Details

analyze1.6s (8.8%)

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
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 (36.6%)

Results

1.9s	1601×	body	8192	exit
1.9s	1861×	body	1024	valid
751.0ms	3902×	body	128	valid
722.0ms	1358×	body	512	valid
426.0ms	312×	body	2048	valid
256.0ms	823×	body	256	valid
229.0ms	1633×	body	128	invalid
122.0ms	252×	body	512	invalid
105.0ms	188×	body	1024	invalid
45.0ms	183×	body	256	invalid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify246.0ms (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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(-.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	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	0.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	4.3b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.6s (8.7%)

Counts

4 → 132

Calls

4 calls:

777.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
506.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
291.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
8.0ms	(*.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:

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)))

simplify159.0ms (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

prune247.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	247	10	257
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	248	10	258

Error

0.0b

Counts

258 → 10

Alt Table

Status	Error	Program
	1.0b	(-.f64 x (/.f64 (log1p.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (expm1.f64 z)) (cbrt.f64 (expm1.f64 z)))) (cbrt.f64 (expm1.f64 z)))) t))
	20.1b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	16.8b	(-.f64 x (*.f64 (/.f64 y t) z))
	23.8b	(-.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))))
	25.0b	(-.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))))
	11.2b	(-.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	31.6b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 t)) (sqrt.f64 t)))
▶	0.8b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	41.0b	(-.f64 x (/.f64 (log1p.f64 (.f64 (.f64 y (sqrt.f64 (expm1.f64 z))) (sqrt.f64 (expm1.f64 z)))) t))
	32.2b	(.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))))

Compiler

Compiled 8692 to 3184 computations (63.4% 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)))
	0.0b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.3b	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))

series1.2s (6.7%)

Counts

2 → 84

Calls

2 calls:

753.0ms	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))
470.0ms	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

rewrite11.0ms (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)))

simplify114.0ms (0.6%)

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

prune243.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	230	9	239

Error

Counts

239 → 9

Alt Table

Status	Error	Program
✓	0.8b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
▶	1.1b	(-.f64 x (.f64 (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t)))) (cbrt.f64 (/.f64 1 t))))
	7.7b	(-.f64 x (.f64 (cbrt.f64 (pow.f64 (log1p.f64 (.f64 y (expm1.f64 z))) 3)) (/.f64 1 t)))
	23.8b	(-.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))))
	25.0b	(-.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))))
	11.2b	(-.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	31.6b	(-.f64 x (.f64 (.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 (/.f64 1 t))) (sqrt.f64 (/.f64 1 t))))
	16.8b	(-.f64 x (*.f64 (/.f64 y t) z))
	32.2b	(.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))))

Compiler

Compiled 6516 to 3299 computations (49.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t)))
✓	0.6b	(cbrt.f64 (/.f64 1 t))
✓	0.6b	(.f64 (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t)))) (cbrt.f64 (/.f64 1 t)))
✓	3.8b	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t))))

series2.0s (10.8%)

Counts

4 → 96

Calls

4 calls:

1.1s	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t))))
779.0ms	(.f64 (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t)))) (cbrt.f64 (/.f64 1 t)))
35.0ms	(*.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t)))
29.0ms	(cbrt.f64 (/.f64 1 t))

rewrite49.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`cbrt-prod_binary64`
93×	`add-sqr-sqrt_binary64`
70×	`times-frac_binary64`
62×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`

Counts

4 → 180

Calls

4 calls:

12.0ms	(.f64 (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t)))) (cbrt.f64 (/.f64 1 t)))
10.0ms	(*.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t)))
7.0ms	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t))))
2.0ms	(cbrt.f64 (/.f64 1 t))

simplify163.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-l_binary64`
527×	`associate-r_binary64`
430×	`fma-neg_binary64`
366×	`fma-def_binary64`
197×	`associate-/r*_binary64`

Counts

276 → 313

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	452	7501
1	1290	6142
2	4918	6138
3	5288	6138

prune485.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	368	1	369
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	369	9	378

