Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	25%	13
75%	0%	25%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample17.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify97.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	10
1	21	10

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

Error

0.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 (-.f64 (*.f64 x x) 3) 6)
0.1b	(/.f64 (-.f64 (*.f64 x x) 3) 6)

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2828`
12×	`times-frac_binary64_2812`
10×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
4×	`difference-of-squares_binary64_2775` `associate-/l*_binary64_2751`
3×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `associate-/r*_binary64_2750`
2×	`associate-/l/_binary64_2753`
1×	`div-inv_binary64_2803` `div-exp_binary64_2857` `flip3--_binary64_2810` `cbrt-undiv_binary64_2840` `div-sub_binary64_2811` `add-log-exp_binary64_2845` `flip--_binary64_2781` `clear-num_binary64_2805` `pow1_binary64_2867` `frac-2neg_binary64_2817`

Counts

1 → 34

Calls

2 calls:

7.0ms	(/.f64 (-.f64 (*.f64 x x) 3) 6)
0.0ms	(/.f64 (-.f64 (*.f64 x x) 3) 6)

series53.0ms (1.8%)

Counts

1 → 6

Calls

1 calls:

53.0ms

(/.f64 (-.f64 (*.f64 x x) 3) 6)

Compiler

Compiled 53 to 54 computations (-1.9% saved)

simplify57.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4883	617
1	4883	617

prune54.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	5	41

Error

Counts

41 → 5

Compiler

Compiled 573 to 392 computations (31.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 x x) 3) 1/6)
0.1b	(.f64 (-.f64 (.f64 x x) 3) 1/6)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_2828`
4×	`associate-l_binary64_2747`
3×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `associate-r*_binary64_2746` `pow1_binary64_2867`
2×	`associate-*l/_binary64_2749`
1×	`*-commutative_binary64_2737` `flip3--_binary64_2810` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `add-log-exp_binary64_2845` `flip--_binary64_2781` `difference-of-squares_binary64_2775` `pow-prod-down_binary64_2877` `unswap-sqr_binary64_2774`

Counts

1 → 21

Calls

2 calls:

7.0ms	(.f64 (-.f64 (.f64 x x) 3) 1/6)
0.0ms	(.f64 (-.f64 (.f64 x x) 3) 1/6)

series46.0ms (1.5%)

Counts

1 → 6

Calls

1 calls:

46.0ms

(*.f64 (-.f64 (*.f64 x x) 3) 1/6)

Compiler

Compiled 53 to 54 computations (-1.9% saved)

simplify74.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4487	306
1	4487	306

prune27.0ms (0.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	27	5	32

Error

Counts

32 → 5

Compiler

Compiled 352 to 236 computations (33% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 6 (-.f64 (*.f64 x x) 3)))
0.1b	(/.f64 6 (-.f64 (*.f64 x x) 3))
0.1b	(/.f64 6 (-.f64 (*.f64 x x) 3))
0.1b	(/.f64 1 (/.f64 6 (-.f64 (*.f64 x x) 3)))

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64_2812`
78×	`add-sqr-sqrt_binary64_2828`
62×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
22×	`associate-/r*_binary64_2750`
16×	`difference-of-squares_binary64_2775`
15×	`add-exp-log_binary64_2844`
11×	`associate-/r/_binary64_2752`
9×	`add-cbrt-cube_binary64_2842`
8×	`div-exp_binary64_2857`
6×	`div-inv_binary64_2803` `associate-/l*_binary64_2751`
5×	`flip3--_binary64_2810` `flip--_binary64_2781`
4×	`cbrt-undiv_binary64_2840`
3×	`pow1_binary64_2867`
2×	`1-exp_binary64_2850` `rec-exp_binary64_2856` `add-log-exp_binary64_2845` `clear-num_binary64_2805` `frac-2neg_binary64_2817`
1×	`pow-flip_binary64_2880` `inv-pow_binary64_2891`

