Details

analyze2.5s (0.4%)

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%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample216.0ms (0%)

Algorithm

1×

intervals

Results

71.0ms	181×	body	128	valid
21.0ms	29×	body	2048	valid
15.0ms	15×	body	4096	valid
12.0ms	12×	body	1024	valid
10.0ms	12×	body	256	valid
2.0ms	23×	body	128	nan
2.0ms	7×	body	512	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify1.0s (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (539.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune30.0ms (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: 30.3b

Counts

2 → 2

Compiler

Compiled 37 to 28 computations (24.3% saved)

localize48.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.8b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite487.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `times-frac_binary64`
10×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

197.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
60.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
42.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
27.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

series1.0s (0.2%)

Counts

4 → 12

Calls

4 calls:

361.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
340.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
233.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
105.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify627.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (536.0ms)

Iter	Nodes	Cost
0	4956	1903
1	4956	1903

prune1.8s (0.3%)

Pruning

47 alts after pruning (46 fresh and 1 done)

	Pruned	Kept	Total
New	47	45	92
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	47	47	94

Merged error: 5.9b

Counts

94 → 47

Compiler

Compiled 2853 to 933 computations (67.3% saved)

localize50.0ms (0%)

Local error

Found 4 expressions with local error:

1.8b	(+.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
22.0b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
22.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite136.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-pow1_binary64` `sqrt-div_binary64`
22×	`pow1_binary64`
11×	`pow1/2_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `add-sqr-sqrt_binary64` `flip--_binary64`
7×	`sqrt-prod_binary64`
6×	`add-cube-cbrt_binary64`
5×	`pow-prod-up_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64`
2×	`distribute-lft-out_binary64` `associate-r/_binary64` `associate-l/_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `pow-plus_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64` `+-commutative_binary64` `flip-+_binary64` `pow2_binary64`

Counts

4 → 77

Calls

4 calls:

49.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
23.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
21.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
13.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series800.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

254.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
229.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
194.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
122.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))

simplify287.0ms (0%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (205.0ms)

Iter	Nodes	Cost
0	4879	1563
1	4879	1563

prune2.7s (0.5%)

Pruning

60 alts after pruning (58 fresh and 2 done)

	Pruned	Kept	Total
New	74	15	89
Fresh	2	43	45
Picked	0	1	1
Done	0	1	1
Total	76	60	136

Merged error: 5.9b

Counts

136 → 60

Compiler

Compiled 3717 to 1342 computations (63.9% saved)

localize60.0ms (0%)

Local error

Found 4 expressions with local error:

1.8b	(+.f64 (neg.f64 b_2) (pow.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) 1/2))
22.0b	(pow.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) 1/2)
22.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite152.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64`
14×	`pow-pow_binary64`
11×	`*-un-lft-identity_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64` `add-exp-log_binary64`
6×	`sqrt-prod_binary64`
5×	`pow-prod-up_binary64`
4×	`add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `pow-sqr_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sqrt-pow2_binary64` `neg-sub0_binary64` `sqr-pow_binary64` `associate-+l-_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `unpow1/2_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `pow2_binary64`

Counts

4 → 76

Calls

4 calls:

53.0ms	(pow.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) 1/2)
30.0ms	(+.f64 (neg.f64 b_2) (pow.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) 1/2))
19.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series975.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(pow.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) 1/2)
240.0ms	(+.f64 (neg.f64 b_2) (pow.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) 1/2))
236.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
232.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify335.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (233.0ms)

Iter	Nodes	Cost
0	5076	1175

prune3.2s (0.5%)

Pruning

76 alts after pruning (73 fresh and 3 done)

	Pruned	Kept	Total
New	70	18	88
Fresh	2	55	57
Picked	0	1	1
Done	0	2	2
Total	72	76	148

Merged error: 5.8b

Counts

148 → 76

Compiler

Compiled 3828 to 1493 computations (61% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite74.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 86

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
19.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
12.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series841.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

354.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
231.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
141.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
111.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify307.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (176.0ms)

Iter	Nodes	Cost
0	4916	2170
1	4916	2170

prune2.9s (0.5%)

Pruning

101 alts after pruning (97 fresh and 4 done)

	Pruned	Kept	Total
New	69	29	98
Fresh	4	68	72
Picked	0	1	1
Done	0	3	3
Total	73	101	174

Merged error: 5.8b

Counts

174 → 101

Compiler

Compiled 1941 to 336 computations (82.7% saved)

regimes16.4s (2.7%)

Compiler: Compiled 18581 to 10912 computations (41.3% saved)

bsearch9.4min (93.8%)

Steps

Iters	Range		Point
8	3.038584557487637e-42	1.3181125444953113e-37	6.4659222647242875e-40
7	-4.61083063234545e+65	-7.07741903210063e+63	-4.511782849328831e+65

Compiler

Compiled 1 to 3 computations (-200% saved)

Details

analyze2.5s (0.4%)

sample216.0ms (0%)

simplify1.0s (0.2%)

prune30.0ms (0%)

localize48.0ms (0%)

rewrite487.0ms (0.1%)

series1.0s (0.2%)

simplify627.0ms (0.1%)

prune1.8s (0.3%)

localize50.0ms (0%)

rewrite136.0ms (0%)

series800.0ms (0.1%)

simplify287.0ms (0%)

prune2.7s (0.5%)

localize60.0ms (0%)

rewrite152.0ms (0%)

series975.0ms (0.2%)

simplify335.0ms (0.1%)

prune3.2s (0.5%)

localize18.0ms (0%)

rewrite74.0ms (0%)

series841.0ms (0.1%)

simplify307.0ms (0.1%)

prune2.9s (0.5%)

regimes16.4s (2.7%)

bsearch9.4min (93.8%)

Profiling