Error

Counts

378 → 9

Alt Table

Status	Error	Program
▶	1.1b	(-.f64 x (.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 (/.f64 1 t))))
	31.6b	(-.f64 x (.f64 (.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 (/.f64 1 t))) (sqrt.f64 (/.f64 1 t))))
✓	0.8b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
✓	1.1b	(-.f64 x (.f64 (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t)))) (cbrt.f64 (/.f64 1 t))))
	7.7b	(-.f64 x (.f64 (cbrt.f64 (pow.f64 (log1p.f64 (.f64 y (expm1.f64 z))) 3)) (/.f64 1 t)))
	23.8b	(-.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))))
	11.2b	(-.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	16.8b	(-.f64 x (*.f64 (/.f64 y t) z))
	32.2b	(.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))))

Compiler

Compiled 12714 to 7864 computations (38.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (/.f64 1 t))
✓	0.6b	(cbrt.f64 t)
✓	0.6b	(.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 (/.f64 1 t)))
✓	3.9b	(/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t)))

series1.9s (10.2%)

Counts

3 → 84

Calls

3 calls:

1.0s	(/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
816.0ms	(.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 (/.f64 1 t)))
29.0ms	(cbrt.f64 t)

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
23×	`times-frac_binary64`
22×	`cbrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
17×	`add-exp-log_binary64`

Counts

3 → 87

Calls

3 calls:

10.0ms	(.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 (/.f64 1 t)))
5.0ms	(/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
1.0ms	(cbrt.f64 t)

simplify93.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

368×	`associate-l_binary64`
364×	`associate-r_binary64`
364×	`fma-def_binary64`
256×	`associate-/r*_binary64`
231×	`times-frac_binary64`

Counts

171 → 201

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	434	5930
1	1296	4816
2	5175	4816

prune284.0ms (1.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	246	9	255

Error

Counts

255 → 9

Alt Table

Status	Error	Program
✓	1.1b	(-.f64 x (.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 (/.f64 1 t))))
	31.6b	(-.f64 x (.f64 (.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) (sqrt.f64 (/.f64 1 t))) (sqrt.f64 (/.f64 1 t))))
✓	0.8b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
✓	1.1b	(-.f64 x (.f64 (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 (/.f64 1 t)) (cbrt.f64 (/.f64 1 t)))) (cbrt.f64 (/.f64 1 t))))
	7.7b	(-.f64 x (.f64 (cbrt.f64 (pow.f64 (log1p.f64 (.f64 y (expm1.f64 z))) 3)) (/.f64 1 t)))
	23.8b	(-.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))))
	11.2b	(-.f64 x (cbrt.f64 (.f64 (.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t) (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
	16.8b	(-.f64 x (*.f64 (/.f64 y t) z))
	32.2b	(.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))))

Compiler

Compiled 8415 to 4297 computations (48.9% saved)

regimes994.0ms (5.5%)

Accuracy

Total 0.7b remaining (79.3%)

Threshold costs 0.7b (79.3%)

Counts

128 → 1

Compiler

Compiled 22738 to 15197 computations (33.2% 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	12	14
1	17	14
2	23	14
3	27	14
4	30	14
5	31	14
6	30	14

end122.0ms (0.7%)

Compiler: Compiled 217 to 135 computations (37.8% saved)

Details

analyze1.6s (8.8%)

sample6.7s (36.6%)

simplify246.0ms (1.4%)

prune3.0ms (0%)

localize7.0ms (0%)

series1.6s (8.7%)

rewrite23.0ms (0.1%)

simplify159.0ms (0.9%)

prune247.0ms (1.4%)

localize8.0ms (0%)

series1.2s (6.7%)

rewrite11.0ms (0.1%)

simplify114.0ms (0.6%)

prune243.0ms (1.3%)

localize11.0ms (0.1%)

series2.0s (10.8%)

rewrite49.0ms (0.3%)

simplify163.0ms (0.9%)

prune485.0ms (2.7%)

localize14.0ms (0.1%)

series1.9s (10.2%)

rewrite24.0ms (0.1%)

simplify93.0ms (0.5%)

prune284.0ms (1.6%)

regimes994.0ms (5.5%)

simplify2.0ms (0%)

end122.0ms (0.7%)

Profiling