Details

analyze277.0ms (5.7%)

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)

sample58.0ms (1.2%)

Algorithm

1×

intervals

Results

29.0ms	80×	body	1024	valid
9.0ms	42×	body	512	valid
8.0ms	25×	body	2048	valid
4.0ms	94×	body	128	valid
2.0ms	15×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify100.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune2.0ms (0.1%)

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)

localize7.0ms (0.1%)

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))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_2806`
6×	`add-sqr-sqrt_binary64_2828`
5×	`add-log-exp_binary64_2845` `add-cube-cbrt_binary64_2841` `pow1_binary64_2867`
4×	`add-exp-log_binary64_2844` `log-prod_binary64_2892`
3×	`add-cbrt-cube_binary64_2842` `flip-+_binary64_2780` `flip3-+_binary64_2809` `sqrt-prod_binary64_2822`
2×	`sqrt-div_binary64_2823` `distribute-lft-out_binary64_2757` `log-div_binary64_2893`
1×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-log-exp_binary64_2847` `rem-sqrt-square_binary64_2819` `sum-log_binary64_2897` `log-pow_binary64_2895` `+-commutative_binary64_2736`

Counts

3 → 42

Calls

3 calls:

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

series92.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
28.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
19.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5224	862

prune73.0ms (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)

localize8.0ms (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))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_2828`
15×	`associate-l_binary64_2747`
13×	`add-exp-log_binary64_2844`
10×	`-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `associate-r*_binary64_2746`
8×	`unpow-prod-down_binary64_2885` `add-log-exp_binary64_2845`
7×	`add-cbrt-cube_binary64_2842` `unswap-sqr_binary64_2774`
6×	`prod-exp_binary64_2855`
4×	`cube-prod_binary64_2834` `sqr-pow_binary64_2778`
3×	`pow1_binary64_2867`
2×	`pow-exp_binary64_2874` `*-commutative_binary64_2737` `diff-log_binary64_2898` `pow-to-exp_binary64_2875` `cbrt-unprod_binary64_2839`
1×	`cancel-sign-sub-inv_binary64_2772` `associate--l+_binary64_2743` `flip3--_binary64_2810` `unpow3_binary64_2872` `sub-neg_binary64_2799` `sum-log_binary64_2897` `flip--_binary64_2781` `cube-mult_binary64_2836`

Counts

3 → 70

Calls

3 calls:

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)
6.0ms	(*.f64 3/40 (pow.f64 x 5))

series96.0ms (2%)

Counts

3 → 9

Calls

3 calls:

37.0ms	(*.f64 3/40 (pow.f64 x 5))
32.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
27.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5018	1015

prune84.0ms (1.7%)

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)

localize14.0ms (0.3%)

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)))))

rewrite112.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64_2812`
97×	`*-un-lft-identity_binary64_2806`
87×	`add-sqr-sqrt_binary64_2828`
80×	`cancel-sign-sub-inv_binary64_2772`
74×	`add-cube-cbrt_binary64_2841`
42×	`associate-+r+_binary64_2738`
31×	`cube-prod_binary64_2834` `unpow-prod-down_binary64_2885`
18×	`add-log-exp_binary64_2845`
12×	`associate-/r*_binary64_2750`
11×	`sqr-pow_binary64_2778`
10×	`add-exp-log_binary64_2844` `unpow3_binary64_2872` `cube-mult_binary64_2836`
9×	`distribute-lft-out_binary64_2757`
6×	`add-cbrt-cube_binary64_2842` `distribute-lft-out--_binary64_2758` `log-prod_binary64_2892`
5×	`sum-log_binary64_2897` `difference-of-squares_binary64_2775` `pow1_binary64_2867`
4×	`diff-log_binary64_2898`
3×	`div-inv_binary64_2803` `div-exp_binary64_2857` `flip-+_binary64_2780` `flip3-+_binary64_2809` `associate-/l*_binary64_2751`
2×	`associate--l+_binary64_2743` `log-div_binary64_2893` `sub-neg_binary64_2799` `frac-sub_binary64_2815`
1×	`pow-exp_binary64_2874` `flip3--_binary64_2810` `cbrt-undiv_binary64_2840` `associate-+r-_binary64_2740` `rem-log-exp_binary64_2847` `pow-to-exp_binary64_2875` `flip--_binary64_2781` `clear-num_binary64_2805` `log-pow_binary64_2895` `frac-2neg_binary64_2817` `+-commutative_binary64_2736`