Counts

2 → 129

Calls

4 calls:

10.0ms	(/.f64 1 (/.f64 6 (-.f64 (*.f64 x x) 3)))
6.0ms	(/.f64 6 (-.f64 (*.f64 x x) 3))
0.0ms	(/.f64 6 (-.f64 (*.f64 x x) 3))
0.0ms	(/.f64 1 (/.f64 6 (-.f64 (*.f64 x x) 3)))

series83.0ms (2.7%)

Counts

2 → 14

Calls

2 calls:

48.0ms	(/.f64 1 (/.f64 6 (-.f64 (*.f64 x x) 3)))
35.0ms	(/.f64 6 (-.f64 (*.f64 x x) 3))

Compiler

Compiled 202 to 195 computations (3.5% saved)

simplify82.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4891	2820
1	4891	2820

prune143.0ms (4.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	143	5	148

Error

Counts

148 → 5

Compiler

Compiled 2372 to 1727 computations (27.2% saved)

localize11.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.2b	(cbrt.f64 (-.f64 (*.f64 x x) 3))
0.2b	(cbrt.f64 (-.f64 (*.f64 x x) 3))
0.2b	(cbrt.f64 (-.f64 (*.f64 x x) 3))
0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) 3)) (cbrt.f64 (-.f64 (.f64 x x) 3))) (sqrt.f64 6)) (/.f64 (cbrt.f64 (-.f64 (*.f64 x x) 3)) (sqrt.f64 6)))
0.2b	(cbrt.f64 (-.f64 (*.f64 x x) 3))
0.2b	(/.f64 (cbrt.f64 (-.f64 (*.f64 x x) 3)) (sqrt.f64 6))
0.2b	(.f64 (cbrt.f64 (-.f64 (.f64 x x) 3)) (cbrt.f64 (-.f64 (*.f64 x x) 3)))
0.9b	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) 3)) (cbrt.f64 (-.f64 (*.f64 x x) 3))) (sqrt.f64 6))

rewrite64.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64_2828`
52×	`cbrt-prod_binary64_2837`
48×	`times-frac_binary64_2812`
47×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
30×	`sqrt-prod_binary64_2822`
28×	`cbrt-div_binary64_2838`
14×	`flip3--_binary64_2810` `flip--_binary64_2781`
13×	`add-exp-log_binary64_2844`
12×	`associate-/r*_binary64_2750` `difference-of-squares_binary64_2775`
11×	`pow1_binary64_2867`
10×	`associate-/l/_binary64_2753`
8×	`frac-times_binary64_2816` `add-cbrt-cube_binary64_2842` `associate-/l*_binary64_2751`
7×	`associate-l_binary64_2747` `pow1/3_binary64_2888` `swap-sqr_binary64_2773` `associate-r_binary64_2746`
4×	`add-log-exp_binary64_2845` `associate-r/_binary64_2748` `associate-l/_binary64_2749` `unswap-sqr_binary64_2774`
3×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
2×	`pow-sqr_binary64_2779` `div-inv_binary64_2803` `prod-exp_binary64_2855` `pow-prod-up_binary64_2876` `cbrt-unprod_binary64_2839` `clear-num_binary64_2805` `pow-prod-down_binary64_2877` `frac-2neg_binary64_2817`
1×	`*-commutative_binary64_2737` `pow2_binary64_2887` `pow-plus_binary64_2869`

Counts

4 → 169

Calls

8 calls:

15.0ms	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) 3)) (cbrt.f64 (-.f64 (*.f64 x x) 3))) (sqrt.f64 6))
15.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x x) 3)) (cbrt.f64 (-.f64 (*.f64 x x) 3)))
8.0ms	(/.f64 (cbrt.f64 (-.f64 (*.f64 x x) 3)) (sqrt.f64 6))
4.0ms	(cbrt.f64 (-.f64 (*.f64 x x) 3))
0.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) 3)) (cbrt.f64 (-.f64 (.f64 x x) 3))) (sqrt.f64 6)) (/.f64 (cbrt.f64 (-.f64 (*.f64 x x) 3)) (sqrt.f64 6)))

series370.0ms (12.3%)

