Details

analyze107.0ms (1.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 29 to 22 computations (24.1% saved)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify50.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4981	40
1	4981	40

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.4b

Counts

2 → 1

Compiler

Compiled 54 to 41 computations (24.1% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.2b	(*.f64 PI.f64 t)
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
0.5b	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-*r/_binary64`
16×	`pow1_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`flip3--_binary64` `associate-r_binary64` `associate-/r/_binary64` `flip--_binary64` `sqrt-div_binary64`
7×	`pow-prod-down_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
1×	`associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 94

Calls

4 calls:

19.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
11.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
7.0ms	(.f64 3 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)

series600.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

355.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
180.0ms	(.f64 (.f64 PI.f64 t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v))))))
36.0ms	(.f64 3 (.f64 v v))
29.0ms	(*.f64 PI.f64 t)

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4974	2769
1	4974	2769

prune194.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	98	8	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	9	107

Merged error: 0.1b

Counts

107 → 9

Compiler

Compiled 4061 to 2515 computations (38.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
0.3b	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
0.5b	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))

rewrite57.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`associate-*r/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`pow1_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
9×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
8×	`associate-/r/_binary64`
7×	`pow-prod-down_binary64`
6×	`associate-r_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
1×	`associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 96

Calls

4 calls:

18.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
10.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
9.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
6.0ms	(.f64 3 (.f64 v v))

series770.0ms (13.8%)

Counts

4 → 12

Calls

4 calls:

372.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v))))
195.0ms	(.f64 PI.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))))
169.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
33.0ms	(.f64 3 (.f64 v v))

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5610	3090

prune209.0ms (3.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	6	1	7
Picked	1	0	1
Done	0	1	1
Total	109	8	117

Merged error: 0.1b

Counts

117 → 8

Compiler

Compiled 4146 to 2697 computations (34.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.3b	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))) PI.f64))
0.3b	(.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))) PI.f64)
0.5b	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`associate-*r/_binary64`
10×	`*-un-lft-identity_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
8×	`associate-r_binary64`
7×	`pow-prod-down_binary64` `associate-l_binary64`
6×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `associate-*l/_binary64`
3×	`cbrt-undiv_binary64` `associate-/l_binary64` `times-frac_binary64` `div-exp_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64`
1×	`associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 88

Calls

4 calls:

14.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))) PI.f64))
11.0ms	(.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))) PI.f64)
9.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
6.0ms	(.f64 3 (.f64 v v))

series712.0ms (12.8%)

Counts

4 → 12

Calls

4 calls:

318.0ms	(/.f64 (-.f64 1 (.f64 (.f64 v v) 5)) (.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))) PI.f64))
190.0ms	(.f64 (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (*.f64 v v)))))) PI.f64)
167.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
37.0ms	(.f64 3 (.f64 v v))

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5149	2510

prune183.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	101	7	108

Merged error: 0.0b

Counts

108 → 7

Compiler

Compiled 3658 to 2374 computations (35.1% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 v v))
0.3b	(/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))
0.4b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 (*.f64 v v) 5))) PI.f64))
0.5b	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))

rewrite80.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
32×	`times-frac_binary64`
27×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
20×	`sqrt-prod_binary64`
18×	`associate-l_binary64`
13×	`pow1_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`sqrt-div_binary64`
6×	`associate-/l*_binary64`
5×	`pow-prod-down_binary64` `unswap-sqr_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
3×	`div-inv_binary64` `*-commutative_binary64`
2×	`associate-/l/_binary64`
1×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 132

Calls

4 calls:

26.0ms	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 (*.f64 v v) 5))) PI.f64))
13.0ms	(/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))
9.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
7.0ms	(.f64 3 (.f64 v v))

series768.0ms (13.8%)

Counts

4 → 12

Calls

4 calls:

324.0ms	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 (*.f64 v v) 5))) PI.f64))
255.0ms	(/.f64 (sqrt.f64 (-.f64 1 (.f64 (.f64 v v) 5))) (.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))))
151.0ms	(.f64 t (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v))))))
37.0ms	(.f64 3 (.f64 v v))

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5042	4875

prune328.0ms (5.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	2	2	4
Picked	1	0	1
Done	1	1	2
Total	144	7	151

Merged error: 0b

Counts

151 → 7

Compiler

Compiled 6448 to 4196 computations (34.9% saved)

regimes124.0ms (2.2%)

Compiler: Compiled 1607 to 1189 computations (26% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	43
1	78	43

end0.0ms (0%)

sample917.0ms (16.5%)

Algorithm

1×

intervals

Results

513.0ms	8000×	body	128	valid
1.0ms	12×	body	128	nan

Compiler

Compiled 364 to 270 computations (25.8% saved)

Details

analyze107.0ms (1.9%)

sample24.0ms (0.4%)

simplify50.0ms (0.9%)

prune5.0ms (0.1%)

localize18.0ms (0.3%)

rewrite52.0ms (0.9%)

series600.0ms (10.8%)

simplify70.0ms (1.3%)

prune194.0ms (3.5%)

localize19.0ms (0.3%)

rewrite57.0ms (1%)

series770.0ms (13.8%)

simplify58.0ms (1%)

prune209.0ms (3.8%)

localize16.0ms (0.3%)

rewrite52.0ms (0.9%)

series712.0ms (12.8%)

simplify53.0ms (0.9%)

prune183.0ms (3.3%)

localize18.0ms (0.3%)

rewrite80.0ms (1.4%)

series768.0ms (13.8%)

simplify84.0ms (1.5%)

prune328.0ms (5.9%)

regimes124.0ms (2.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample917.0ms (16.5%)

Profiling