Details

analyze126.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 66 to 53 computations (19.7% saved)

sample145.0ms (0.1%)

Algorithm

1×

intervals

Results

121.0ms

256×

body

128

valid

Compiler

Compiled 132 to 106 computations (19.7% saved)

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-neg_binary64`
578×	`times-frac_binary64`
564×	`cancel-sign-sub-inv_binary64`
389×	`fma-def_binary64`
380×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	93
1	91	69
2	270	69
3	825	69
4	2840	69
5	4839	69
6	5074	69

prune23.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

12.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.8b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

Status

Error

Program

▶

12.8b

(-.f64 1 (*.f64 (*.f64 (/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (*.f64 (/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (*.f64 (/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (*.f64 (/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (*.f64 (/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))) (exp.f64 (neg.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))

Compiler

Compiled 241 to 190 computations (21.2% saved)

localize60.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
✓	0.2b	(.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496)))))))
✓	0.4b	(+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))
✓	12.8b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

rewrite126.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
17×	`add-exp-log_binary64`

Counts

4 → 118

Calls

4 calls:

44.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))
23.0ms	(.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496)))))))
12.0ms	(/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
6.0ms	(+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))

series2.4s (1.6%)

Counts

4 → 36

Calls

4 calls:

1.3s	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))
739.0ms	(+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496))))))))
321.0ms	(.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -5125037576950889/18014398509481984 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 -6544414927309881/4503599627370496 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 4780145094533421/4503599627370496)))))))
42.0ms	(/.f64 1 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))

simplify389.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

644×	`times-frac_binary64`
477×	`fma-neg_binary64`
310×	`cancel-sign-sub-inv_binary64`
261×	`exp-prod_binary64`
219×	`distribute-rgt-neg-in_binary64`

Counts

154 → 294

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	11138
1	671	8493
2	2462	8125
3	4608	8125
4	5025	8125

prune776.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	291	3	294
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	292	3	295

Error

12.8b

Counts

295 → 3

Alt Table

Status	Error	Program
	12.8b	(log.f64 (exp.f64 (+.f64 1 (/.f64 (/.f64 (-.f64 -2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (exp.f64 (*.f64 x x))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)))))
	12.8b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 2295300911148351/9007199254740992 (expm1.f64 (log1p.f64 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))
▶	12.8b	(/.f64 (-.f64 1 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3)) (fma.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) (fma.f64 (exp.f64 (neg.f64 (*.f64 x x))) (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) 1) 1))

Compiler

Compiled 17020 to 12647 computations (25.7% saved)

localize40.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)))
✓	0.4b	(+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)))
✓	0.7b	(pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3)
✓	12.3b	(-.f64 1 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3))

rewrite444.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

852×	`times-frac_binary64`
722×	`*-un-lft-identity_binary64`
564×	`add-sqr-sqrt_binary64`
530×	`add-cube-cbrt_binary64`
330×	`prod-diff_binary64`

Counts

3 → 618

Calls

3 calls:

91.0ms

(-.f64 1 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3))

35.0ms

(pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3)

32.0ms

(+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)))

series1.5min (59.6%)

Counts

3 → 36

Calls

3 calls:

1.5min

(-.f64 1 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3))

621.0ms

(pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3)

245.0ms

(+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)))

simplify2.9s (2%)

Algorithm

1×	egg-herbie

Counts

654 → 940

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6076	236001

prune3.2s (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	968	3	971
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	971	3	974

Error

12.0b

Counts

974 → 3

Alt Table

Status	Error	Program
	12.1b	(/.f64 (.f64 (+.f64 1 (sqrt.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3))) (-.f64 1 (sqrt.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3)))) (fma.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) (fma.f64 (exp.f64 (neg.f64 (*.f64 x x))) (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) 1) 1))
	12.8b	(/.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) 1) 3) (pow.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (exp.f64 (.f64 x x))) 3))) (fma.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) (fma.f64 (exp.f64 (neg.f64 (.f64 x x))) (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) 1) 1))
▶	12.1b	(/.f64 (-.f64 1 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3)))) (fma.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) (fma.f64 (exp.f64 (neg.f64 (*.f64 x x))) (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) 1) 1))

Compiler

Compiled 130135 to 93273 computations (28.3% saved)

localize31.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)))
	0.4b	(+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)))
	0.7b	(pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3)
✓	12.3b	(-.f64 1 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3))))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`

Counts

1 → 32

Calls

1 calls:

3.0ms

(-.f64 1 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3))))

series5.0s (3.3%)

Counts

1 → 12

Calls

1 calls:

5.0s

(-.f64 1 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3))))

simplify177.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

619×	`associate-+r+_binary64`
426×	`fma-def_binary64`
330×	`associate-+l+_binary64`
222×	`times-frac_binary64`
197×	`associate-/r*_binary64`

Counts

44 → 86

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	459	7754
1	1305	6904
2	5197	6904

prune908.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	428	2	430
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	430	3	433

