Details

analyze3.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 65 to 53 computations (18.5% saved)

sample40.0ms (0.1%)

Algorithm

1×

intervals

Results

31.0ms

256×

body

128

valid

Compiler

Compiled 129 to 106 computations (17.8% saved)

simplify55.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5105	83

prune12.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 15.6b

Counts

2 → 2

Compiler

Compiled 170 to 134 computations (21.2% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
0.1b	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
0.5b	(+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))
15.5b	(-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))

rewrite142.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
9×	`distribute-lft-out_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
6×	`associate-/r*_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 96

Calls

4 calls:

41.0ms	(-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))
38.0ms	(+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))
30.0ms	(/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
14.0ms	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))

series4.6s (11.4%)

Counts

4 → 12

Calls

4 calls:

2.3s	(-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))
995.0ms	(+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))
986.0ms	(/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
250.0ms	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))

simplify116.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4969	7396
1	4969	7396

prune496.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	103	7	110

Merged error: 15.5b

Counts

110 → 7

Compiler

Compiled 8509 to 6283 computations (26.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)
0.2b	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
0.3b	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))
15.5b	(-.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))

rewrite122.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
72×	`times-frac_binary64`
55×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
30×	`unpow-prod-down_binary64`
20×	`associate-/r*_binary64`
18×	`cube-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out_binary64`
10×	`sqr-pow_binary64`
9×	`add-cbrt-cube_binary64`
7×	`associate-/l*_binary64`
6×	`add-log-exp_binary64` `div-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
5×	`pow1_binary64`
4×	`unpow2_binary64` `cube-div_binary64`
3×	`pow-to-exp_binary64` `flip3-+_binary64` `pow-unpow_binary64` `flip-+_binary64` `pow-exp_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 170

Calls

4 calls:

61.0ms	(-.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))
16.0ms	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))
7.0ms	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
5.0ms	(pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)

series3.0s (7.4%)

Counts

4 → 12

Calls

4 calls:

2.3s	(-.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))
390.0ms	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))
173.0ms	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
89.0ms	(pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)

simplify104.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5355	7469

prune1.1s (2.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	183	6	189

Merged error: 15.5b

Counts

189 → 6

Compiler

Compiled 13282 to 9878 computations (25.6% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
0.3b	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
0.3b	(pow.f64 (cbrt.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 3)
15.5b	(-.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2)) (pow.f64 (cbrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

rewrite294.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64`
56×	`times-frac_binary64`
48×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
33×	`unpow-prod-down_binary64`
16×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
10×	`sqr-pow_binary64`
9×	`distribute-lft-out_binary64` `unpow2_binary64`
8×	`add-cbrt-cube_binary64`
7×	`associate-/l*_binary64`
6×	`add-log-exp_binary64` `cube-prod_binary64` `div-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `pow-exp_binary64`
2×	`cbrt-div_binary64` `flip3-+_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `cube-div_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow1/3_binary64` `rem-cube-cbrt_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 155

Calls

4 calls:

230.0ms	(-.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2)) (pow.f64 (cbrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))
16.0ms	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
10.0ms	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
5.0ms	(pow.f64 (cbrt.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 3)

series3.1s (7.8%)

Counts

4 → 12

Calls

4 calls:

2.3s	(-.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2)) (pow.f64 (cbrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))
314.0ms	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
313.0ms	(pow.f64 (cbrt.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) 3)
171.0ms	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))

simplify113.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5057	6663

prune1.0s (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	167	6	173

Merged error: 15.5b

Counts

173 → 6

Compiler

Compiled 13580 to 10170 computations (25.1% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))
0.5b	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2))))))
0.9b	(pow.f64 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) 3)
14.9b	(-.f64 1 (pow.f64 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) 3))

rewrite366.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
52×	`add-sqr-sqrt_binary64`
40×	`add-cube-cbrt_binary64`
32×	`distribute-lft-out_binary64`
29×	`unpow-prod-down_binary64` `cube-prod_binary64`
22×	`add-exp-log_binary64`
21×	`add-cbrt-cube_binary64`
12×	`associate-/r_binary64` `associate-l*_binary64`
8×	`sqr-pow_binary64` `associate-/r/_binary64` `difference-of-squares_binary64`
7×	`flip3-+_binary64` `pow1_binary64` `div-exp_binary64` `flip-+_binary64` `associate-*l/_binary64`
6×	`add-log-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
5×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64`
4×	`associate-r_binary64` `associate-/l*_binary64` `div-inv_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `associate-*r/_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 187

Calls

4 calls:

130.0ms	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2))))))
68.0ms	(-.f64 1 (pow.f64 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) 3))
62.0ms	(pow.f64 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) 3)
17.0ms	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))

series18.4s (46%)

Counts

4 → 12

Calls

4 calls:

10.5s	(-.f64 1 (pow.f64 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) 3))
4.9s	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) (+.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2))))))
2.6s	(pow.f64 (/.f64 (+.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))) (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) (exp.f64 (pow.f64 (fabs.f64 x) 2)))) 3)
397.0ms	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))

simplify200.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5292	20267

prune4.6s (11.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	198	7	205

Merged error: 15.5b

Counts

205 → 7

Compiler

Compiled 39534 to 31330 computations (20.8% saved)

regimes138.0ms (0.3%)

Compiler: Compiled 2204 to 1760 computations (20.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	154	105
1	154	105

end0.0ms (0%)

sample1.9s (4.8%)

Algorithm

1×

intervals

Results

987.0ms

8000×

body

128

valid

Compiler

Compiled 1231 to 984 computations (20.1% saved)

Details

analyze3.0ms (0%)

sample40.0ms (0.1%)

simplify55.0ms (0.1%)

prune12.0ms (0%)

localize21.0ms (0.1%)

rewrite142.0ms (0.4%)

series4.6s (11.4%)

simplify116.0ms (0.3%)

prune496.0ms (1.2%)

localize26.0ms (0.1%)

rewrite122.0ms (0.3%)

series3.0s (7.4%)

simplify104.0ms (0.3%)

prune1.1s (2.8%)

localize28.0ms (0.1%)

rewrite294.0ms (0.7%)

series3.1s (7.8%)

simplify113.0ms (0.3%)

prune1.0s (2.6%)

localize41.0ms (0.1%)

rewrite366.0ms (0.9%)

series18.4s (46%)

simplify200.0ms (0.5%)

prune4.6s (11.4%)

regimes138.0ms (0.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.9s (4.8%)

Profiling