Details

analyze2.4s (9.6%)

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)

sample102.0ms (0.4%)

Algorithm

1×

intervals

Results

27.0ms	57×	body	1024	valid
15.0ms	118×	body	128	valid
14.0ms	13×	body	2048	valid
13.0ms	46×	body	512	valid
4.0ms	22×	body	256	valid
3.0ms	52×	body	128	nan
3.0ms	32×	body	128	overflowed
1.0ms	5×	body	1024	nan
1.0ms	6×	body	512	nan
0.0ms	3×	body	256	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify251.0ms (1%)

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

prune4.0ms (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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 52 to 35 computations (32.7% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 z)
✓	0.0b	(*.f64 y (expm1.f64 z))
✓	0.3b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.1b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series1.3s (5.1%)

Counts

4 → 96

Calls

4 calls:

855.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
416.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
7.0ms	(*.f64 y (expm1.f64 z))
2.0ms	(expm1.f64 z)

rewrite8.0ms (0%)

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:

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

simplify147.0ms (0.6%)

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

prune206.0ms (0.8%)

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

0.2b

Counts

160 → 7

Alt Table

Status	Error	Program
	18.7b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	20.0b	(-.f64 x (*.f64 (/.f64 y t) z))
	0.7b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))
▶	0.4b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	17.4b	(-.f64 x (/.f64 (*.f64 y (-.f64 (exp.f64 z) 1)) t))
	0.7b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
✓	0.3b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 4356 to 2205 computations (49.4% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(expm1.f64 z)
	0.0b	(*.f64 y (expm1.f64 z))
	0.3b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.2b	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))

series842.0ms (3.3%)

Counts

1 → 36

Calls

1 calls:

842.0ms

(*.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))

simplify92.0ms (0.4%)

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

prune214.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

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

Error

0.2b

Counts

189 → 7

Alt Table

Status	Error	Program
	18.7b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	20.0b	(-.f64 x (*.f64 (/.f64 y t) z))
	0.7b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))
✓	0.4b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	17.4b	(-.f64 x (/.f64 (*.f64 y (-.f64 (exp.f64 z) 1)) t))
▶	0.7b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
✓	0.3b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 4910 to 2612 computations (46.8% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))
✓	0.5b	(.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)))
	4.1b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
✓	15.0b	(cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

series6.4s (25.5%)

Counts

3 → 108

Calls

3 calls:

3.2s

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

1.9s

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

1.4s

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

rewrite91.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`cbrt-prod_binary64`
78×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-cube-cbrt_binary64`

Counts

3 → 160

Calls

3 calls:

24.0ms

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

20.0ms

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

4.0ms

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

simplify497.0ms (2%)

Algorithm

1×	egg-herbie

Rules

756×	`associate-/l*_binary64`
419×	`*-commutative_binary64`
242×	`+-commutative_binary64`
192×	`fma-def_binary64`
182×	`associate-+r+_binary64`

Counts

268 → 363

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1164	18311
1	3562	16895
2	5831	16895

prune2.0s (7.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	723	0	723
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	723	7	730

Error

0.2b

Counts

730 → 7

Alt Table

Status	Error	Program
	18.7b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	20.0b	(-.f64 x (*.f64 (/.f64 y t) z))
▶	0.7b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))
✓	0.4b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	17.4b	(-.f64 x (/.f64 (*.f64 y (-.f64 (exp.f64 z) 1)) t))
✓	0.7b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
✓	0.3b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 50387 to 20389 computations (59.5% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
✓	0.6b	(cbrt.f64 t)
✓	0.9b	(/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	3.4b	(/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t)))

series3.5s (13.8%)

Counts

4 → 96

Calls

4 calls:

1.9s	(/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
1.4s	(/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
67.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
61.0ms	(cbrt.f64 t)

rewrite53.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
43×	`cbrt-prod_binary64`

Counts

4 → 152

Calls

4 calls:

13.0ms	(/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
10.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
8.0ms	(/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
1.0ms	(cbrt.f64 t)

simplify315.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

385×	`associate-r_binary64`
365×	`fma-def_binary64`
363×	`fma-neg_binary64`
344×	`associate-l_binary64`
304×	`associate-/r*_binary64`

Counts

248 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	491	7358
1	1373	6060
2	4891	6056
3	5185	6056

prune584.0ms (2.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	334	0	334
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	334	7	341

Error

0.2b

Counts

341 → 7

Alt Table

Status	Error	Program
	18.7b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	20.0b	(-.f64 x (*.f64 (/.f64 y t) z))
✓	0.7b	(-.f64 x (/.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)))
✓	0.4b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	17.4b	(-.f64 x (/.f64 (*.f64 y (-.f64 (exp.f64 z) 1)) t))
✓	0.7b	(-.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t)) (cbrt.f64 (/.f64 (log1p.f64 (.f64 y (expm1.f64 z))) t))) (cbrt.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))))
✓	0.3b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))

Compiler

Compiled 10111 to 3899 computations (61.4% saved)

regimes1.1s (4.3%)

Accuracy

Total 0.9b remaining (88.9%)

Threshold costs 0.9b (88.9%)

Counts

77 → 1

Compiler

Compiled 15572 to 9275 computations (40.4% saved)

simplify5.0ms (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

end1.0ms (0%)

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

sample5.1s (20.2%)

Algorithm

1×

intervals

Results

1.6s	1787×	body	1024	valid
703.0ms	1344×	body	512	valid
597.0ms	3813×	body	128	valid
573.0ms	324×	body	2048	valid
228.0ms	732×	body	256	valid
181.0ms	1535×	body	128	nan
118.0ms	196×	body	1024	nan
105.0ms	852×	body	128	overflowed
91.0ms	234×	body	512	nan
44.0ms	186×	body	256	nan
2.0ms	17×	body	128	invalid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 161 to 98 computations (39.1% saved)

Details

analyze2.4s (9.6%)

sample102.0ms (0.4%)

simplify251.0ms (1%)

prune4.0ms (0%)

localize8.0ms (0%)

series1.3s (5.1%)

rewrite8.0ms (0%)

simplify147.0ms (0.6%)

prune206.0ms (0.8%)

localize11.0ms (0%)

series842.0ms (3.3%)

rewrite8.0ms (0%)

simplify92.0ms (0.4%)

prune214.0ms (0.8%)

localize12.0ms (0%)

series6.4s (25.5%)

rewrite91.0ms (0.4%)

simplify497.0ms (2%)

prune2.0s (7.8%)

localize29.0ms (0.1%)

series3.5s (13.8%)

rewrite53.0ms (0.2%)

simplify315.0ms (1.2%)

prune584.0ms (2.3%)

regimes1.1s (4.3%)

simplify5.0ms (0%)

end1.0ms (0%)

sample5.1s (20.2%)

Profiling