Details

analyze1000.0ms (12%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1992	72
1	1992	72
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 (0.5%)

Algorithm

1×

intervals

Results

8.0ms	36×	body	2048	valid
8.0ms	166×	body	128	valid
4.0ms	18×	body	4096	valid
3.0ms	21×	body	1024	valid
2.0ms	14×	body	512	valid
1.0ms	21×	body	128	nan
0.0ms	6×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

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

Error

33.0b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
23.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite136.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

32.8b

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

Counts

4 → 86

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.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))

Compiler

Compiled 2014 to 333 computations (83.5% saved)

series643.0ms (7.7%)

Error

4.9b

Counts

4 → 68

Calls

4 calls:

186.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
143.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
142.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
125.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2619 to 1844 computations (29.6% saved)

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5061	2934

prune116.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	146	8	154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	146	9	155

Error

4.8b

Counts

155 → 9

Compiler

Compiled 2745 to 581 computations (78.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.3b	(/.f64 a (-.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))
23.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite227.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

162×	`times-frac_binary64`
146×	`add-sqr-sqrt_binary64`
113×	`*-un-lft-identity_binary64`
81×	`add-cube-cbrt_binary64`
32×	`difference-of-squares_binary64`
30×	`associate-/r*_binary64`
19×	`sqrt-prod_binary64`
17×	`add-exp-log_binary64`
16×	`distribute-lft-out--_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`div-exp_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`pow1_binary64` `add-log-exp_binary64` `div-inv_binary64` `associate-/l*_binary64`
4×	`cbrt-undiv_binary64`
2×	`sqrt-div_binary64` `frac-2neg_binary64` `clear-num_binary64` `1-exp_binary64` `rec-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `diff-log_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 188

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
9.0ms	(/.f64 a (-.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 5534 to 1252 computations (77.4% saved)

series737.0ms (8.9%)

Error

4.8b

Counts

4 → 69

Calls

4 calls:

241.0ms	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
188.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
130.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
129.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2903 to 2115 computations (27.1% saved)

simplify105.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5051	6825

prune200.0ms (2.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	255	2	257
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	256	10	266

Error

4.8b

Counts

266 → 10

Compiler

Compiled 5880 to 1261 computations (78.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.5b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
23.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite115.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

30×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `associate-r_binary64`
11×	`times-frac_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`cancel-sign-sub-inv_binary64` `prod-exp_binary64` `difference-of-squares_binary64`
3×	`unswap-sqr_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `div-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `associate-*l/_binary64` `distribute-lft-out--_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 → 87

Calls

4 calls:

19.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
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 2156 to 599 computations (72.2% saved)

series633.0ms (7.6%)

Error

4.8b

Counts

4 → 68

Calls

4 calls:

182.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
152.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
129.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
122.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2881 to 2118 computations (26.5% saved)

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5057	2686

prune114.0ms (1.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	155	10	165

Error

4.8b

Counts

165 → 10

Compiler

Compiled 2846 to 865 computations (69.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
23.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite71.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64` `*-un-lft-identity_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3--_binary64` `sqrt-div_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `diff-log_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64`

Counts

4 → 54

Calls

4 calls:

4.0ms	(-.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))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1844 to 280 computations (84.8% saved)

series606.0ms (7.3%)

Error

4.8b

Counts

4 → 72

Calls

4 calls:

138.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
136.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
136.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
136.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 4874 to 2656 computations (45.5% saved)

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5006	1646

prune98.0ms (1.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	126	10	136

Error

4.8b

Counts

136 → 10

Compiler

Compiled 3486 to 501 computations (85.6% saved)

regimes967.0ms (11.6%)

Accuracy

Total 5.5b remaining (47.7%)

Threshold costs 0b (0%)

Compiler

Compiled 5364 to 3206 computations (40.2% saved)

bsearch69.0ms (0.8%)

Steps

Iters	Range		Point
10	0.005192092670447274	4665099061.651386	5.306656373450917
9	-1.0919942003521123e+157	-2.8681501044897114e+148	-7.809991262491265e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	89	56
1	89	56

end0.0ms (0%)

sample2.1s (25.1%)

Algorithm

1×

intervals

Results

228.0ms	5195×	body	128	valid
223.0ms	1109×	body	2048	valid
117.0ms	715×	body	1024	valid
107.0ms	431×	body	4096	valid
46.0ms	349×	body	512	valid
31.0ms	807×	body	128	nan
16.0ms	201×	body	256	valid
11.0ms	261×	body	128	invalid

Compiler

Compiled 1385 to 830 computations (40.1% saved)

Details

analyze1000.0ms (12%)

sample41.0ms (0.5%)

simplify71.0ms (0.9%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite136.0ms (1.6%)

series643.0ms (7.7%)

simplify92.0ms (1.1%)

prune116.0ms (1.4%)

localize10.0ms (0.1%)

rewrite227.0ms (2.7%)

series737.0ms (8.9%)

simplify105.0ms (1.3%)

prune200.0ms (2.4%)

localize9.0ms (0.1%)

rewrite115.0ms (1.4%)

series633.0ms (7.6%)

simplify69.0ms (0.8%)

prune114.0ms (1.4%)

localize11.0ms (0.1%)

rewrite71.0ms (0.9%)

series606.0ms (7.3%)

simplify60.0ms (0.7%)

prune98.0ms (1.2%)

regimes967.0ms (11.6%)

bsearch69.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.1s (25.1%)

Profiling