Details

analyze1.8s (7.3%)

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
3.1%	96.7%	0.2%	8
4.7%	95.1%	0.2%	9
4.7%	95.1%	0.2%	10
18.7%	81.1%	0.2%	11
24.6%	67.4%	8%	12
28.7%	63.4%	8%	13
28.7%	63.4%	8%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample9.1s (36.5%)

Results

3.0s	1559×	body	8192	exit
2.2s	1845×	body	1024	valid
994.0ms	3930×	body	128	valid
950.0ms	1392×	body	512	valid
669.0ms	317×	body	2048	valid
470.0ms	1539×	body	128	invalid
325.0ms	772×	body	256	valid
144.0ms	195×	body	1024	invalid
126.0ms	260×	body	512	invalid
57.0ms	169×	body	256	invalid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify357.0ms (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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

1.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.3b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	21.9b	(-.f64 x (/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t))

Compiler

Compiled 86 to 59 computations (31.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	0.0b	(*.f64 y (expm1.f64 z))
✓	0.5b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.0b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)

series2.7s (11%)

Counts

4 → 132

Calls

4 calls:

1.4s	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
868.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
472.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))
7.0ms	(*.f64 y (expm1.f64 z))

rewrite43.0ms (0.2%)

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:

11.0ms	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
6.0ms	(*.f64 y (expm1.f64 z))
4.0ms	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
1.0ms	(log1p.f64 (*.f64 y (expm1.f64 z)))

simplify322.0ms (1.3%)

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

prune427.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	251	6	257
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	252	7	259

Error

0.2b

Counts

259 → 7

Alt Table

Status	Error	Program
	1.4b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
	31.8b	(-.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)))))))
	18.6b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	16.3b	(-.f64 x (*.f64 (/.f64 y t) z))
▶	1.3b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
✓	1.3b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	12.4b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t) 3)))

Compiler

Compiled 8663 to 3239 computations (62.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
	0.0b	(*.f64 y (expm1.f64 z))
	0.5b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.1b	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))

series2.1s (8.6%)

Counts

2 → 84

Calls

2 calls:

1.2s	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))
958.0ms	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

rewrite23.0ms (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:

11.0ms	(.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t))
5.0ms	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))

simplify155.0ms (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

prune363.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	229	7	236

Error

0.2b

Counts

236 → 7

Alt Table

Status	Error	Program
	18.6b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	16.3b	(-.f64 x (*.f64 (/.f64 y t) z))
	20.5b	(-.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)))
▶	1.4b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
✓	1.3b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
✓	1.3b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
	12.4b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t) 3)))

Compiler

Compiled 6357 to 3228 computations (49.2% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
✓	0.2b	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))
	0.5b	(log1p.f64 (*.f64 y (expm1.f64 z)))
✓	4.0b	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)

series2.7s (10.8%)

Counts

3 → 84

Calls

3 calls:

1.2s	(/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t)
1.1s	(log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))
330.0ms	(expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 52

Calls

3 calls:

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

simplify106.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-def_binary64`
313×	`associate-r_binary64`
272×	`associate-+l+_binary64`
271×	`associate-l_binary64`
177×	`associate-/r*_binary64`

Counts

136 → 175

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	464	4678
1	1404	4129
2	5039	4129

prune393.0ms (1.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	220	7	227

Error

0.2b

Counts

227 → 7

Alt Table

Status	Error	Program
	18.6b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	16.3b	(-.f64 x (*.f64 (/.f64 y t) z))
	20.5b	(-.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)))
✓	1.4b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
✓	1.3b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
✓	1.3b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
▶	12.4b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t) 3)))

Compiler

Compiled 7730 to 4156 computations (46.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t) 3)
	0.5b	(log1p.f64 (*.f64 y (expm1.f64 z)))
	4.0b	(/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t)
✓	25.8b	(cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t) 3))

series2.3s (9.2%)

Counts

2 → 72

Calls

2 calls:

1.2s	(pow.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t) 3)
1.1s	(cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t) 3))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
32×	`cbrt-prod_binary64`
32×	`add-cube-cbrt_binary64`

Counts

2 → 92

Calls

2 calls:

3.0ms	(cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t) 3))
3.0ms	(pow.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t) 3)

simplify185.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

621×	`times-frac_binary64`
582×	`associate-/r*_binary64`
438×	`associate-/l*_binary64`
430×	`fma-def_binary64`
152×	`*-commutative_binary64`

Counts

164 → 163

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	619	7554
1	1973	6844
2	5577	6844

prune663.0ms (2.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	274	7	281

Error

0.2b

Counts

281 → 7

Alt Table

Status	Error	Program
	18.6b	(-.f64 x (.f64 (sqrt.f64 (log1p.f64 (.f64 y (expm1.f64 z)))) (/.f64 (sqrt.f64 (log1p.f64 (*.f64 y (expm1.f64 z)))) t)))
	16.3b	(-.f64 x (*.f64 (/.f64 y t) z))
	20.5b	(-.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)))
✓	1.4b	(-.f64 x (/.f64 (expm1.f64 (log1p.f64 (log1p.f64 (*.f64 y (expm1.f64 z))))) t))
✓	1.3b	(-.f64 x (.f64 (log1p.f64 (.f64 y (expm1.f64 z))) (/.f64 1 t)))
✓	1.3b	(-.f64 x (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t))
✓	12.4b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 (log1p.f64 (*.f64 y (expm1.f64 z))) t) 3)))

Compiler

Compiled 12089 to 6905 computations (42.9% saved)

regimes861.0ms (3.4%)

Accuracy

Total 1.0b remaining (85.5%)

Threshold costs 1.0b (85.5%)

Counts

54 → 1

Compiler

Compiled 13642 to 9053 computations (33.6% saved)

simplify3.0ms (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

end141.0ms (0.6%)

Compiler: Compiled 152 to 103 computations (32.2% saved)

Details

analyze1.8s (7.3%)

sample9.1s (36.5%)

simplify357.0ms (1.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series2.7s (11%)

rewrite43.0ms (0.2%)

simplify322.0ms (1.3%)

prune427.0ms (1.7%)

localize15.0ms (0.1%)

series2.1s (8.6%)

rewrite23.0ms (0.1%)

simplify155.0ms (0.6%)

prune363.0ms (1.5%)

localize21.0ms (0.1%)

series2.7s (10.8%)

rewrite5.0ms (0%)

simplify106.0ms (0.4%)

prune393.0ms (1.6%)

localize14.0ms (0.1%)

series2.3s (9.2%)

rewrite15.0ms (0.1%)

simplify185.0ms (0.7%)

prune663.0ms (2.7%)

regimes861.0ms (3.4%)

simplify3.0ms (0%)

end141.0ms (0.6%)

Profiling