Details

analyze259.0ms (5.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample64.0ms (1.3%)

Algorithm

1×

intervals

Results

28.0ms	75×	body	1024	valid
12.0ms	53×	body	512	valid
11.0ms	36×	body	2048	valid
4.0ms	77×	body	128	valid
2.0ms	14×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify167.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune5.0ms (0.1%)

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: 54.0b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.8b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.7b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_3519`
6×	`add-sqr-sqrt_binary64_3541`
5×	`add-log-exp_binary64_3558` `add-cube-cbrt_binary64_3554` `pow1_binary64_3580`
4×	`log-prod_binary64_3605` `add-exp-log_binary64_3557`
3×	`add-cbrt-cube_binary64_3555` `flip-+_binary64_3493` `flip3-+_binary64_3522` `sqrt-prod_binary64_3535`
2×	`log-div_binary64_3606` `sqrt-div_binary64_3536` `distribute-lft-out_binary64_3470`
1×	`log-pow_binary64_3608` `+-commutative_binary64_3449` `sqrt-pow1_binary64_3537` `sum-log_binary64_3610` `rem-sqrt-square_binary64_3532` `pow1/2_binary64_3599` `rem-log-exp_binary64_3560`

Counts

3 → 42

Calls

3 calls:

7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series176.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

89.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
53.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
33.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4924	862
1	4924	862

prune130.0ms (2.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

Compiler

Compiled 1874 to 1343 computations (28.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
20.4b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_3541`
15×	`associate-l_binary64_3460`
13×	`add-exp-log_binary64_3557`
10×	`associate-r_binary64_3459` `*-un-lft-identity_binary64_3519` `add-cube-cbrt_binary64_3554`
8×	`unpow-prod-down_binary64_3598` `add-log-exp_binary64_3558`
7×	`add-cbrt-cube_binary64_3555` `unswap-sqr_binary64_3487`
6×	`prod-exp_binary64_3568`
4×	`cube-prod_binary64_3547` `sqr-pow_binary64_3491`
3×	`pow1_binary64_3580`
2×	`pow-exp_binary64_3587` `pow-to-exp_binary64_3588` `diff-log_binary64_3611` `cbrt-unprod_binary64_3552` `*-commutative_binary64_3450`
1×	`sum-log_binary64_3610` `flip--_binary64_3494` `cancel-sign-sub-inv_binary64_3485` `sub-neg_binary64_3512` `cube-mult_binary64_3549` `unpow3_binary64_3585` `flip3--_binary64_3523` `associate--l+_binary64_3456`

Counts

3 → 70

Calls

3 calls:

7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(*.f64 3/40 (pow.f64 x 5))

series168.0ms (3.4%)

Counts

3 → 9

Calls

3 calls:

62.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
60.0ms	(*.f64 3/40 (pow.f64 x 5))
46.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify92.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4851	1006
1	4851	1006

prune83.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	79	4	83

Merged error: 0b

Counts

83 → 4

Compiler

Compiled 1450 to 1123 computations (22.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1/2 x))
0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.2b	(/.f64 1/8 (pow.f64 x 3))
9.7b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite260.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64_3525`
68×	`*-un-lft-identity_binary64_3519`
65×	`add-sqr-sqrt_binary64_3541`
52×	`add-cube-cbrt_binary64_3554`
40×	`cancel-sign-sub-inv_binary64_3485`
22×	`unpow-prod-down_binary64_3598` `cube-prod_binary64_3547`
12×	`associate-/r*_binary64_3463`
11×	`add-log-exp_binary64_3558`
10×	`add-exp-log_binary64_3557`
8×	`sqr-pow_binary64_3491`
7×	`cube-mult_binary64_3549` `unpow3_binary64_3585`
6×	`add-cbrt-cube_binary64_3555` `log-prod_binary64_3605` `distribute-lft-out_binary64_3470`
5×	`difference-of-squares_binary64_3488` `pow1_binary64_3580`
4×	`distribute-lft-out--_binary64_3471`
3×	`flip-+_binary64_3493` `flip3-+_binary64_3522` `div-exp_binary64_3570` `associate-/l*_binary64_3464`
2×	`diff-log_binary64_3611` `sum-log_binary64_3610` `log-div_binary64_3606` `div-inv_binary64_3516` `frac-sub_binary64_3528`
1×	`pow-exp_binary64_3587` `log-pow_binary64_3608` `+-commutative_binary64_3449` `pow-to-exp_binary64_3588` `cbrt-undiv_binary64_3553` `flip--_binary64_3494` `clear-num_binary64_3518` `sub-neg_binary64_3512` `rem-log-exp_binary64_3560` `flip3--_binary64_3523` `associate--l+_binary64_3456` `frac-2neg_binary64_3530`

