-.f64 x (/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t))
	31.7b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (sqrt.f64 t))))
	0.9b	(-.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (cbrt.f64 t))))
	17.7b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	0.9b	(-.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)))
	34.6b	(.f64 (sqrt.f64 (-.f64 x (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (sqrt.f64 (-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	16.9b	(-.f64 x (*.f64 (/.f64 y t) z))

Compiler

Compiled 5948 to 3013 computations (49.3% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.0b	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
✓	0.5b	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
✓	3.6b	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

series3.3s (15.4%)

Counts

3 → 120

Calls

3 calls:

1.6s	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))
1.2s	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
511.0ms	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))

rewrite74.0ms (0.3%)

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:

15.0ms	(-.f64 x (/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))))
6.0ms	(/.f64 1 (/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z)))))
2.0ms	(/.f64 t (log1p.f64 (*.f64 y (expm1.f64 z))))

simplify474.0ms (2.2%)

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

prune898.0ms (4.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	511	2	513
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	514	8	522

Error

Counts

522 → 8

Alt Table

Status	Error	Program
▶	0.6b	(-.f64 x (/.f64 1 (.f64 t (/.f64 1 (log1p.f64 (.f64 y (expm1.f64 z)))))))
	6.4b	(-.f64 x (/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t))
✓	0.6b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	31.7b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (sqrt.f64 t))))
	17.7b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	0.9b	(-.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)))
	0.9b	(+.f64 x (neg.f64 (/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (cbrt.f64 t)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))))
	16.9b	(-.f64 x (*.f64 (/.f64 y t) z))

Compiler

Compiled 23061 to 9413 computations (59.2% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.1b	(/.f64 1 (log1p.f64 (*.f64 y (expm1.f64 z))))
✓	0.5b	(/.f64 1 (.f64 t (/.f64 1 (log1p.f64 (.f64 y (expm1.f64 z))))))
✓	3.7b	(.f64 t (/.f64 1 (log1p.f64 (.f64 y (expm1.f64 z)))))

series2.6s (12.2%)

Counts

3 → 96

Calls

3 calls:

1.3s	(.f64 t (/.f64 1 (log1p.f64 (.f64 y (expm1.f64 z)))))
852.0ms	(/.f64 1 (.f64 t (/.f64 1 (log1p.f64 (.f64 y (expm1.f64 z))))))
415.0ms	(/.f64 1 (log1p.f64 (*.f64 y (expm1.f64 z))))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-exp-log_binary64`
28×	`add-sqr-sqrt_binary64`
23×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`

Counts

3 → 113

Calls

3 calls:

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

simplify214.0ms (1%)

Algorithm

1×	egg-herbie

Rules

663×	`times-frac_binary64`
596×	`associate-/r*_binary64`
451×	`associate-/l*_binary64`
416×	`fma-def_binary64`
183×	`*-commutative_binary64`

Counts

209 → 244

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	654	7568
1	1989	6771
2	5133	6771

prune607.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	289	8	297

Error

Counts

297 → 8

Alt Table

Status	Error	Program
✓	0.6b	(-.f64 x (/.f64 1 (.f64 t (/.f64 1 (log1p.f64 (.f64 y (expm1.f64 z)))))))
	6.4b	(-.f64 x (/.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) 3)) t))
✓	0.6b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	31.7b	(-.f64 x (.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (sqrt.f64 t))))
	17.7b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	0.9b	(-.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)))
	0.9b	(+.f64 x (neg.f64 (/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (cbrt.f64 t)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))))
	16.9b	(-.f64 x (*.f64 (/.f64 y t) z))

Compiler

Compiled 11550 to 6542 computations (43.4% saved)

regimes1.2s (5.7%)

Accuracy

Total 0.9b remaining (79.7%)

Threshold costs 0.9b (79.7%)

Counts

86 → 1

Compiler

Compiled 16549 to 10740 computations (35.1% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	18	14
2	24	14
3	32	14
4	34	14
5	35	14
6	33	14

end1.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample4.9s (23.1%)

Algorithm

1×

intervals

Results

1.6s	1814×	body	1024	valid
698.0ms	1384×	body	512	valid
558.0ms	3765×	body	128	valid
470.0ms	285×	body	2048	valid
215.0ms	752×	body	256	valid
172.0ms	1649×	body	128	nan
110.0ms	191×	body	1024	nan
95.0ms	248×	body	512	nan
90.0ms	800×	body	128	overflowed
35.0ms	155×	body	256	nan
2.0ms	15×	body	128	invalid

Compiler

Compiled 183 to 118 computations (35.5% saved)

Details

analyze2.3s (10.8%)

sample173.0ms (0.8%)

simplify272.0ms (1.3%)

prune7.0ms (0%)

localize16.0ms (0.1%)

series1.8s (8.6%)

rewrite20.0ms (0.1%)

simplify187.0ms (0.9%)

prune241.0ms (1.1%)

localize8.0ms (0%)

series1.5s (6.9%)

rewrite13.0ms (0.1%)

simplify116.0ms (0.5%)

prune229.0ms (1.1%)

localize9.0ms (0%)

series3.3s (15.4%)

rewrite74.0ms (0.3%)

simplify474.0ms (2.2%)

prune898.0ms (4.3%)

localize27.0ms (0.1%)

series2.6s (12.2%)

rewrite22.0ms (0.1%)

simplify214.0ms (1%)

prune607.0ms (2.9%)

regimes1.2s (5.7%)

simplify5.0ms (0%)

end1.0ms (0%)

sample4.9s (23.1%)

Profiling