Details

analyze25.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	59×	body	1024	valid
5.0ms	134×	body	128	valid
3.0ms	37×	body	512	valid
2.0ms	10×	body	2048	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	30.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
1.7b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite125.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

29.5b

Rules

64×	`sqrt-prod_binary64`
57×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
42×	`prod-diff_binary64`
33×	`add-cube-cbrt_binary64`

Counts

2 → 95

Calls

2 calls:

8.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 1497 to 737 computations (50.8% saved)

series20.0ms (0.4%)

Error

29.3b

Counts

2 → 9

Calls

2 calls:

10.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 232 to 177 computations (23.7% saved)

simplify152.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1015×	`fma-neg_binary64`
568×	`unswap-sqr_binary64`
488×	`div-sub_binary64`
454×	`fma-def_binary64`
448×	`associate-l_binary64`

Counts

104 → 84

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2569
1	249	1380
2	697	1160
3	3333	1157
4	4449	1125
5	4670	1125
6	5140	1125

prune24.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	2	85

Error

0.1b

Counts

85 → 2

Alt Table

Status	Error	Program
✓	30.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
▶	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 359 to 243 computations (32.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite177.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

57×	`*-un-lft-identity_binary64`
28×	`sqrt-prod_binary64`
22×	`distribute-lft-out_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`

Counts

3 → 91

Calls

3 calls:

8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 1240 to 894 computations (27.9% saved)

series38.0ms (0.8%)

Error

0.1b

Counts

3 → 12

Calls

3 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(sqrt.f64 (+.f64 1 x))
10.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 261 to 214 computations (18% saved)

simplify191.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-neg_binary64`
558×	`cancel-sign-sub-inv_binary64`
538×	`times-frac_binary64`
389×	`associate-l_binary64`
311×	`associate-r_binary64`

Counts

103 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1334
1	207	1241
2	448	1235
3	1137	1231
4	2560	1231
5	4233	1231
6	4960	1231
7	4997	1231
8	4836	1231

prune28.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	45	6	51

Error

0.1b

Counts

51 → 6

Alt Table

Status	Error	Program
✓	30.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	14.9b	(/.f64 1 (+.f64 (/.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (-.f64 (fma.f64 x x 1) x))) (sqrt.f64 x)))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	10.5b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	9.5b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
▶	0.3b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))

Compiler

Compiled 553 to 395 computations (28.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))

rewrite266.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

55×	`add-sqr-sqrt_binary64`
29×	`cbrt-prod_binary64`
28×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 128

Calls

4 calls:

18.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
14.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
2.0ms	(cbrt.f64 (+.f64 1 x))
2.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 3069 to 2394 computations (22% saved)

series175.0ms (3.5%)

Error

0.1b

Counts

4 → 30

Calls

4 calls:

32.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
29.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
23.0ms	(cbrt.f64 (+.f64 1 x))
22.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1894 to 1582 computations (16.5% saved)

simplify189.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-def_binary64`
467×	`fma-neg_binary64`
325×	`unswap-sqr_binary64`
296×	`*-commutative_binary64`
262×	`cancel-sign-sub-inv_binary64`

Counts

158 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	3718
1	511	3089
2	1231	2654
3	2614	2367
4	4605	2367
5	4827	2367

prune142.0ms (2.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	134	7	141

Error

0.0b

Counts

141 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
▶	0.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
✓	30.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	0.7b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
	10.5b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.4b	(/.f64 1 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (fabs.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
✓	0.3b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))

Compiler

Compiled 2160 to 1596 computations (26.1% saved)

localize37.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))

rewrite705.0ms (14.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

387×	`times-frac_binary64`
347×	`*-un-lft-identity_binary64`
329×	`sqrt-prod_binary64`
227×	`add-sqr-sqrt_binary64`
192×	`add-cube-cbrt_binary64`

Counts

4 → 351

Calls

4 calls:

56.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
20.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
5.0ms	(cbrt.f64 (+.f64 1 x))
5.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 11753 to 8933 computations (24% saved)

series150.0ms (3%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

53.0ms	(cbrt.f64 (+.f64 1 x))
35.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
18.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
12.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 2650 to 2141 computations (19.2% saved)

simplify572.0ms (11.5%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
494×	`fma-neg_binary64`
434×	`*-commutative_binary64`
377×	`unswap-sqr_binary64`
265×	`cancel-sign-sub-inv_binary64`

Counts

381 → 359

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	360	20962
1	803	18409
2	1880	15146
3	3226	13339
4	4475	12965
5	4927	12965
6	4829	12965

prune249.0ms (5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	355	4	359
Fresh	3	0	3
Picked	0	1	1
Done	1	2	3
Total	359	7	366

Error

Counts

366 → 7

Alt Table

Status	Error	Program
	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	0.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
	30.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	0.4b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (hypot.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3/2) (pow.f64 x 3/4))) (sqrt.f64 (+.f64 (.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))))
	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (/.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
	0.4b	(/.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))))
	0.4b	(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))

Compiler

Compiled 4458 to 3244 computations (27.2% saved)

regimes700.0ms (14.1%)

Accuracy

Total 0.1b remaining (80.6%)

Threshold costs 0.1b (80.6%)

Compiler

Compiled 18670 to 14268 computations (23.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	12	14
2	11	14

end2.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample947.0ms (19%)

Algorithm

1×

intervals

Results

274.0ms	1991×	body	1024	valid
154.0ms	4293×	body	128	valid
101.0ms	992×	body	512	valid
39.0ms	222×	body	2048	valid
34.0ms	502×	body	256	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 270 to 206 computations (23.7% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze25.0ms (0.5%)

sample26.0ms (0.5%)

simplify14.0ms (0.3%)

prune1.0ms (0%)

localize6.0ms (0.1%)

rewrite125.0ms (2.5%)

series20.0ms (0.4%)

simplify152.0ms (3.1%)

prune24.0ms (0.5%)

localize6.0ms (0.1%)

rewrite177.0ms (3.6%)

series38.0ms (0.8%)

simplify191.0ms (3.8%)

prune28.0ms (0.6%)

localize9.0ms (0.2%)

rewrite266.0ms (5.3%)

series175.0ms (3.5%)

simplify189.0ms (3.8%)

prune142.0ms (2.9%)

localize37.0ms (0.7%)

rewrite705.0ms (14.2%)

series150.0ms (3%)

simplify572.0ms (11.5%)

prune249.0ms (5%)

regimes700.0ms (14.1%)

simplify3.0ms (0.1%)

end2.0ms (0%)

sample947.0ms (19%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11