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)

sample37.0ms (0.2%)

Algorithm

1×

intervals

Results

29.0ms

256×

body

128

valid

Compiler

Compiled 129 to 106 computations (17.8% saved)

simplify149.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5204	79

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 14.0b

Counts

2 → 1

Compiler

Compiled 102 to 82 computations (19.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
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)))))
13.9b	(-.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 x x)))))

rewrite144.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_2465`
28×	`times-frac_binary64_2471`
27×	`add-sqr-sqrt_binary64_2487`
24×	`add-cube-cbrt_binary64_2500`
10×	`cancel-sign-sub-inv_binary64_2431` `distribute-lft-out_binary64_2416`
8×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `associate-/l*_binary64_2410`
6×	`flip3-+_binary64_2468` `associate-/r*_binary64_2409` `flip-+_binary64_2439` `associate-/r/_binary64_2411`
4×	`associate-/l/_binary64_2412` `pow1_binary64_2526`
3×	`div-inv_binary64_2462`
2×	`associate-*l/_binary64_2408` `difference-of-squares_binary64_2434` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `frac-2neg_binary64_2476`
1×	`+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `diff-log_binary64_2557` `flip3--_binary64_2469`

Counts

4 → 106

Calls

4 calls:

44.0ms	(-.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 x x)))))
34.0ms	(+.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))))
13.0ms	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))

series2.6s (15.9%)

Counts

4 → 12

Calls

4 calls:

1.5s	(-.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 x x)))))
515.0ms	(+.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)))))
493.0ms	(/.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))))
127.0ms	(/.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))

simplify159.0ms (1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4901	8743
1	4901	8743

prune605.0ms (3.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	4	119

Merged error: 13.9b

Counts

119 → 4

Compiler

Compiled 8932 to 6646 computations (25.6% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
0.5b	(cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
0.5b	(cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
13.9b	(-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))) (.f64 (cbrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (cbrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (/.f64 (cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (cbrt.f64 (+.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 x x)))))

rewrite69.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_2465`
12×	`add-sqr-sqrt_binary64_2487` `cbrt-prod_binary64_2496`
10×	`cancel-sign-sub-inv_binary64_2431`
9×	`add-cube-cbrt_binary64_2500`
6×	`add-log-exp_binary64_2504` `cbrt-div_binary64_2497`
4×	`flip3-+_binary64_2468` `times-frac_binary64_2471` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526` `distribute-lft-out_binary64_2416`
3×	`pow1/3_binary64_2547`
2×	`associate-*l/_binary64_2408` `difference-of-squares_binary64_2434` `associate-/r/_binary64_2411`
1×	`flip--_binary64_2440` `distribute-lft-out--_binary64_2417` `sub-neg_binary64_2458` `div-inv_binary64_2462` `diff-log_binary64_2557` `flip3--_binary64_2469`

Counts

4 → 66

Calls

4 calls:

26.0ms	(-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))) (.f64 (cbrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (cbrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (/.f64 (cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (cbrt.f64 (+.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 x x)))))
9.0ms	(cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
9.0ms	(cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
9.0ms	(cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))

series2.2s (13.1%)

Counts

4 → 12

Calls

4 calls:

1.5s	(-.f64 1 (/.f64 (+.f64 2295300911148351/9007199254740992 (/.f64 (+.f64 -5125037576950889/18014398509481984 (/.f64 (+.f64 6401478394306903/4503599627370496 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))) (.f64 (cbrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (cbrt.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (/.f64 (cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (cbrt.f64 (+.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 x x)))))
214.0ms	(cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
212.0ms	(cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
208.0ms	(cbrt.f64 (+.f64 -6544414927309881/4503599627370496 (/.f64 4780145094533421/4503599627370496 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))

simplify109.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4921	4866
1	4921	4866

prune505.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Merged error: 13.9b

Counts

82 → 4

Compiler

Compiled 7946 to 6056 computations (23.8% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)
0.2b	(/.f64 5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
0.3b	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
13.9b	(-.f64 1 (/.f64 (+.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 6544414927309881/4503599627370496 (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 x x)))))

rewrite122.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_2465`
42×	`times-frac_binary64_2471`
37×	`add-sqr-sqrt_binary64_2487`
34×	`add-cube-cbrt_binary64_2500`
15×	`unpow-prod-down_binary64_2544` `cancel-sign-sub-inv_binary64_2431`
12×	`add-exp-log_binary64_2503`
11×	`associate-/r*_binary64_2409` `distribute-lft-out_binary64_2416`
9×	`add-cbrt-cube_binary64_2501`
6×	`add-log-exp_binary64_2504` `associate-/l*_binary64_2410`
5×	`distribute-lft-out--_binary64_2417` `sqr-pow_binary64_2437` `pow1_binary64_2526`
4×	`unpow2_binary64_2530` `div-exp_binary64_2516` `associate-/r/_binary64_2411`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `cube-prod_binary64_2493` `div-inv_binary64_2462` `pow-unpow_binary64_2542`
2×	`associate-*l/_binary64_2408` `difference-of-squares_binary64_2434` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `frac-2neg_binary64_2476` `cube-div_binary64_2494`
1×	`rem-cube-cbrt_binary64_2488` `associate--r-_binary64_2404` `unpow3_binary64_2531` `flip--_binary64_2440` `associate-+r-_binary64_2399` `div-sub_binary64_2470` `sub-neg_binary64_2458` `cube-mult_binary64_2495` `diff-log_binary64_2557` `pow-pow_binary64_2537` `flip3--_binary64_2469`

