Details

analyze475.0ms (5.5%)

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)

sample110.0ms (1.3%)

Algorithm

1×

intervals

Results

55.0ms	80×	body	1024	valid
17.0ms	42×	body	512	valid
14.0ms	25×	body	2048	valid
8.0ms	94×	body	128	valid
3.0ms	15×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify172.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune4.0ms (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: 49.9b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.9b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.5b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
13.1b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_3829`
6×	`add-sqr-sqrt_binary64_3851`
5×	`add-log-exp_binary64_3868` `add-cube-cbrt_binary64_3864` `pow1_binary64_3890`
4×	`log-prod_binary64_3915` `add-exp-log_binary64_3867`
3×	`flip3-+_binary64_3832` `flip-+_binary64_3803` `sqrt-prod_binary64_3845` `add-cbrt-cube_binary64_3865`
2×	`distribute-lft-out_binary64_3780` `sqrt-div_binary64_3846` `log-div_binary64_3916`
1×	`rem-log-exp_binary64_3870` `rem-sqrt-square_binary64_3842` `sum-log_binary64_3920` `pow1/2_binary64_3909` `+-commutative_binary64_3759` `sqrt-pow1_binary64_3847` `log-pow_binary64_3918`

Counts

3 → 42

Calls

3 calls:

18.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
13.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
9.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series170.0ms (2%)

Counts

3 → 9

Calls

3 calls:

90.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
48.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
32.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5224	862

prune133.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Merged error: 0b

Counts

52 → 5

Compiler

Compiled 841 to 559 computations (33.5% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.2b	(*.f64 (pow.f64 x 3) 1/6)
16.0b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_3851`
15×	`associate-l_binary64_3770`
13×	`add-exp-log_binary64_3867`
10×	`add-cube-cbrt_binary64_3864` `-un-lft-identity_binary64_3829` `associate-r*_binary64_3769`
8×	`add-log-exp_binary64_3868` `unpow-prod-down_binary64_3908`
7×	`unswap-sqr_binary64_3797` `add-cbrt-cube_binary64_3865`
6×	`prod-exp_binary64_3878`
4×	`cube-prod_binary64_3857` `sqr-pow_binary64_3801`
3×	`pow1_binary64_3890`
2×	`pow-exp_binary64_3897` `*-commutative_binary64_3760` `pow-to-exp_binary64_3898` `cbrt-unprod_binary64_3862` `diff-log_binary64_3921`
1×	`cancel-sign-sub-inv_binary64_3795` `flip--_binary64_3804` `cube-mult_binary64_3859` `sum-log_binary64_3920` `unpow3_binary64_3895` `flip3--_binary64_3833` `sub-neg_binary64_3822` `associate--l+_binary64_3766`

Counts

3 → 70

Calls

3 calls:

12.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
12.0ms	(*.f64 (pow.f64 x 3) 1/6)
11.0ms	(*.f64 3/40 (pow.f64 x 5))

series139.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

52.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
47.0ms	(*.f64 3/40 (pow.f64 x 5))
41.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify120.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5018	1015

prune157.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	79	5	84

Merged error: 0b

Counts

84 → 5

Compiler

Compiled 1485 to 1150 computations (22.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.1b	(/.f64 1/8 (pow.f64 x 3))
11.4b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite218.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64_3835`
97×	`*-un-lft-identity_binary64_3829`
87×	`add-sqr-sqrt_binary64_3851`
80×	`cancel-sign-sub-inv_binary64_3795`
74×	`add-cube-cbrt_binary64_3864`
42×	`associate-+r+_binary64_3761`
31×	`cube-prod_binary64_3857` `unpow-prod-down_binary64_3908`
18×	`add-log-exp_binary64_3868`
12×	`associate-/r*_binary64_3773`
11×	`sqr-pow_binary64_3801`
10×	`cube-mult_binary64_3859` `add-exp-log_binary64_3867` `unpow3_binary64_3895`
9×	`distribute-lft-out_binary64_3780`
6×	`log-prod_binary64_3915` `add-cbrt-cube_binary64_3865` `distribute-lft-out--_binary64_3781`
5×	`sum-log_binary64_3920` `pow1_binary64_3890` `difference-of-squares_binary64_3798`
4×	`diff-log_binary64_3921`
3×	`flip3-+_binary64_3832` `div-inv_binary64_3826` `div-exp_binary64_3880` `flip-+_binary64_3803` `associate-/l*_binary64_3774`
2×	`log-div_binary64_3916` `frac-sub_binary64_3838` `sub-neg_binary64_3822` `associate--l+_binary64_3766`
1×	`flip--_binary64_3804` `rem-log-exp_binary64_3870` `associate-+r-_binary64_3763` `pow-exp_binary64_3897` `flip3--_binary64_3833` `clear-num_binary64_3828` `cbrt-undiv_binary64_3863` `+-commutative_binary64_3759` `frac-2neg_binary64_3840` `pow-to-exp_binary64_3898` `log-pow_binary64_3918`

