Details

analyze606.0ms (8.8%)

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)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	47×	body	2048	valid
7.0ms	157×	body	128	valid
4.0ms	24×	body	1024	valid
2.0ms	7×	body	4096	valid
1.0ms	32×	body	128	nan
1.0ms	11×	body	512	valid
1.0ms	10×	body	256	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify192.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	309	18
1	309	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: 37.2b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.1%)

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)
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite49.0ms (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:

16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series494.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
121.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4877	2170
1	4877	2170

prune107.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	8	99

Merged error: 6.3b

Counts

99 → 8

Compiler

Compiled 2086 to 419 computations (79.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.7b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
11.8b	(/.f64 (neg.f64 (.f64 a c)) (+.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)))

rewrite66.0ms (1%)

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:

17.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
10.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series832.0ms (12.1%)

Counts

4 → 12

Calls

4 calls:

366.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
288.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
122.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
56.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify113.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5345	8089

prune199.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	229	8	237

Merged error: 6.2b

Counts

237 → 8

Compiler

Compiled 6624 to 906 computations (86.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
1.0b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.4b	(-.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

55×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
15×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
12×	`distribute-lft-out_binary64`
10×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `neg-mul-1_binary64`
4×	`associate-/r*_binary64`
3×	`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` `neg-sub0_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_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 → 109

Calls

4 calls:

11.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
7.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series628.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

347.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
116.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
106.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
59.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4961	3067
1	4961	3067

prune106.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	121	8	129

Merged error: 6.2b

Counts

129 → 8

Compiler

Compiled 2888 to 696 computations (75.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite60.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64`
124×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
71×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
24×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
7×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 164

Calls

4 calls:

19.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series512.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

230.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
115.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
111.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
56.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify107.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5062	5163

prune143.0ms (2.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	175	9	184

Merged error: 6.2b

Counts

184 → 9

Compiler

Compiled 4314 to 825 computations (80.9% saved)

regimes646.0ms (9.4%)

Compiler: Compiled 3132 to 1928 computations (38.4% saved)

bsearch96.0ms (1.4%)

Steps

Iters	Range	Point
9	2.469885637543814e+144	1.0090532180616067e+153	8.735804081561547e+144
8	-4.1256061386695466e-284	-1.1339359672340362e-287	-5.036860681113749e-287
8	-8.518981934126228e+92	-1.4741903711088306e+88	-1.4440350239887892e+90

Iters

Range

Point

2.469885637543814e+144

1.0090532180616067e+153

8.735804081561547e+144

-4.1256061386695466e-284

-1.1339359672340362e-287

-5.036860681113749e-287

-8.518981934126228e+92

-1.4741903711088306e+88

-1.4440350239887892e+90

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	133	79
1	133	79

end0.0ms (0%)

sample1.6s (23.8%)

Algorithm

1×

intervals

Results

234.0ms	1153×	body	2048	valid
223.0ms	5142×	body	128	valid
123.0ms	769×	body	1024	valid
106.0ms	415×	body	4096	valid
42.0ms	347×	body	512	valid
32.0ms	789×	body	128	nan
14.0ms	174×	body	256	valid
11.0ms	257×	body	128	invalid

Compiler

Compiled 832 to 508 computations (38.9% saved)

Details

analyze606.0ms (8.8%)

sample41.0ms (0.6%)

simplify192.0ms (2.8%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite49.0ms (0.7%)

series494.0ms (7.2%)

simplify72.0ms (1.1%)

prune107.0ms (1.5%)

localize11.0ms (0.2%)

rewrite66.0ms (1%)

series832.0ms (12.1%)

simplify113.0ms (1.6%)

prune199.0ms (2.9%)

localize12.0ms (0.2%)

rewrite38.0ms (0.6%)

series628.0ms (9.1%)

simplify82.0ms (1.2%)

prune106.0ms (1.5%)

localize10.0ms (0.1%)

rewrite60.0ms (0.9%)

series512.0ms (7.4%)

simplify107.0ms (1.6%)

prune143.0ms (2.1%)

regimes646.0ms (9.4%)

bsearch96.0ms (1.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.6s (23.8%)

Profiling