Details

analyze606.0ms (9.9%)

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%	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)

sample36.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	173×	body	128	valid
7.0ms	35×	body	2048	valid
4.0ms	15×	body	4096	valid
4.0ms	22×	body	1024	valid
1.0ms	6×	body	512	valid
1.0ms	17×	body	128	nan
0.0ms	9×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify192.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	309	18
1	309	18

prune8.0ms (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

Merged error: 34.6b

Counts

2 → 2

Compiler

Compiled 62 to 47 computations (24.2% saved)

localize11.0ms (0.2%)

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)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.4b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite47.0ms (0.8%)

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:

18.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series476.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
121.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
119.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4836	1903
1	4836	1903

prune380.0ms (6.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	87	7	94

Merged error: 5.8b

Counts

94 → 7

Compiler

Compiled 7661 to 3694 computations (51.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
2.4b	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
8.6b	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite63.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`times-frac_binary64`
60×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
13×	`sqrt-prod_binary64`
10×	`associate-/r*_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `flip--_binary64`
6×	`cancel-sign-sub-inv_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`diff-log_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64`

Counts

4 → 141

Calls

4 calls:

19.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
13.0ms	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series893.0ms (14.6%)

Counts

4 → 12

Calls

4 calls:

384.0ms	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
293.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
120.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
97.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4930	4513
1	4930	4513

prune238.0ms (3.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	154	6	160

Merged error: 5.7b

Counts

160 → 6

Compiler

Compiled 5905 to 1859 computations (68.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
11×	`sqrt-prod_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`associate-/r*_binary64` `cancel-sign-sub-inv_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`diff-log_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 95

Calls

4 calls:

15.0ms	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series597.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

338.0ms	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
117.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
94.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
48.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5180	2471

prune104.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	107	6	113

Merged error: 5.7b

Counts

113 → 6

Compiler

Compiled 2788 to 904 computations (67.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 c (/.f64 -1 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
14×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`distribute-lft-out_binary64`
3×	`associate-l_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 76

Calls

4 calls:

14.0ms	(.f64 c (/.f64 -1 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series585.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

325.0ms	(.f64 c (/.f64 -1 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
106.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
98.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
56.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify47.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5077	1635

prune90.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	87	7	94

Merged error: 5.7b

Counts

94 → 7

Compiler

Compiled 2272 to 953 computations (58.1% saved)

regimes156.0ms (2.5%)

Compiler: Compiled 300 to 270 computations (10% saved)

bsearch97.0ms (1.6%)

Steps

Iters	Range	Point
7	7.908407481357268e+108	9.535715968496006e+110	6.131514456820294e+110
10	-4.822286377140539e-234	-5.129087287670054e-244	-2.8524283535901695e-236
10	-3.6543682154259916e+104	-4.426090594272416e+89	-7.831503509870294e+92

Iters

Range

Point

7.908407481357268e+108

9.535715968496006e+110

6.131514456820294e+110

-4.822286377140539e-234

-5.129087287670054e-244

-2.8524283535901695e-236

-3.6543682154259916e+104

-4.426090594272416e+89

-7.831503509870294e+92

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	116	82
1	116	82

end0.0ms (0%)

sample1.1s (18.6%)

Algorithm

1×

intervals

Results

229.0ms	5252×	body	128	valid
226.0ms	1133×	body	2048	valid
110.0ms	701×	body	1024	valid
87.0ms	352×	body	4096	valid
44.0ms	363×	body	512	valid
36.0ms	789×	body	128	nan
16.0ms	199×	body	256	valid
12.0ms	269×	body	128	invalid

Compiler

Compiled 167 to 130 computations (22.2% saved)

Details

analyze606.0ms (9.9%)

sample36.0ms (0.6%)

simplify192.0ms (3.1%)

prune8.0ms (0.1%)

localize11.0ms (0.2%)

rewrite47.0ms (0.8%)

series476.0ms (7.8%)

simplify72.0ms (1.2%)

prune380.0ms (6.2%)

localize10.0ms (0.2%)

rewrite63.0ms (1%)

series893.0ms (14.6%)

simplify95.0ms (1.6%)

prune238.0ms (3.9%)

localize11.0ms (0.2%)

rewrite43.0ms (0.7%)

series597.0ms (9.7%)

simplify81.0ms (1.3%)

prune104.0ms (1.7%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series585.0ms (9.5%)

simplify47.0ms (0.8%)

prune90.0ms (1.5%)

regimes156.0ms (2.5%)

bsearch97.0ms (1.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (18.6%)

Profiling