Counts

4 → 26

Calls

4 calls:

140.0ms	(/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x x) 3)) (cbrt.f64 (-.f64 (*.f64 x x) 3))) (sqrt.f64 6))
88.0ms	(/.f64 (cbrt.f64 (-.f64 (*.f64 x x) 3)) (sqrt.f64 6))
86.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x x) 3)) (cbrt.f64 (-.f64 (*.f64 x x) 3)))
56.0ms	(cbrt.f64 (-.f64 (*.f64 x x) 3))

Compiler

Compiled 1201 to 1055 computations (12.2% saved)

simplify106.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4966	4360
1	4966	4360

prune372.0ms (12.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	195	5	200

Error

Counts

200 → 5

Compiler

Compiled 6346 to 4453 computations (29.8% saved)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	135	673
1	135	673

regimes215.0ms (7.2%)

Compiler: Compiled 2230 to 1791 computations (19.7% saved)

bsearch0.0ms (0%)

regimes49.0ms (1.6%)

Compiler: Compiled 172 to 162 computations (5.8% saved)

bsearch0.0ms (0%)

regimes33.0ms (1.1%)

Compiler: Compiled 81 to 80 computations (1.2% saved)

bsearch0.0ms (0%)

regimes41.0ms (1.4%)

Compiler: Compiled 36 to 38 computations (-5.6% saved)

bsearch11.0ms (0.4%)

Steps

Iters	Range		Point
10	0.4824925384698944	704421607190.2083	3.0220778588967407

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes8.0ms (0.3%)

Compiler: Compiled 6 to 10 computations (-66.7% saved)

bsearch0.0ms (0%)

regimes8.0ms (0.3%)

Compiler: Compiled 5 to 8 computations (-60% saved)

bsearch0.0ms (0%)

regimes9.0ms (0.3%)

Accuracy

Total 0.1b remaining (99.6%)

Threshold costs 0.1b (99.6%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 37 to 34 computations (8.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	51
1	24	51

end0.0ms (0%)

sample891.0ms (29.6%)

Algorithm

1×

intervals

Results

191.0ms

8000×

body

128

valid

Compiler

Compiled 491 to 399 computations (18.7% saved)

Pareto

0.44805238585241636

Details

analyze3.0ms (0.1%)

sample17.0ms (0.6%)

simplify97.0ms (3.2%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite10.0ms (0.3%)

series53.0ms (1.8%)

simplify57.0ms (1.9%)

prune54.0ms (1.8%)

localize4.0ms (0.1%)

rewrite9.0ms (0.3%)

series46.0ms (1.5%)

simplify74.0ms (2.5%)

prune27.0ms (0.9%)

localize6.0ms (0.2%)

rewrite28.0ms (0.9%)

series83.0ms (2.7%)

simplify82.0ms (2.7%)

prune143.0ms (4.7%)

localize11.0ms (0.4%)

rewrite64.0ms (2.1%)

series370.0ms (12.3%)

simplify106.0ms (3.5%)

prune372.0ms (12.4%)

simplify12.0ms (0.4%)

regimes215.0ms (7.2%)

bsearch0.0ms (0%)

regimes49.0ms (1.6%)

bsearch0.0ms (0%)

regimes33.0ms (1.1%)

bsearch0.0ms (0%)

regimes41.0ms (1.4%)

bsearch11.0ms (0.4%)

regimes8.0ms (0.3%)

bsearch0.0ms (0%)

regimes8.0ms (0.3%)

bsearch0.0ms (0%)

regimes9.0ms (0.3%)

bsearch4.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample891.0ms (29.6%)

Profiling