Error

11.9b

Counts

433 → 3

Alt Table

Status	Error	Program
	12.8b	(/.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) 1) 3) (pow.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (exp.f64 (.f64 x x))) 3))) (fma.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) (fma.f64 (exp.f64 (neg.f64 (.f64 x x))) (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) 1) 1))
	12.1b	(/.f64 (.f64 (+.f64 1 (sqrt.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 1475339155889891/4503599627370496 (fabs.f64 x) 1))) (fma.f64 1475339155889891/4503599627370496 (fabs.f64 x) 1))) (fma.f64 1475339155889891/4503599627370496 (fabs.f64 x) 1))) (fma.f64 1475339155889891/4503599627370496 (fabs.f64 x) 1))) (fma.f64 1475339155889891/4503599627370496 (fabs.f64 x) 1)) (exp.f64 (.f64 x x))) 3))) (-.f64 1 (sqrt.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 1475339155889891/4503599627370496 (fabs.f64 x) 1))) (fma.f64 1475339155889891/4503599627370496 (fabs.f64 x) 1))) (fma.f64 1475339155889891/4503599627370496 (fabs.f64 x) 1))) (fma.f64 1475339155889891/4503599627370496 (fabs.f64 x) 1))) (fma.f64 1475339155889891/4503599627370496 (fabs.f64 x) 1)) (exp.f64 (.f64 x x))) 3)))) (fma.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) (fma.f64 (exp.f64 (neg.f64 (*.f64 x x))) (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) 1) 1))
▶	11.9b	(/.f64 (/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3))) 3)) (+.f64 (.f64 1 1) (+.f64 (.f64 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3))) (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3)))) (.f64 1 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3))))))) (fma.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) (fma.f64 (exp.f64 (neg.f64 (*.f64 x x))) (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) 1) 1))

Compiler

Compiled 39207 to 28121 computations (28.3% saved)

localize48.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.7b	(pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3)
	0.7b	(pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3)
	0.7b	(pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3)
✓	10.7b	(-.f64 (pow.f64 1 3) (pow.f64 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3))) 3))

rewrite92.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`prod-diff_binary64`
109×	`add-sqr-sqrt_binary64`
98×	`*-un-lft-identity_binary64`
96×	`cube-prod_binary64`
96×	`unpow-prod-down_binary64`

Counts

1 → 212

Calls

1 calls:

13.0ms

(-.f64 (pow.f64 1 3) (pow.f64 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3))) 3))

series17.2s (11.5%)

Counts

1 → 12

Calls

1 calls:

17.2s

(-.f64 (pow.f64 1 3) (pow.f64 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (*.f64 x x))) 3))) 3))

simplify2.6s (1.7%)

Algorithm

1×	egg-herbie

Rules

983×	`fma-def_binary64`
774×	`times-frac_binary64`
273×	`+-commutative_binary64`
251×	`associate-+r+_binary64`
205×	`*-commutative_binary64`

Counts

224 → 446

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1070	63081
1	3128	62781
2	5246	62781

prune7.1s (4.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	2656	2	2658
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	2658	3	2661

Error

11.9b

Counts

2661 → 3

Alt Table

Status	Error	Program
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	11.9b	(/.f64 (/.f64 (/.f64 (-.f64 (pow.f64 (pow.f64 1 3) 3) (pow.f64 (pow.f64 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3))) 3) 3)) (+.f64 (.f64 (pow.f64 1 3) (pow.f64 1 3)) (+.f64 (.f64 (pow.f64 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3))) 3) (pow.f64 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3))) 3)) (.f64 (pow.f64 1 3) (pow.f64 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3))) 3))))) (+.f64 (.f64 1 1) (+.f64 (.f64 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3))) (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3)))) (.f64 1 (log1p.f64 (expm1.f64 (pow.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) 3))))))) (fma.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) (fma.f64 (exp.f64 (neg.f64 (*.f64 x x))) (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) 1) 1))
	12.8b	(/.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) 1) 3) (pow.f64 (/.f64 (sqrt.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (exp.f64 (.f64 x x))) 3))) (fma.f64 (/.f64 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) (exp.f64 (.f64 x x))) (fma.f64 (exp.f64 (neg.f64 (.f64 x x))) (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1))) (fma.f64 (fabs.f64 x) 1475339155889891/4503599627370496 1)) 1) 1))

Compiler

Compiled 190553 to 140746 computations (26.1% saved)

regimes3.0s (2%)

Accuracy

Total 0.0b remaining (0.1%)

Threshold costs 0.0b (0.1%)

Compiler

Compiled 149502 to 109589 computations (26.7% saved)

simplify19.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	687
1	67	687
2	74	687
3	79	687
4	81	687
5	78	687

end7.0ms (0%)

Compiler: Compiled 452 to 330 computations (27% saved)

sample13.6s (9.1%)

Algorithm

1×

intervals

Results

1.2s

8000×

body

128

valid

Compiler

Compiled 2060 to 1527 computations (25.9% saved)

Details

analyze126.0ms (0.1%)

sample145.0ms (0.1%)

simplify85.0ms (0.1%)

prune23.0ms (0%)

localize60.0ms (0%)

rewrite126.0ms (0.1%)

series2.4s (1.6%)

simplify389.0ms (0.3%)

prune776.0ms (0.5%)

localize40.0ms (0%)

rewrite444.0ms (0.3%)

series1.5min (59.6%)

simplify2.9s (2%)

prune3.2s (2.1%)

localize31.0ms (0%)

rewrite11.0ms (0%)

series5.0s (3.3%)

simplify177.0ms (0.1%)

prune908.0ms (0.6%)

localize48.0ms (0%)

rewrite92.0ms (0.1%)

series17.2s (11.5%)

simplify2.6s (1.7%)

prune7.1s (4.8%)

regimes3.0s (2%)

simplify19.0ms (0%)

end7.0ms (0%)

sample13.6s (9.1%)

Profiling