Details

analyze611.0ms (9.6%)

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)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	177×	body	128	valid
7.0ms	34×	body	2048	valid
6.0ms	12×	body	4096	valid
4.0ms	23×	body	1024	valid
1.0ms	27×	body	128	nan
1.0ms	8×	body	512	valid
0.0ms	7×	body	128	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify171.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune6.0ms (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: 31.5b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.2%)

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)
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite46.0ms (0.7%)

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:

19.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series247.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
65.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
31.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4916	2170
1	4916	2170

prune106.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	9	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	10	99

Merged error: 5.9b

Counts

99 → 10

Compiler

Compiled 2094 to 428 computations (79.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
2.9b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
10.5b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
21.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite59.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
31×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_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 → 217

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.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))

series416.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
148.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
52.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
26.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify112.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5794	8071

prune189.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	230	9	239

Merged error: 5.8b

Counts

239 → 9

Compiler

Compiled 6613 to 905 computations (86.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.5b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite27.0ms (0.4%)

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`
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` `cancel-sign-sub-inv_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 → 72

Calls

4 calls:

8.0ms	(/.f64 c (+.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))

series299.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
54.0ms	(+.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)))
26.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4968	1696
1	4968	1696

prune67.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	84	9	93

Merged error: 5.8b

Counts

93 → 9

Compiler

Compiled 1746 to 446 computations (74.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.3b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
10.6b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
15.3b	(+.f64 b_2 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
21.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
21×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
8×	`distribute-lft-out_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `log-prod_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-sum_binary64` `associate-/l*_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
5×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
4×	`associate-/r*_binary64` `sqrt-div_binary64`
3×	`log-pow_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `exp-diff_binary64` `log-div_binary64` `flip--_binary64` `flip-+_binary64`
1×	`neg-sub0_binary64` `cbrt-undiv_binary64` `rem-exp-log_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `distribute-frac-neg_binary64` `sum-log_binary64`

Counts

4 → 99

Calls

4 calls:

12.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
9.0ms	(+.f64 b_2 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
6.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series969.0ms (15.2%)

Counts

4 → 12

Calls

4 calls:

730.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
97.0ms	(+.f64 b_2 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
88.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
54.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5018	2738

prune83.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	111	9	120

Merged error: 5.8b

Counts

120 → 9

Compiler

Compiled 2828 to 549 computations (80.6% saved)

regimes729.0ms (11.5%)

Compiler: Compiled 3804 to 2372 computations (37.6% saved)

bsearch85.0ms (1.3%)

Steps

Iters	Range	Point
8	7.482650775739311e+127	2.0282509964117963e+130	1.3087301913739546e+130
6	-4.319302067298372e-220	-8.600580235552874e-221	-8.836772076318503e-221
9	-2.5295753076693812e+138	-3.1670677211042097e+132	-1.3685265296938615e+138

Iters

Range

Point

7.482650775739311e+127

2.0282509964117963e+130

1.3087301913739546e+130

-4.319302067298372e-220

-8.600580235552874e-221

-8.836772076318503e-221

-2.5295753076693812e+138

-3.1670677211042097e+132

-1.3685265296938615e+138

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	79
1	102	79

end0.0ms (0%)

sample1.8s (28.2%)

Algorithm

1×

intervals

Results

256.0ms	1199×	body	2048	valid
246.0ms	5140×	body	128	valid
121.0ms	716×	body	1024	valid
111.0ms	419×	body	4096	valid
45.0ms	363×	body	512	valid
37.0ms	821×	body	128	nan
14.0ms	163×	body	256	valid
12.0ms	270×	body	128	invalid

Compiler

Compiled 1000 to 619 computations (38.1% saved)

Details

analyze611.0ms (9.6%)

sample40.0ms (0.6%)

simplify171.0ms (2.7%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite46.0ms (0.7%)

series247.0ms (3.9%)

simplify78.0ms (1.2%)

prune106.0ms (1.7%)

localize11.0ms (0.2%)

rewrite59.0ms (0.9%)

series416.0ms (6.5%)

simplify112.0ms (1.8%)

prune189.0ms (3%)

localize11.0ms (0.2%)

rewrite27.0ms (0.4%)

series299.0ms (4.7%)

simplify84.0ms (1.3%)

prune67.0ms (1.1%)

localize14.0ms (0.2%)

rewrite41.0ms (0.6%)

series969.0ms (15.2%)

simplify52.0ms (0.8%)

prune83.0ms (1.3%)

regimes729.0ms (11.5%)

bsearch85.0ms (1.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.8s (28.2%)

Profiling