Details

analyze1.2s (11.1%)

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)

sample41.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	42×	body	2048	valid
7.0ms	164×	body	128	valid
4.0ms	15×	body	4096	valid
3.0ms	19×	body	1024	valid
1.0ms	12×	body	512	valid
1.0ms	22×	body	128	nan
0.0ms	4×	body	256	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

prune4.0ms (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

37.0b

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)
0.3b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
25.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite172.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

36.8b

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:

18.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
11.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2360 to 368 computations (84.4% saved)

series696.0ms (6.6%)

Error

7.5b

Counts

4 → 67

Calls

4 calls:

214.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
143.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
141.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
138.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

Compiler

Compiled 2499 to 1714 computations (31.4% saved)

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4970	3346
1	4970	3346

prune145.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	154	9	163
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	154	10	164

Error

7.4b

Counts

164 → 10

Compiler

Compiled 3066 to 611 computations (80.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
12.2b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
25.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite181.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

7.4b

Rules

66×	`times-frac_binary64`
58×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`sqrt-prod_binary64` `associate-/r/_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `flip--_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`sqrt-div_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l/_binary64` `diff-log_binary64` `sub-neg_binary64`

Counts

4 → 129

Calls

4 calls:

13.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
11.0ms	(/.f64 (.f64 a c) (-.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)))

Compiler

Compiled 3886 to 521 computations (86.6% saved)

series867.0ms (8.2%)

Error

7.4b

Counts

4 → 69

Calls

4 calls:

275.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
239.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
155.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
144.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)

Compiler

Compiled 3531 to 2134 computations (39.6% saved)

simplify146.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4950	5148
1	4950	5148

prune176.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	200	8	208

Error

7.4b

Counts

208 → 8

Compiler

Compiled 4606 to 848 computations (81.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite120.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.4b

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-/r*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64`
3×	`associate-/l*_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `associate-/r/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 85

Calls

4 calls:

9.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
7.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
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 2170 to 502 computations (76.9% saved)

series769.0ms (7.3%)

Error

7.4b

Counts

4 → 71

Calls

4 calls:

222.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
175.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
169.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
137.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3176 to 2248 computations (29.2% saved)

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5125	3119

prune151.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	156	8	164

Error

7.4b

Counts

164 → 8

Compiler

Compiled 3128 to 920 computations (70.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite147.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

7.4b

Rules

41×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
24×	`associate-r_binary64`
20×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `difference-of-squares_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64` `prod-exp_binary64`
3×	`unswap-sqr_binary64` `associate-l_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `div-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_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 → 91

Calls

4 calls:

18.0ms	(.f64 c (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
12.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2519 to 833 computations (66.9% saved)

series820.0ms (7.8%)

Error

7.4b

Counts

4 → 71

Calls

4 calls:

245.0ms	(.f64 c (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
171.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
165.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
159.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3446 to 2530 computations (26.6% saved)

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5278	2888

prune138.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	161	9	170

Error

7.4b

Counts

170 → 9

Compiler

Compiled 3396 to 1211 computations (64.3% saved)

regimes1.6s (14.8%)

Accuracy

Total 0.9b remaining (13.5%)

Threshold costs 0.9b (13.5%)

Compiler

Compiled 6430 to 3918 computations (39.1% saved)

bsearch109.0ms (1%)

Steps

Iters	Range	Point
8	1.6621865169664383e+118	5.129650521579702e+120	4.5829281059216323e+120
6	8.963326552883708e-271	8.197791807140359e-270	1.0584144284358635e-270
9	-1.0451269989421558e+143	-1.1049780562537373e+138	-1.344663677076728e+139

Iters

Range

Point

1.6621865169664383e+118

5.129650521579702e+120

4.5829281059216323e+120

8.963326552883708e-271

8.197791807140359e-270

1.0584144284358635e-270

-1.0451269989421558e+143

-1.1049780562537373e+138

-1.344663677076728e+139

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	83	73
1	83	73

end0.0ms (0%)

sample2.8s (26.5%)

Algorithm

1×

intervals

Results

293.0ms	1156×	body	2048	valid
270.0ms	5176×	body	128	valid
151.0ms	710×	body	1024	valid
125.0ms	417×	body	4096	valid
58.0ms	350×	body	512	valid
38.0ms	750×	body	128	nan
22.0ms	191×	body	256	valid
13.0ms	264×	body	128	invalid

Compiler

Compiled 1631 to 995 computations (39% saved)

Details

analyze1.2s (11.1%)

sample41.0ms (0.4%)

simplify88.0ms (0.8%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite172.0ms (1.6%)

series696.0ms (6.6%)

simplify83.0ms (0.8%)

prune145.0ms (1.4%)

localize9.0ms (0.1%)

rewrite181.0ms (1.7%)

series867.0ms (8.2%)

simplify146.0ms (1.4%)

prune176.0ms (1.7%)

localize15.0ms (0.1%)

rewrite120.0ms (1.1%)

series769.0ms (7.3%)

simplify55.0ms (0.5%)

prune151.0ms (1.4%)

localize10.0ms (0.1%)

rewrite147.0ms (1.4%)

series820.0ms (7.8%)

simplify73.0ms (0.7%)

prune138.0ms (1.3%)

regimes1.6s (14.8%)

bsearch109.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.8s (26.5%)

Profiling