Details

analyze1.1s (10.8%)

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)

sample42.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	178×	body	128	valid
7.0ms	33×	body	2048	valid
4.0ms	24×	body	1024	valid
2.0ms	10×	body	512	valid
2.0ms	6×	body	4096	valid
1.0ms	19×	body	128	nan
1.0ms	5×	body	256	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

prune5.0ms (0%)

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

Error

35.1b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize11.0ms (0.1%)

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)
0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite180.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

34.8b

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×	`diff-log_binary64` `associate-/r*_binary64`
2×	`sqrt-div_binary64` `sub-neg_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `neg-sub0_binary64` `associate--l-_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 96

Calls

4 calls:

15.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
12.0ms	(/.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))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2360 to 368 computations (84.4% saved)

series822.0ms (7.8%)

Error

7.7b

Counts

4 → 81

Calls

4 calls:

216.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
184.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
172.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
155.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 3241 to 2280 computations (29.7% saved)

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5857	3911

prune192.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	165	12	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	166	12	178

Error

7.6b

Counts

178 → 12

Compiler

Compiled 3526 to 865 computations (75.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite157.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

31×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `associate-r_binary64`
11×	`times-frac_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64`
8×	`sqrt-prod_binary64`
7×	`pow1_binary64` `cancel-sign-sub-inv_binary64` `associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`difference-of-squares_binary64` `distribute-lft-out--_binary64` `prod-exp_binary64`
3×	`diff-log_binary64` `unswap-sqr_binary64`
2×	`sqrt-div_binary64` `sub-neg_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `neg-sub0_binary64` `associate--l-_binary64` `pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64` `un-div-inv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

31.0ms	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
9.0ms	(-.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))

Compiler

Compiled 2454 to 640 computations (73.9% saved)

series811.0ms (7.7%)

Error

7.6b

Counts

4 → 81

Calls

4 calls:

214.0ms	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
192.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
176.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
159.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3523 to 2566 computations (27.2% saved)

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4957	3537
1	4957	3537

prune180.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	172	3	175
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	176	11	187

Error

7.6b

Counts

187 → 11

Compiler

Compiled 3537 to 1148 computations (67.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.3b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
16.3b	(/.f64 (*.f64 a c) a)
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite94.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

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

Counts

4 → 63

Calls

4 calls:

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

Compiler

Compiled 1577 to 295 computations (81.3% saved)

series610.0ms (5.8%)

Error

7.6b

Counts

4 → 67

Calls

4 calls:

228.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
154.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
144.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
23.0ms	(/.f64 (*.f64 a c) a)

Compiler

Compiled 3423 to 2075 computations (39.4% saved)

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5275	2016

prune133.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	131	10	141

Error

7.6b

Counts

141 → 10

Compiler

Compiled 2833 to 702 computations (75.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.3b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite112.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

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

Counts

4 → 79

Calls

4 calls:

12.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
11.0ms	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
6.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1876 to 324 computations (82.7% saved)

series865.0ms (8.2%)

Error

7.6b

Counts

4 → 82

Calls

4 calls:

272.0ms	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
207.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.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 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3540 to 2454 computations (30.7% saved)

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5231	3327

prune146.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	162	9	171

Error

7.6b

Counts

171 → 9

Compiler

Compiled 2961 to 766 computations (74.1% saved)

regimes1.6s (15.1%)

Accuracy

Total 1.4b remaining (19.3%)

Threshold costs 0b (0%)

Compiler

Compiled 6516 to 4019 computations (38.3% saved)

bsearch83.0ms (0.8%)

Steps

Iters	Range	Point
9	1.0209793952461718e+36	1.929731811938187e+41	1.8998356024445367e+41
9	1.2950968775378066e-258	1.2819388198100383e-249	3.486989568159793e-258
3	-9.954154286899505e+123	-8.328958146635244e+123	-9.446280493066924e+123

Iters

Range

Point

1.0209793952461718e+36

1.929731811938187e+41

1.8998356024445367e+41

1.2950968775378066e-258

1.2819388198100383e-249

3.486989568159793e-258

-9.954154286899505e+123

-8.328958146635244e+123

-9.446280493066924e+123

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	82
1	101	82

end0.0ms (0%)

sample2.9s (27.8%)

Algorithm

1×

intervals

Results

314.0ms	1128×	body	2048	valid
275.0ms	5154×	body	128	valid
164.0ms	743×	body	1024	valid
132.0ms	396×	body	4096	valid
62.0ms	418×	body	512	valid
38.0ms	771×	body	128	nan
19.0ms	161×	body	256	valid
15.0ms	253×	body	128	invalid

Compiler

Compiled 1640 to 1014 computations (38.2% saved)

Details

analyze1.1s (10.8%)

sample42.0ms (0.4%)

simplify79.0ms (0.7%)

prune5.0ms (0%)

localize11.0ms (0.1%)

rewrite180.0ms (1.7%)

series822.0ms (7.8%)

simplify101.0ms (1%)

prune192.0ms (1.8%)

localize18.0ms (0.2%)

rewrite157.0ms (1.5%)

series811.0ms (7.7%)

simplify86.0ms (0.8%)

prune180.0ms (1.7%)

localize11.0ms (0.1%)

rewrite94.0ms (0.9%)

series610.0ms (5.8%)

simplify74.0ms (0.7%)

prune133.0ms (1.3%)

localize10.0ms (0.1%)

rewrite112.0ms (1.1%)

series865.0ms (8.2%)

simplify69.0ms (0.6%)

prune146.0ms (1.4%)

regimes1.6s (15.1%)

bsearch83.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.9s (27.8%)

Profiling