Counts

4 → 203

Calls

4 calls:

35.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
26.0ms	(-.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 1/8 (pow.f64 x 3))

series106.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
23.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
22.0ms	(/.f64 1/8 (pow.f64 x 3))
20.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify91.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4897	3393
1	4897	3393

prune268.0ms (5.5%)

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)

localize12.0ms (0.2%)

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))))

rewrite107.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64_2806`
73×	`add-sqr-sqrt_binary64_2828` `times-frac_binary64_2812`
47×	`add-cube-cbrt_binary64_2841`
26×	`unpow-prod-down_binary64_2885`
19×	`associate-/r*_binary64_2750`
15×	`add-exp-log_binary64_2844`
14×	`cube-prod_binary64_2834`
11×	`log-prod_binary64_2892`
10×	`sqr-pow_binary64_2778` `difference-of-squares_binary64_2775`
9×	`add-log-exp_binary64_2845`
8×	`add-cbrt-cube_binary64_2842`
6×	`div-exp_binary64_2857` `distribute-lft-out_binary64_2757` `distribute-lft-out--_binary64_2758` `frac-sub_binary64_2815` `associate-/l*_binary64_2751`
5×	`cancel-sign-sub-inv_binary64_2772` `log-div_binary64_2893` `pow1_binary64_2867`
4×	`unpow3_binary64_2872` `cube-mult_binary64_2836`
2×	`pow-exp_binary64_2874` `div-inv_binary64_2803` `flip3--_binary64_2810` `cbrt-undiv_binary64_2840` `diff-log_binary64_2898` `pow-to-exp_binary64_2875` `flip-+_binary64_2780` `flip--_binary64_2781` `frac-add_binary64_2814` `flip3-+_binary64_2809` `clear-num_binary64_2805` `frac-2neg_binary64_2817`
1×	`associate--r+_binary64_2742` `rem-log-exp_binary64_2847` `sub-neg_binary64_2799` `sum-log_binary64_2897` `log-pow_binary64_2895`

Counts

4 → 164

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))))
37.0ms	(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))

series124.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
31.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
31.0ms	(/.f64 1/16 (pow.f64 x 5))
22.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify92.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5284	3670

prune270.0ms (5.6%)

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)

regimes175.0ms (3.6%)

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

bsearch37.0ms (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)

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%)

sample2.4s (50.6%)

Algorithm

1×

intervals

Results

923.0ms	2501×	body	1024	valid
399.0ms	1189×	body	2048	valid
257.0ms	1223×	body	512	valid
119.0ms	2426×	body	128	valid
76.0ms	610×	body	256	valid
23.0ms	51×	body	4096	valid

Compiler

Compiled 458 to 351 computations (23.4% saved)

Details

analyze277.0ms (5.7%)

sample58.0ms (1.2%)

simplify100.0ms (2.1%)

prune2.0ms (0.1%)

localize7.0ms (0.1%)

rewrite20.0ms (0.4%)

series92.0ms (1.9%)

simplify65.0ms (1.4%)

prune73.0ms (1.5%)

localize8.0ms (0.2%)

rewrite24.0ms (0.5%)

series96.0ms (2%)

simplify70.0ms (1.5%)

prune84.0ms (1.7%)

localize14.0ms (0.3%)

rewrite112.0ms (2.3%)

series106.0ms (2.2%)

simplify91.0ms (1.9%)

prune268.0ms (5.5%)

localize12.0ms (0.2%)

rewrite107.0ms (2.2%)

series124.0ms (2.6%)

simplify92.0ms (1.9%)

prune270.0ms (5.6%)

regimes175.0ms (3.6%)

bsearch37.0ms (0.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.4s (50.6%)

Profiling