Details

analyze932.0ms (6.9%)

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)

sample59.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	43×	body	2048	valid
10.0ms	156×	body	128	valid
6.0ms	27×	body	1024	valid
5.0ms	16×	body	4096	valid
2.0ms	10×	body	512	valid
1.0ms	23×	body	128	nan
0.0ms	7×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify274.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune8.0ms (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

Error

37.3b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.4b	(-.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))
23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite48.0ms (0.4%)

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

8 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))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

series641.0ms (4.8%)

Counts

4 → 56

Calls

4 calls:

220.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
154.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
139.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
128.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)

Compiler

Compiled 1366 to 1118 computations (18.2% saved)

simplify126.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5860	2569

prune274.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	8	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Error

6.2b

Counts

143 → 8

Compiler

Compiled 2450 to 456 computations (81.4% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

10.4b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
5.3b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
0.8b	(-.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))
5.3b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
10.4b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite101.0ms (0.8%)

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

8 calls:

30.0ms	(/.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)))))
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

series818.0ms (6.1%)

Counts

4 → 56

Calls

4 calls:

268.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
206.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
187.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
157.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1831 to 1334 computations (27.1% saved)

simplify167.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4937	8543
1	4937	8543

prune322.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	270	3	273
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	274	7	281

Error

6.2b

Counts

281 → 7

Compiler

Compiled 7160 to 954 computations (86.7% saved)

localize19.0ms (0.1%)

Local error

Found 8 expressions with local error:

23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.8b	(-.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))))
0.3b	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.3b	(/.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))
23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite56.0ms (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

8 calls:

14.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
11.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
11.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))

series730.0ms (5.4%)

Counts

4 → 61

Calls

4 calls:

261.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
171.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
158.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
140.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

Compiler

Compiled 1639 to 1332 computations (18.7% saved)

simplify108.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4966	2194
1	4966	2194

prune162.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	133	7	140

Error

6.2b

Counts

140 → 7

Compiler

Compiled 2244 to 541 computations (75.9% saved)

localize24.0ms (0.2%)

Local error

Found 8 expressions with local error:

17.2b	(/.f64 (neg.f64 (.f64 a c)) (.f64 a (+.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))
0.5b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.1b	(.f64 a (+.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))
17.2b	(/.f64 (neg.f64 (.f64 a c)) (.f64 a (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

8 calls:

20.0ms	(/.f64 (neg.f64 (.f64 a c)) (.f64 a (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
6.0ms	(-.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))))
0.0ms	(.f64 a (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))

series859.0ms (6.4%)

Counts

4 → 61

Calls

4 calls:

322.0ms	(/.f64 (neg.f64 (.f64 a c)) (.f64 a (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
203.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
186.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
147.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1933 to 1421 computations (26.5% saved)

simplify101.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4963	2058
1	4963	2058

prune120.0ms (0.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	131	7	138

Error

6.2b

Counts

138 → 7

Compiler

Compiled 2396 to 468 computations (80.5% saved)

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	633	1884
1	633	1884

regimes960.0ms (7.1%)

Accuracy

Total 1.1b remaining (16.9%)

Threshold costs 0b (0%)

Compiler

Compiled 3507 to 2013 computations (42.6% saved)

bsearch111.0ms (0.8%)

Steps

Iters	Range	Point
4	3.2475280783869584e+131	5.5931955652772054e+131	4.51778818962992e+131
10	-3.0513825003363876e-243	-3.1032370431554206e-258	-5.584163476997717e-250
5	-4.143108432896019e+151	-1.2948687948194796e+151	-1.575768253013841e+151

Iters

Range

Point

3.2475280783869584e+131

5.5931955652772054e+131

4.51778818962992e+131

-3.0513825003363876e-243

-3.1032370431554206e-258

-5.584163476997717e-250

-4.143108432896019e+151

-1.2948687948194796e+151

-1.575768253013841e+151

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	94	75
1	94	75

end0.0ms (0%)

sample6.3s (46.8%)

Algorithm

1×

intervals

Results

393.0ms	1185×	body	2048	valid
345.0ms	5136×	body	128	valid
182.0ms	716×	body	1024	valid
158.0ms	397×	body	4096	valid
77.0ms	400×	body	512	valid
52.0ms	807×	body	128	nan
21.0ms	166×	body	256	valid
16.0ms	232×	body	128	invalid

Compiler

Compiled 3615 to 2065 computations (42.9% saved)

Pareto

-0.09374289400138648

Details

analyze932.0ms (6.9%)

sample59.0ms (0.4%)

simplify274.0ms (2%)

prune8.0ms (0.1%)

localize10.0ms (0.1%)

rewrite48.0ms (0.4%)

series641.0ms (4.8%)

simplify126.0ms (0.9%)

prune274.0ms (2%)

localize11.0ms (0.1%)

rewrite101.0ms (0.8%)

series818.0ms (6.1%)

simplify167.0ms (1.2%)

prune322.0ms (2.4%)

localize19.0ms (0.1%)

rewrite56.0ms (0.4%)

series730.0ms (5.4%)

simplify108.0ms (0.8%)

prune162.0ms (1.2%)

localize24.0ms (0.2%)

rewrite45.0ms (0.3%)

series859.0ms (6.4%)

simplify101.0ms (0.8%)

prune120.0ms (0.9%)

simplify51.0ms (0.4%)

regimes960.0ms (7.1%)

bsearch111.0ms (0.8%)

simplify5.0ms (0%)

end0.0ms (0%)

sample6.3s (46.8%)

Profiling