Details

analyze265.0ms (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)

sample71.0ms (1.5%)

Algorithm

1×

intervals

Results

32.0ms	83×	body	1024	valid
17.0ms	48×	body	2048	valid
10.0ms	45×	body	512	valid
3.0ms	61×	body	128	valid
2.0ms	18×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify161.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune2.0ms (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: 53.5b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.5b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_2773`
6×	`add-sqr-sqrt_binary64_2794`
5×	`pow1_binary64_2831` `add-cube-cbrt_binary64_2805` `add-log-exp_binary64_2809`
4×	`add-exp-log_binary64_2808` `log-prod_binary64_2856`
3×	`flip3-+_binary64_2776` `add-cbrt-cube_binary64_2806` `sqrt-prod_binary64_2788` `flip-+_binary64_2747`
2×	`log-div_binary64_2857` `sqrt-div_binary64_2789` `distribute-lft-out_binary64_2726`
1×	`rem-log-exp_binary64_2811` `sqrt-pow1_binary64_2790` `sum-log_binary64_2861` `+-commutative_binary64_2705` `pow1/2_binary64_2850` `log-pow_binary64_2859` `rem-sqrt-square_binary64_2786`

Counts

3 → 42

Calls

3 calls:

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

series183.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

88.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
58.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
37.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5385	862

prune64.0ms (1.3%)

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 812 to 538 computations (33.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
19.8b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2794`
15×	`associate-l_binary64_2716`
14×	`add-exp-log_binary64_2808`
11×	`add-cube-cbrt_binary64_2805` `add-log-exp_binary64_2809` `*-un-lft-identity_binary64_2773`
10×	`associate-r_binary64_2715`
8×	`unpow-prod-down_binary64_2849` `add-cbrt-cube_binary64_2806`
7×	`unswap-sqr_binary64_2741`
6×	`prod-exp_binary64_2819`
4×	`sqr-pow_binary64_2745` `pow1_binary64_2831` `cube-prod_binary64_2798`
2×	`pow-exp_binary64_2838` `cbrt-unprod_binary64_2803` `pow-to-exp_binary64_2839` `diff-log_binary64_2862` `sum-log_binary64_2861` `*-commutative_binary64_2706`
1×	`unpow3_binary64_2836` `sub-neg_binary64_2766` `flip3-+_binary64_2776` `flip3--_binary64_2777` `cube-mult_binary64_2800` `flip--_binary64_2748` `associate--l+_binary64_2712` `+-commutative_binary64_2705` `flip-+_binary64_2747`

Counts

4 → 80

Calls

4 calls:

8.0ms	(*.f64 3/40 (pow.f64 x 5))
6.0ms	(-.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)
3.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))

series348.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
60.0ms	(*.f64 3/40 (pow.f64 x 5))
58.0ms	(*.f64 (pow.f64 x 3) 1/6)
53.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4967	1201
1	4967	1201

prune95.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	92	4	96

Merged error: 0b

Counts

96 → 4

Compiler

Compiled 1691 to 1310 computations (22.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/8 (pow.f64 x 3))
0.1b	(/.f64 1/16 (pow.f64 x 5))
12.9b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
22.8b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite116.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_2794`
71×	`times-frac_binary64_2779`
68×	`*-un-lft-identity_binary64_2773`
46×	`add-cube-cbrt_binary64_2805`
26×	`unpow-prod-down_binary64_2849`
19×	`associate-/r*_binary64_2719`
15×	`add-exp-log_binary64_2808`
14×	`cube-prod_binary64_2798`
11×	`log-prod_binary64_2856`
10×	`sqr-pow_binary64_2745` `difference-of-squares_binary64_2742`
9×	`add-log-exp_binary64_2809`
8×	`add-cbrt-cube_binary64_2806`
6×	`div-exp_binary64_2821` `frac-sub_binary64_2782` `distribute-lft-out--_binary64_2727` `associate-/l*_binary64_2720`
5×	`log-div_binary64_2857` `pow1_binary64_2831`
4×	`unpow3_binary64_2836` `cube-mult_binary64_2800` `distribute-lft-out_binary64_2726`
2×	`pow-exp_binary64_2838` `cbrt-undiv_binary64_2804` `frac-2neg_binary64_2784` `pow-to-exp_binary64_2839` `diff-log_binary64_2862` `frac-add_binary64_2781` `div-inv_binary64_2770` `flip3-+_binary64_2776` `flip3--_binary64_2777` `flip--_binary64_2748` `clear-num_binary64_2772` `flip-+_binary64_2747`
1×	`rem-log-exp_binary64_2811` `associate--r+_binary64_2711` `sub-neg_binary64_2766` `sum-log_binary64_2861` `log-pow_binary64_2859`

