Details

analyze934.0ms (16.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1992	80
1	1992	80
0	3	3
1	3	3

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)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

7.0ms	156×	body	128	valid
6.0ms	32×	body	2048	valid
5.0ms	32×	body	1024	valid
4.0ms	15×	body	4096	valid
2.0ms	16×	body	512	valid
1.0ms	24×	body	128	nan
0.0ms	5×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

prune5.0ms (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: 33.4b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% 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)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.7b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
20.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite45.0ms (0.8%)

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×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_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`

Counts

4 → 96

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
9.0ms	(-.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)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series219.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
62.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
56.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
28.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4941	2578
1	4941	2578

prune108.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	99	9	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	9	109

Merged error: 4.1b

Counts

109 → 9

Compiler

Compiled 2419 to 464 computations (80.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.5b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
8.9b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
20.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`difference-of-squares_binary64`
10×	`associate-/r/_binary64`
9×	`associate-/r*_binary64` `sqrt-prod_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`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` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 124

Calls

4 calls:

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

series418.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
150.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
55.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
26.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5043	3819

prune113.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	137	8	145

Merged error: 4.1b

Counts

145 → 8

Compiler

Compiled 3507 to 580 computations (83.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.9b	(.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
4.5b	(/.f64 (.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))) a)
20.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
24×	`-un-lft-identity_binary64` `associate-r*_binary64`
22×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64` `sqrt-prod_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `associate-l*_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
2×	`associate-*r/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

15.0ms	(.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
13.0ms	(/.f64 (.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series414.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
147.0ms	(/.f64 (.f64 a (/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))) a)
54.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
27.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4913	2126
1	4913	2126

prune80.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	106	8	114

Merged error: 4.1b

Counts

114 → 8

Compiler

Compiled 2480 to 516 computations (79.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.7b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
20.2b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite55.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
132×	`add-sqr-sqrt_binary64`
131×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
19×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 182

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
11.0ms	(-.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)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series235.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
59.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
49.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
27.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify96.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5030	5933

prune152.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Merged error: 4.1b

Counts

202 → 8

Compiler

Compiled 4889 to 905 computations (81.5% saved)

regimes653.0ms (11.5%)

Compiler: Compiled 3240 to 1969 computations (39.2% saved)

bsearch84.0ms (1.5%)

Steps

Iters	Range	Point
8	4.4010758541015276e+63	1.9617957783804162e+67	1.8022734823957402e+67
6	5.570762419876352e-192	4.132697234470958e-191	5.807851341715086e-192
9	-1.9544929856771155e+136	-4.4114096596996475e+130	-6.744634285002952e+133

Iters

Range

Point

4.4010758541015276e+63

1.9617957783804162e+67

1.8022734823957402e+67

5.570762419876352e-192

4.132697234470958e-191

5.807851341715086e-192

-1.9544929856771155e+136

-4.4114096596996475e+130

-6.744634285002952e+133

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	121	79
1	121	79

end0.0ms (0%)

sample1.6s (28.2%)

Algorithm

1×

intervals

Results

233.0ms	1129×	body	2048	valid
223.0ms	5186×	body	128	valid
118.0ms	766×	body	1024	valid
98.0ms	397×	body	4096	valid
42.0ms	361×	body	512	valid
36.0ms	847×	body	128	nan
13.0ms	161×	body	256	valid
11.0ms	270×	body	128	invalid

Compiler

Compiled 848 to 515 computations (39.3% saved)

Details

analyze934.0ms (16.4%)

sample39.0ms (0.7%)

simplify72.0ms (1.3%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite45.0ms (0.8%)

series219.0ms (3.8%)

simplify71.0ms (1.2%)

prune108.0ms (1.9%)

localize9.0ms (0.2%)

rewrite43.0ms (0.8%)

series418.0ms (7.3%)

simplify77.0ms (1.4%)

prune113.0ms (2%)

localize10.0ms (0.2%)

rewrite44.0ms (0.8%)

series414.0ms (7.3%)

simplify90.0ms (1.6%)

prune80.0ms (1.4%)

localize10.0ms (0.2%)

rewrite55.0ms (1%)

series235.0ms (4.1%)

simplify96.0ms (1.7%)

prune152.0ms (2.7%)

regimes653.0ms (11.5%)

bsearch84.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (28.2%)

Profiling