Counts

4 → 156

Calls

4 calls:

208.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
24.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
7.0ms	(+.f64 x (/.f64 1/2 x))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series218.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
62.0ms	(+.f64 x (/.f64 1/2 x))
45.0ms	(/.f64 1/8 (pow.f64 x 3))
41.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify93.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4928	2556
1	4928	2556

prune177.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	168	4	172

Merged error: 0b

Counts

172 → 4

Compiler

Compiled 3206 to 2338 computations (27.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.2b	(/.f64 1/8 (pow.f64 x 3))
12.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
17.5b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite112.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64_3519`
73×	`add-sqr-sqrt_binary64_3541` `times-frac_binary64_3525`
47×	`add-cube-cbrt_binary64_3554`
26×	`unpow-prod-down_binary64_3598`
19×	`associate-/r*_binary64_3463`
15×	`add-exp-log_binary64_3557`
14×	`cube-prod_binary64_3547`
11×	`log-prod_binary64_3605`
10×	`difference-of-squares_binary64_3488` `sqr-pow_binary64_3491`
9×	`add-log-exp_binary64_3558`
8×	`add-cbrt-cube_binary64_3555`
6×	`div-exp_binary64_3570` `associate-/l*_binary64_3464` `frac-sub_binary64_3528` `distribute-lft-out--_binary64_3471` `distribute-lft-out_binary64_3470`
5×	`log-div_binary64_3606` `cancel-sign-sub-inv_binary64_3485` `pow1_binary64_3580`
4×	`cube-mult_binary64_3549` `unpow3_binary64_3585`
2×	`pow-exp_binary64_3587` `flip-+_binary64_3493` `pow-to-exp_binary64_3588` `flip3-+_binary64_3522` `diff-log_binary64_3611` `cbrt-undiv_binary64_3553` `flip--_binary64_3494` `clear-num_binary64_3518` `div-inv_binary64_3516` `frac-add_binary64_3527` `flip3--_binary64_3523` `frac-2neg_binary64_3530`
1×	`associate--r+_binary64_3455` `log-pow_binary64_3608` `sum-log_binary64_3610` `sub-neg_binary64_3512` `rem-log-exp_binary64_3560`

Counts

4 → 164

Calls

4 calls:

43.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
38.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

series233.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
61.0ms	(/.f64 1/16 (pow.f64 x 5))
50.0ms	(/.f64 1/8 (pow.f64 x 3))
47.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4966	3700
1	4966	3700

prune269.0ms (5.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	176	4	180

Merged error: 0b

Counts

180 → 4

Compiler

Compiled 4168 to 3314 computations (20.5% saved)

regimes22.0ms (0.4%)

Compiler: Compiled 56 to 47 computations (16.1% saved)

bsearch46.0ms (0.9%)

Steps

Iters	Range		Point
10	0.6133395137864166	213158136477.41104	0.9595302535145758
11	-7910618638.644347	-2.4053904822129223e-21	-1.0827450898202535

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.2s (43.7%)

Algorithm

1×

intervals

Results

966.0ms	2522×	body	1024	valid
410.0ms	1219×	body	2048	valid
267.0ms	1267×	body	512	valid
113.0ms	2351×	body	128	valid
71.0ms	596×	body	256	valid
21.0ms	45×	body	4096	valid

Compiler

Compiled 139 to 111 computations (20.1% saved)

Details

analyze259.0ms (5.2%)

sample64.0ms (1.3%)

simplify167.0ms (3.4%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

rewrite21.0ms (0.4%)

series176.0ms (3.5%)

simplify54.0ms (1.1%)

prune130.0ms (2.6%)

localize9.0ms (0.2%)

rewrite24.0ms (0.5%)

series168.0ms (3.4%)

simplify92.0ms (1.8%)

prune83.0ms (1.7%)

localize10.0ms (0.2%)

rewrite260.0ms (5.2%)

series218.0ms (4.4%)

simplify93.0ms (1.9%)

prune177.0ms (3.6%)

localize12.0ms (0.2%)

rewrite112.0ms (2.3%)

series233.0ms (4.7%)

simplify81.0ms (1.6%)

prune269.0ms (5.4%)

regimes22.0ms (0.4%)

bsearch46.0ms (0.9%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (43.7%)

Profiling