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)

sample46.0ms (0.1%)

Algorithm

1×

intervals

Results

37.0ms

256×

body

128

valid

Compiler

Compiled 129 to 106 computations (17.8% saved)

simplify218.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5105	83

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 13.8b

Counts

2 → 1

Compiler

Compiled 117 to 93 computations (20.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.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)))))))
0.1b	(.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))))))))
13.7b	(-.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))))))

rewrite61.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_2794`
30×	`associate-l_binary64_2716`
22×	`times-frac_binary64_2779` `add-exp-log_binary64_2808` `*-un-lft-identity_binary64_2773`
20×	`add-cube-cbrt_binary64_2805`
14×	`add-cbrt-cube_binary64_2806`
8×	`pow1_binary64_2831` `add-log-exp_binary64_2809` `prod-exp_binary64_2819`
7×	`flip3-+_binary64_2776` `flip-+_binary64_2747`
6×	`unswap-sqr_binary64_2741` `associate-r_binary64_2715`
4×	`cbrt-unprod_binary64_2803` `associate-/r/_binary64_2721` `div-exp_binary64_2821` `associate-*r/_binary64_2717` `frac-times_binary64_2783`
3×	`distribute-rgt-in_binary64_2725` `distribute-lft-in_binary64_2724`
2×	`cbrt-undiv_binary64_2804` `pow-prod-down_binary64_2841` `div-inv_binary64_2770` `1-exp_binary64_2814` `-commutative_binary64_2706` `associate-+r+_binary64_2707` `rec-exp_binary64_2820` `associate-l/_binary64_2718`
1×	`diff-log_binary64_2862` `sub-neg_binary64_2766` `flip3--_binary64_2777` `flip--_binary64_2748` `sum-log_binary64_2861` `+-commutative_binary64_2705`

Counts

4 → 110

Calls

4 calls:

13.0ms	(.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)))))))
13.0ms	(.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)))))
4.0ms	(+.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))))))))
4.0ms	(-.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))))))

series4.8s (11.3%)

Counts

4 → 12

Calls

4 calls:

2.3s	(-.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))))))
1.0s	(+.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))))))))
975.0ms	(.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)))))))
555.0ms	(.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)))))

simplify119.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5085	7939

prune686.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	5	123

Merged error: 13.7b

Counts

123 → 5

Compiler

Compiled 9779 to 7258 computations (25.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.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))))
0.4b	(+.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)))))
13.7b	(log.f64 (exp.f64 (-.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 (pow.f64 (fabs.f64 x) 2)))))))
13.7b	(-.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 (pow.f64 (fabs.f64 x) 2)))))

rewrite178.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_2773`
21×	`add-sqr-sqrt_binary64_2794`
15×	`add-cube-cbrt_binary64_2805`
12×	`times-frac_binary64_2779`
8×	`add-log-exp_binary64_2809`
7×	`log-pow_binary64_2859`
6×	`exp-prod_binary64_2822` `add-exp-log_binary64_2808` `add-cbrt-cube_binary64_2806`
5×	`pow1_binary64_2831` `distribute-lft-out_binary64_2726`
4×	`difference-of-squares_binary64_2742` `log-prod_binary64_2856` `associate-/l*_binary64_2720`
3×	`flip3-+_binary64_2776` `associate-/r*_binary64_2719` `flip-+_binary64_2747`
2×	`associate-/r/_binary64_2721` `associate-/l/_binary64_2722` `sub-neg_binary64_2766` `distribute-lft-out--_binary64_2727`
1×	`rem-log-exp_binary64_2811` `cbrt-undiv_binary64_2804` `exp-sum_binary64_2816` `frac-2neg_binary64_2784` `log-div_binary64_2857` `exp-diff_binary64_2818` `diff-log_binary64_2862` `div-inv_binary64_2770` `flip3--_binary64_2777` `div-exp_binary64_2821` `flip--_binary64_2748` `sum-log_binary64_2861` `clear-num_binary64_2772` `+-commutative_binary64_2705`

Counts

4 → 81

Calls

4 calls:

47.0ms	(log.f64 (exp.f64 (-.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 (pow.f64 (fabs.f64 x) 2)))))))
43.0ms	(-.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 (pow.f64 (fabs.f64 x) 2)))))
36.0ms	(+.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)))))
36.0ms	(/.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))))

series8.8s (20.4%)

Counts

4 → 12

Calls

4 calls:

4.5s	(log.f64 (exp.f64 (-.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 (pow.f64 (fabs.f64 x) 2)))))))
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 (pow.f64 (fabs.f64 x) 2)))))
1.0s	(+.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)))))
988.0ms	(/.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))))

simplify140.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4982	8172
1	4982	8172

prune524.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	92	6	98

Merged error: 13.7b

Counts

98 → 6

Compiler

Compiled 7924 to 6210 computations (21.6% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016)))
13.7b	(log.f64 (exp.f64 (-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016))) (-.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)))))))
13.7b	(-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016))) (-.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)))))
15.2b	(.f64 (/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016))) (-.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))