Counts

4 → 203

Calls

4 calls:

60.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
54.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
50.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
11.0ms	(/.f64 1/8 (pow.f64 x 3))

series213.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
45.0ms	(/.f64 1/8 (pow.f64 x 3))
42.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
36.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify157.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4897	3393
1	4897	3393

prune448.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	215	5	220

Merged error: 0b

Counts

220 → 5

Compiler

Compiled 4448 to 3189 computations (28.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/8 (pow.f64 x 3))
0.4b	(/.f64 1/16 (pow.f64 x 5))
13.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
19.2b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite178.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64_3829`
73×	`times-frac_binary64_3835` `add-sqr-sqrt_binary64_3851`
47×	`add-cube-cbrt_binary64_3864`
26×	`unpow-prod-down_binary64_3908`
19×	`associate-/r*_binary64_3773`
15×	`add-exp-log_binary64_3867`
14×	`cube-prod_binary64_3857`
11×	`log-prod_binary64_3915`
10×	`difference-of-squares_binary64_3798` `sqr-pow_binary64_3801`
9×	`add-log-exp_binary64_3868`
8×	`add-cbrt-cube_binary64_3865`
6×	`div-exp_binary64_3880` `distribute-lft-out--_binary64_3781` `distribute-lft-out_binary64_3780` `associate-/l*_binary64_3774` `frac-sub_binary64_3838`
5×	`cancel-sign-sub-inv_binary64_3795` `pow1_binary64_3890` `log-div_binary64_3916`
4×	`cube-mult_binary64_3859` `unpow3_binary64_3895`
2×	`frac-add_binary64_3837` `flip3-+_binary64_3832` `div-inv_binary64_3826` `flip--_binary64_3804` `flip-+_binary64_3803` `pow-exp_binary64_3897` `flip3--_binary64_3833` `clear-num_binary64_3828` `cbrt-undiv_binary64_3863` `frac-2neg_binary64_3840` `pow-to-exp_binary64_3898` `diff-log_binary64_3921`
1×	`rem-log-exp_binary64_3870` `sum-log_binary64_3920` `associate--r+_binary64_3765` `log-pow_binary64_3918` `sub-neg_binary64_3822`

Counts

4 → 164

Calls

4 calls:

67.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
66.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
9.0ms	(/.f64 1/8 (pow.f64 x 3))
8.0ms	(/.f64 1/16 (pow.f64 x 5))

series213.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
55.0ms	(/.f64 1/16 (pow.f64 x 5))
50.0ms	(/.f64 1/8 (pow.f64 x 3))
42.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify165.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5284	3670

prune455.0ms (5.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	176	5	181

Merged error: 0b

Counts

181 → 5

Compiler

Compiled 4148 to 3300 computations (20.4% saved)

regimes337.0ms (3.9%)

Compiler: Compiled 1350 to 1028 computations (23.9% saved)

bsearch69.0ms (0.8%)

Steps

Iters	Range		Point
8	0.0012366449246195626	8.698264358620834	0.9535421595855004
9	-22.299910306173505	-5.1896511360859975e-08	-1.0567132446638723

Compiler

Compiled 1 to 1 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample4.4s (51.3%)

Algorithm

1×

intervals

Results

1.7s	2501×	body	1024	valid
731.0ms	1189×	body	2048	valid
465.0ms	1223×	body	512	valid
202.0ms	2426×	body	128	valid
129.0ms	610×	body	256	valid
42.0ms	51×	body	4096	valid

Compiler

Compiled 458 to 351 computations (23.4% saved)

Details

analyze475.0ms (5.5%)

sample110.0ms (1.3%)

simplify172.0ms (2%)

prune4.0ms (0.1%)

localize13.0ms (0.2%)

rewrite45.0ms (0.5%)

series170.0ms (2%)

simplify102.0ms (1.2%)

prune133.0ms (1.5%)

localize16.0ms (0.2%)

rewrite46.0ms (0.5%)

series139.0ms (1.6%)

simplify120.0ms (1.4%)

prune157.0ms (1.8%)

localize20.0ms (0.2%)

rewrite218.0ms (2.5%)

series213.0ms (2.5%)

simplify157.0ms (1.8%)

prune448.0ms (5.2%)

localize24.0ms (0.3%)

rewrite178.0ms (2.1%)

series213.0ms (2.5%)

simplify165.0ms (1.9%)

prune455.0ms (5.3%)

regimes337.0ms (3.9%)

bsearch69.0ms (0.8%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample4.4s (51.3%)

Profiling