Details

analyze1.3s (11.5%)

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample80.0ms (0.7%)

Algorithm

1×

intervals

Results

51.0ms	256×	body	128	valid
3.0ms	20×	body	128	nan
2.0ms	11×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify466.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (149.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune25.0ms (0.2%)

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: 20.0b

Counts

2 → 2

Compiler

Compiled 110 to 76 computations (30.9% saved)

localize48.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite72.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64`
4×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

25.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
12.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series1.1s (9.1%)

Counts

4 → 12

Calls

4 calls:

333.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a)))) b) (.f64 2 a))
259.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
242.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
222.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify104.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4993	2035
1	4993	2035

prune394.0ms (3.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	10	86
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 7.3b

Counts

88 → 11

Compiler

Compiled 4192 to 2523 computations (39.8% saved)

localize46.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`difference-of-squares_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `distribute-lft-out--_binary64`

Counts

4 → 59

Calls

4 calls:

16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series880.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

243.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
215.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
213.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
208.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify167.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	4833	1470
1	4833	1470

prune342.0ms (3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	70	12	82

Merged error: 7.3b

Counts

82 → 12

Compiler

Compiled 4577 to 2766 computations (39.6% saved)

localize54.0ms (0.5%)

Local error

Found 4 expressions with local error:

7.9b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

11.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
7.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))

series914.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

243.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
236.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
223.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
212.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5244	1361

prune300.0ms (2.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	68	12	80

Merged error: 7.3b

Counts

80 → 12

Compiler

Compiled 4050 to 2461 computations (39.2% saved)

localize44.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite68.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `distribute-lft-out_binary64` `sqrt-prod_binary64`
5×	`associate-/l*_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`distribute-rgt-neg-in_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`associate-/r*_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

27.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
18.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series1.1s (9.3%)

Counts

4 → 12

Calls

4 calls:

393.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
236.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
228.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
222.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify99.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4930	1910
1	4930	1910

prune277.0ms (2.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	85	12	97

Merged error: 7.3b

Counts

97 → 12

Compiler

Compiled 3727 to 2135 computations (42.7% saved)

regimes521.0ms (4.5%)

Compiler: Compiled 2190 to 1502 computations (31.4% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 38 to 26 computations (31.6% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	148	485
1	148	485

end0.0ms (0%)

sample3.0s (26.1%)

Algorithm

1×

intervals

Results

1.4s	8000×	body	128	valid
107.0ms	646×	body	128	nan
62.0ms	371×	body	128	invalid

Compiler

Compiled 887 to 578 computations (34.8% saved)

Details

analyze1.3s (11.5%)

sample80.0ms (0.7%)

simplify466.0ms (4%)

prune25.0ms (0.2%)

localize48.0ms (0.4%)

rewrite72.0ms (0.6%)

series1.1s (9.1%)

simplify104.0ms (0.9%)

prune394.0ms (3.4%)

localize46.0ms (0.4%)

rewrite45.0ms (0.4%)

series880.0ms (7.6%)

simplify167.0ms (1.4%)

prune342.0ms (3%)

localize54.0ms (0.5%)

rewrite41.0ms (0.4%)

series914.0ms (7.9%)

simplify76.0ms (0.7%)

prune300.0ms (2.6%)

localize44.0ms (0.4%)

rewrite68.0ms (0.6%)

series1.1s (9.3%)

simplify99.0ms (0.9%)

prune277.0ms (2.4%)

regimes521.0ms (4.5%)

bsearch6.0ms (0.1%)

simplify12.0ms (0.1%)

end0.0ms (0%)

sample3.0s (26.1%)

Profiling