rewrite124.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64_2773`
35×	`add-sqr-sqrt_binary64_2794`
25×	`times-frac_binary64_2779`
24×	`add-cube-cbrt_binary64_2805`
18×	`associate-l_binary64_2716`
11×	`add-exp-log_binary64_2808` `add-cbrt-cube_binary64_2806`
7×	`pow1_binary64_2831` `distribute-lft-out_binary64_2726` `log-pow_binary64_2859`
6×	`exp-prod_binary64_2822` `add-log-exp_binary64_2809`
5×	`flip3--_binary64_2777` `flip--_binary64_2748`
4×	`associate-/r/_binary64_2721` `difference-of-squares_binary64_2742` `sub-neg_binary64_2766` `log-prod_binary64_2856` `associate-/l*_binary64_2720`
3×	`associate-/r_binary64_2719` `associate-r*_binary64_2715`
2×	`cbrt-unprod_binary64_2803` `cbrt-undiv_binary64_2804` `associate-/l/_binary64_2722` `unswap-sqr_binary64_2741` `div-inv_binary64_2770` `div-exp_binary64_2821` `distribute-lft-out--_binary64_2727` `associate-*r/_binary64_2717` `prod-exp_binary64_2819` `frac-times_binary64_2783`
1×	`rem-log-exp_binary64_2811` `exp-sum_binary64_2816` `frac-2neg_binary64_2784` `distribute-rgt-in_binary64_2725` `log-div_binary64_2857` `pow-prod-down_binary64_2841` `exp-diff_binary64_2818` `diff-log_binary64_2862` `flip3-+_binary64_2776` `-commutative_binary64_2706` `distribute-lft-in_binary64_2724` `clear-num_binary64_2772` `flip-+_binary64_2747` `associate-l/_binary64_2718`

Counts

4 → 112

Calls

4 calls:

39.0ms	(/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016)))
38.0ms	(.f64 (/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016))) (-.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
12.0ms	(log.f64 (exp.f64 (-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016))) (-.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)))))))
10.0ms	(-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016))) (-.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)))))

series20.3s (47.1%)

Counts

4 → 12

Calls

4 calls:

11.7s	(log.f64 (exp.f64 (-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016))) (-.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)))))))
6.2s	(-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016))) (-.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)))))
1.3s	(.f64 (/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016))) (-.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
1.0s	(/.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 (pow.f64 (fabs.f64 x) 2) 2176625624901896097756115991881/20282409603651670423947251286016)))

simplify169.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4935	12541
1	4935	12541

prune990.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	124	6	130

Merged error: 13.7b

Counts

130 → 6

Compiler

Compiled 12395 to 9669 computations (22% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4))
0.3b	(/.f64 6544414927309881/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))
0.5b	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
13.7b	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (+.f64 (/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4)) (-.f64 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 6544414927309881/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

rewrite59.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`times-frac_binary64_2779`
62×	`add-cube-cbrt_binary64_2805` `add-sqr-sqrt_binary64_2794` `*-un-lft-identity_binary64_2773`
36×	`unpow-prod-down_binary64_2849`
27×	`associate-/r*_binary64_2719`
19×	`add-exp-log_binary64_2808`
12×	`sqr-pow_binary64_2745` `cube-prod_binary64_2798`
10×	`add-cbrt-cube_binary64_2806`
9×	`div-exp_binary64_2821` `associate-/l*_binary64_2720`
6×	`add-log-exp_binary64_2809`
4×	`unpow2_binary64_2835` `unpow3_binary64_2836` `pow1_binary64_2831` `cube-mult_binary64_2800`
3×	`pow-exp_binary64_2838` `cbrt-undiv_binary64_2804` `frac-2neg_binary64_2784` `pow-to-exp_binary64_2839` `div-inv_binary64_2770` `clear-num_binary64_2772`
2×	`cube-div_binary64_2799` `associate-/r/_binary64_2721`
1×	`diff-log_binary64_2862` `sub-neg_binary64_2766` `flip3-+_binary64_2776` `flip3--_binary64_2777` `flip--_binary64_2748` `flip-+_binary64_2747`

Counts

4 → 172

Calls

4 calls:

8.0ms	(/.f64 6544414927309881/4503599627370496 (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))
7.0ms	(/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4))
4.0ms	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (+.f64 (/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4)) (-.f64 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 6544414927309881/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))

series2.9s (6.7%)

Counts

4 → 12

Calls

4 calls:

2.3s	(-.f64 1 (.f64 (.f64 (/.f64 1 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (+.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))) (+.f64 (/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4)) (-.f64 (/.f64 -5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 6544414927309881/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)))))) (exp.f64 (neg.f64 (.f64 (fabs.f64 x) (fabs.f64 x))))))
229.0ms	(/.f64 6544414927309881/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3))
211.0ms	(/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4))
173.0ms	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))

simplify93.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5412	5691

prune1.0s (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	184	6	190

Merged error: 13.7b

Counts

190 → 6

Compiler

Compiled 13181 to 9828 computations (25.4% saved)

regimes91.0ms (0.2%)

Compiler: Compiled 1354 to 1090 computations (19.5% saved)

bsearch0.0ms (0%)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	383	99
1	383	99

end0.0ms (0%)

sample1.6s (3.8%)

Algorithm

1×

intervals

Results

962.0ms

8000×

body

128

valid

Compiler

Compiled 802 to 647 computations (19.3% saved)

Details

analyze3.0ms (0%)

sample46.0ms (0.1%)

simplify218.0ms (0.5%)

prune7.0ms (0%)

localize23.0ms (0.1%)

rewrite61.0ms (0.1%)

series4.8s (11.3%)

simplify119.0ms (0.3%)

prune686.0ms (1.6%)

localize25.0ms (0.1%)

rewrite178.0ms (0.4%)

series8.8s (20.4%)

simplify140.0ms (0.3%)

prune524.0ms (1.2%)

localize34.0ms (0.1%)

rewrite124.0ms (0.3%)

series20.3s (47.1%)

simplify169.0ms (0.4%)

prune990.0ms (2.3%)

localize30.0ms (0.1%)

rewrite59.0ms (0.1%)

series2.9s (6.7%)

simplify93.0ms (0.2%)

prune1.0s (2.4%)

regimes91.0ms (0.2%)

bsearch0.0ms (0%)

simplify12.0ms (0%)

end0.0ms (0%)

sample1.6s (3.8%)

Profiling