Details

analyze261.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms	143×	body	160	valid
8.0ms	282×	pre	80	true
6.0ms	113×	body	80	valid
1.0ms	26×	body	80	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify114.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	928	24
1	928	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 27.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
27.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series522.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
128.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
74.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify135.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	6773	2041

prune107.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	6	87

Merged error: 0.4b

Counts

87 → 6

Compiler

Compiled 2093 to 1257 computations (39.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.4b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`associate-/l*_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `insert-posit16` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 102

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
14.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series853.0ms (14.2%)

Counts

4 → 12

Calls

4 calls:

366.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
292.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
124.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
71.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify128.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4929	3120
1	4929	3120

prune173.0ms (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	105	9	114
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	111	9	120

Merged error: 0b

Counts

120 → 9

Compiler

Compiled 3359 to 2078 computations (38.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64` `insert-posit16`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 75

Calls

4 calls:

10.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
6.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series661.0ms (11%)

Counts

4 → 12

Calls

4 calls:

332.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
141.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
71.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify156.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4914	2037
1	4914	2037

prune115.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	87	9	96

Merged error: 0b

Counts

96 → 9

Compiler

Compiled 2448 to 1533 computations (37.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.3b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`div-inv_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

19.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
10.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series757.0ms (12.6%)

Counts

4 → 12

Calls

4 calls:

349.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
220.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
123.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
65.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify151.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4946	2689
1	4946	2689

prune135.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	110	9	119

Merged error: 0b

Counts

119 → 9

Compiler

Compiled 2804 to 1771 computations (36.8% saved)

regimes75.0ms (1.2%)

Compiler: Compiled 813 to 609 computations (25.1% saved)

bsearch0.0ms (0%)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	64	24
1	64	24

end0.0ms (0%)

sample1.4s (23.2%)

Algorithm

1×

intervals

Results

430.0ms	4450×	body	160	valid
275.0ms	8806×	pre	80	true
181.0ms	3550×	body	80	valid
39.0ms	806×	body	80	nan

Compiler

Compiled 315 to 237 computations (24.8% saved)

Details

analyze261.0ms (4.3%)

sample41.0ms (0.7%)

simplify114.0ms (1.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.6%)

series522.0ms (8.7%)

simplify135.0ms (2.2%)

prune107.0ms (1.8%)

localize17.0ms (0.3%)

rewrite50.0ms (0.8%)

series853.0ms (14.2%)

simplify128.0ms (2.1%)

prune173.0ms (2.9%)

localize12.0ms (0.2%)

rewrite31.0ms (0.5%)

series661.0ms (11%)

simplify156.0ms (2.6%)

prune115.0ms (1.9%)

localize12.0ms (0.2%)

rewrite47.0ms (0.8%)

series757.0ms (12.6%)

simplify151.0ms (2.5%)

prune135.0ms (2.2%)

regimes75.0ms (1.2%)

bsearch0.0ms (0%)

simplify9.0ms (0.2%)

end0.0ms (0%)

sample1.4s (23.2%)

Profiling