Counts

4 → 159

Calls

4 calls:

45.0ms	(-.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))

series230.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
60.0ms	(/.f64 1/16 (pow.f64 x 5))
47.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
45.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify60.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4929	3605
1	4929	3605

prune267.0ms (5.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Merged error: 0b

Counts

175 → 4

Compiler

Compiled 4093 to 3255 computations (20.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1/2 x))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.1b	(/.f64 1/8 (pow.f64 x 3))
10.9b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite78.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64_2773`
36×	`times-frac_binary64_2779`
30×	`add-cube-cbrt_binary64_2805` `add-sqr-sqrt_binary64_2794`
15×	`add-log-exp_binary64_2809`
12×	`unpow-prod-down_binary64_2849` `cube-prod_binary64_2798` `associate-/r*_binary64_2719`
10×	`add-exp-log_binary64_2808`
9×	`distribute-lft-out_binary64_2726`
6×	`log-prod_binary64_2856` `add-cbrt-cube_binary64_2806`
5×	`pow1_binary64_2831` `sum-log_binary64_2861`
4×	`sqr-pow_binary64_2745` `unpow3_binary64_2836` `cube-mult_binary64_2800` `distribute-lft-out--_binary64_2727`
3×	`flip3-+_binary64_2776` `div-exp_binary64_2821` `associate-/l*_binary64_2720` `flip-+_binary64_2747`
2×	`log-div_binary64_2857` `diff-log_binary64_2862` `+-commutative_binary64_2705` `associate-+r+_binary64_2707`
1×	`pow-exp_binary64_2838` `rem-log-exp_binary64_2811` `cbrt-undiv_binary64_2804` `frac-2neg_binary64_2784` `pow-to-exp_binary64_2839` `associate-+r-_binary64_2709` `sub-neg_binary64_2766` `div-inv_binary64_2770` `clear-num_binary64_2772` `associate--l+_binary64_2712` `log-pow_binary64_2859`

Counts

4 → 113

Calls

4 calls:

26.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
25.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
6.0ms	(+.f64 x (/.f64 1/2 x))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series217.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
58.0ms	(+.f64 x (/.f64 1/2 x))
46.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
42.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4955	2077
1	4955	2077

prune130.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	125	4	129

Merged error: 0b

Counts

129 → 4

Compiler

Compiled 2462 to 1759 computations (28.6% saved)

regimes23.0ms (0.5%)

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

bsearch37.0ms (0.8%)

Steps

Iters	Range		Point
9	0.6814830664350081	219361.26943641825	0.9586458855915625
9	-3.996062453584732	-1.8155029574833036e-07	-1.0620143966736946

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.2s (45.5%)

Algorithm

1×

intervals

Results

969.0ms	2525×	body	1024	valid
426.0ms	1244×	body	2048	valid
265.0ms	1254×	body	512	valid
113.0ms	2313×	body	128	valid
76.0ms	628×	body	256	valid
17.0ms	36×	body	4096	valid

Compiler

Compiled 139 to 111 computations (20.1% saved)

Details

analyze265.0ms (5.5%)

sample71.0ms (1.5%)

simplify161.0ms (3.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite21.0ms (0.4%)

series183.0ms (3.8%)

simplify83.0ms (1.7%)

prune64.0ms (1.3%)

localize9.0ms (0.2%)

rewrite30.0ms (0.6%)

series348.0ms (7.2%)

simplify56.0ms (1.2%)

prune95.0ms (2%)

localize12.0ms (0.2%)

rewrite116.0ms (2.4%)

series230.0ms (4.8%)

simplify60.0ms (1.3%)

prune267.0ms (5.6%)

localize10.0ms (0.2%)

rewrite78.0ms (1.6%)

series217.0ms (4.5%)

simplify44.0ms (0.9%)

prune130.0ms (2.7%)

regimes23.0ms (0.5%)

bsearch37.0ms (0.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.2s (45.5%)

Profiling