Counts

4 → 133

Calls

4 calls:

84.0ms	(-.f64 1 (/.f64 (+.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 6544414927309881/4503599627370496 (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 x x)))))
6.0ms	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
5.0ms	(/.f64 5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))
4.0ms	(pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)

series1.7s (10.4%)

Counts

4 → 12

Calls

4 calls:

1.5s	(-.f64 1 (/.f64 (+.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 6544414927309881/4503599627370496 (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 x x)))))
94.0ms	(/.f64 6401478394306903/4503599627370496 (pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 2))
55.0ms	(pow.f64 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)
45.0ms	(/.f64 5125037576950889/18014398509481984 (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))

simplify110.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	6071	6373

prune657.0ms (4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	145	4	149

Merged error: 13.9b

Counts

149 → 4

Compiler

Compiled 10319 to 7846 computations (24% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (-.f64 (/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4)) (+.f64 (/.f64 6544414927309881/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)) (/.f64 5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))))
0.4b	(+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
0.6b	(.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))
13.9b	(-.f64 1 (/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (-.f64 (/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4)) (+.f64 (/.f64 6544414927309881/4503599627370496 (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 x x)))))

rewrite210.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64_2487`
104×	`times-frac_binary64_2471`
90×	`*-un-lft-identity_binary64_2465`
63×	`add-cube-cbrt_binary64_2500`
48×	`sqrt-prod_binary64_2481`
30×	`swap-sqr_binary64_2432`
29×	`add-log-exp_binary64_2504`
24×	`associate-r_binary64_2405` `associate-l_binary64_2406`
17×	`cancel-sign-sub-inv_binary64_2431`
16×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
14×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
12×	`sum-log_binary64_2556` `frac-add_binary64_2473`
11×	`pow1_binary64_2526`
10×	`associate-/r/_binary64_2411` `distribute-lft-out_binary64_2416`
9×	`unswap-sqr_binary64_2433`
6×	`associate-+r+_binary64_2397` `frac-sub_binary64_2474`
5×	`distribute-lft-out--_binary64_2417` `div-inv_binary64_2462` `diff-log_binary64_2557`
4×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
3×	`associate-*l/_binary64_2408` `flip--_binary64_2440` `flip3--_binary64_2469`
2×	`difference-of-squares_binary64_2434` `+-commutative_binary64_2395` `associate-+r-_binary64_2399` `sub-neg_binary64_2458`
1×	`associate--r-_binary64_2404` `-commutative_binary64_2396` `frac-times_binary64_2475` `pow-plus_binary64_2528` `associate-+l+_binary64_2398` `associate-r/_binary64_2407` `div-sub_binary64_2470` `pow2_binary64_2546` `pow-prod-down_binary64_2536` `pow-sqr_binary64_2438` `pow-prod-up_binary64_2535`

Counts

4 → 186

Calls

4 calls:

72.0ms	(-.f64 1 (/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (-.f64 (/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4)) (+.f64 (/.f64 6544414927309881/4503599627370496 (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 x x)))))
67.0ms	(+.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (-.f64 (/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4)) (+.f64 (/.f64 6544414927309881/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)) (/.f64 5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))))
24.0ms	(.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))
4.0ms	(+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))

series2.3s (13.8%)

Counts

4 → 12

Calls

4 calls:

1.5s	(-.f64 1 (/.f64 (+.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (-.f64 (/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4)) (+.f64 (/.f64 6544414927309881/4503599627370496 (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 x x)))))
536.0ms	(+.f64 (+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))) (-.f64 (/.f64 4780145094533421/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 4)) (+.f64 (/.f64 6544414927309881/4503599627370496 (pow.f64 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x))) 3)) (/.f64 5125037576950889/18014398509481984 (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))))
122.0ms	(+.f64 2295300911148351/9007199254740992 (.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x))))))
115.0ms	(.f64 (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (.f64 1475339155889891/4503599627370496 (fabs.f64 x)))) (/.f64 (sqrt.f64 6401478394306903/4503599627370496) (+.f64 1 (*.f64 1475339155889891/4503599627370496 (fabs.f64 x)))))

simplify155.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5122	13413

prune1.4s (8.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	198	4	202

Merged error: 13.9b

Counts

202 → 4

Compiler

Compiled 16593 to 12745 computations (23.2% saved)

regimes518.0ms (3.1%)

Compiler: Compiled 9870 to 7918 computations (19.8% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	325	103
1	325	103

end0.0ms (0%)

sample2.7s (16.1%)

Algorithm

1×

intervals

Results

941.0ms

8000×

body

128

valid

Compiler

Compiled 2534 to 2035 computations (19.7% saved)

Details

analyze3.0ms (0%)

sample37.0ms (0.2%)

simplify149.0ms (0.9%)

prune6.0ms (0%)

localize20.0ms (0.1%)

rewrite144.0ms (0.9%)

series2.6s (15.9%)

simplify159.0ms (1%)

prune605.0ms (3.7%)

localize32.0ms (0.2%)

rewrite69.0ms (0.4%)

series2.2s (13.1%)

simplify109.0ms (0.7%)

prune505.0ms (3.1%)

localize24.0ms (0.1%)

rewrite122.0ms (0.7%)

series1.7s (10.4%)

simplify110.0ms (0.7%)

prune657.0ms (4%)

localize29.0ms (0.2%)

rewrite210.0ms (1.3%)

series2.3s (13.8%)

simplify155.0ms (0.9%)

prune1.4s (8.4%)

regimes518.0ms (3.1%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample2.7s (16.1%)

Profiling