Details

analyze259.0ms (5.4%)

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)

sample61.0ms (1.3%)

Algorithm

1×

intervals

Results

29.0ms	81×	body	1024	valid
11.0ms	35×	body	2048	valid
8.0ms	41×	body	512	valid
4.0ms	84×	body	128	valid
2.0ms	14×	body	256	valid
0.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify99.0ms (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%)

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

Error

52.8b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.4b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.2b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.5b	(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:

6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series90.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

48.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
25.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
18.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5224	862

prune71.0ms (1.5%)

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

Error

0.0b

Counts

52 → 4

Compiler

Compiled 830 to 550 computations (33.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
18.6b	(-.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))

series90.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
29.0ms	(*.f64 3/40 (pow.f64 x 5))
29.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5018	1015

prune88.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Error

0.0b

Counts

83 → 5

Compiler

Compiled 1519 to 1178 computations (22.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.2b	(/.f64 1/8 (pow.f64 x 3))
11.2b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite109.0ms (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:

31.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
28.0ms	(-.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)))))
5.0ms	(/.f64 1/8 (pow.f64 x 3))

series105.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
24.0ms	(/.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))))
19.0ms	(-.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 (48.0ms)

Iter	Nodes	Cost
0	4897	3393
1	4897	3393

prune261.0ms (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

Error

0.0b

Counts

220 → 5

Compiler

Compiled 4482 to 3217 computations (28.2% saved)

localize11.0ms (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))
11.9b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
20.0b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite106.0ms (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:

40.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
40.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
5.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

series126.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
30.0ms	(/.f64 1/16 (pow.f64 x 5))
27.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
22.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify88.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5284	3670

prune274.0ms (5.8%)

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

Error

0.0b

Counts

181 → 5

Compiler

Compiled 4148 to 3300 computations (20.4% saved)

regimes192.0ms (4%)

Accuracy

Total 0.2b remaining (88.1%)

Threshold costs 0.2b (88.1%)

Compiler

Compiled 1485 to 1139 computations (23.3% saved)

bsearch33.0ms (0.7%)

Steps

Iters	Range		Point
7	0.013554057386768589	2.325522641061648	0.9575579943942182
9	-4345.151084741531	-0.0036213940033464134	-1.0433820317753442

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 (50.4%)

Algorithm

1×

intervals

Results

890.0ms	2464×	body	1024	valid
380.0ms	1195×	body	2048	valid
250.0ms	1236×	body	512	valid
111.0ms	2418×	body	128	valid
72.0ms	647×	body	256	valid
17.0ms	40×	body	4096	valid

Compiler

Compiled 503 to 388 computations (22.9% saved)

Details

analyze259.0ms (5.4%)

sample61.0ms (1.3%)

simplify99.0ms (2.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite20.0ms (0.4%)

series90.0ms (1.9%)

simplify62.0ms (1.3%)

prune71.0ms (1.5%)

localize9.0ms (0.2%)

rewrite24.0ms (0.5%)

series90.0ms (1.9%)

simplify67.0ms (1.4%)

prune88.0ms (1.8%)

localize11.0ms (0.2%)

rewrite109.0ms (2.3%)

series105.0ms (2.2%)

simplify91.0ms (1.9%)

prune261.0ms (5.5%)

localize11.0ms (0.2%)

rewrite106.0ms (2.2%)

series126.0ms (2.7%)

simplify88.0ms (1.8%)

prune274.0ms (5.8%)

regimes192.0ms (4%)

bsearch33.0ms (0.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.4s (50.4%)

Profiling