Details

analyze1.0s (10.8%)

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 (0.4%)

Algorithm

1×

intervals

Results

8.0ms	167×	body	128	valid
8.0ms	37×	body	2048	valid
4.0ms	13×	body	4096	valid
3.0ms	16×	body	1024	valid
1.0ms	10×	body	512	valid
1.0ms	13×	body	256	valid
1.0ms	22×	body	128	nan
1.0ms	13×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune7.0ms (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

31.8b

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)
1.3b	(-.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))
21.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite137.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

31.5b

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:

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

series712.0ms (7.6%)

Error

3.8b

Counts

4 → 81

Calls

4 calls:

205.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
167.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
134.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
128.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3418 to 2462 computations (28% saved)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4953	3717
1	4953	3717

prune147.0ms (1.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	155	12	167
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	155	13	168

Error

3.7b

Counts

168 → 13

Compiler

Compiled 3350 to 934 computations (72.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
1.3b	(-.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))
21.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite110.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

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` `difference-of-squares_binary64` `prod-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `associate-*l/_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:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
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 2156 to 599 computations (72.2% saved)

series702.0ms (7.5%)

Error

3.7b

Counts

4 → 81

Calls

4 calls:

202.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
175.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
126.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
126.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3700 to 2756 computations (25.5% saved)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4960	3469
1	4960	3469

prune140.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	1	10	11
Picked	0	1	1
Done	1	0	1
Total	169	12	181

Error

3.7b

Counts

181 → 12

Compiler

Compiled 3463 to 1232 computations (64.4% 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)))
1.3b	(-.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))
21.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite203.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

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` `flip--_binary64` `div-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `pow-flip_binary64` `frac-2neg_binary64` `clear-num_binary64`

Counts

4 → 164

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
8.0ms	(-.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 4825 to 1174 computations (75.7% saved)

series716.0ms (7.7%)

Error

3.7b

Counts

4 → 81

Calls

4 calls:

220.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
175.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
124.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
122.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3700 to 2747 computations (25.8% saved)

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4991	6708
1	4991	6708

prune203.0ms (2.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	245	12	257

Error

3.7b

Counts

257 → 12

Compiler

Compiled 5793 to 1514 computations (73.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.3b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite87.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

Rules

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

Counts

4 → 57

Calls

4 calls:

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

Compiler

Compiled 2872 to 336 computations (88.3% saved)

series655.0ms (7%)

Error

3.7b

Counts

4 → 81

Calls

4 calls:

144.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
141.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
140.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
139.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 8675 to 3354 computations (61.3% saved)

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4935	2297
1	4935	2297

prune151.0ms (1.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	138	12	150

Error

3.7b

Counts

150 → 12

Compiler

Compiled 6319 to 883 computations (86% saved)

regimes1.5s (15.6%)

Accuracy

Total 4.8b remaining (47.6%)

Threshold costs 0b (0%)

Compiler

Compiled 6136 to 3762 computations (38.7% saved)

bsearch61.0ms (0.7%)

Steps

Iters	Range		Point
9	6.526673237360562e-20	3.3629564648988603e-13	1.895643606165851e-19
7	-3.1869792289515907e+155	-2.5952742020667376e+153	-8.781336407251623e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	47
1	68	47

end0.0ms (0%)

sample2.3s (25.1%)

Algorithm

1×

intervals

Results

244.0ms	1135×	body	2048	valid
225.0ms	5099×	body	128	valid
122.0ms	727×	body	1024	valid
113.0ms	428×	body	4096	valid
48.0ms	399×	body	512	valid
31.0ms	781×	body	128	nan
17.0ms	212×	body	256	valid
11.0ms	275×	body	128	invalid

Compiler

Compiled 1572 to 967 computations (38.5% saved)

Details

analyze1.0s (10.8%)

sample41.0ms (0.4%)

simplify74.0ms (0.8%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite137.0ms (1.5%)

series712.0ms (7.6%)

simplify77.0ms (0.8%)

prune147.0ms (1.6%)

localize10.0ms (0.1%)

rewrite110.0ms (1.2%)

series702.0ms (7.5%)

simplify77.0ms (0.8%)

prune140.0ms (1.5%)

localize10.0ms (0.1%)

rewrite203.0ms (2.2%)

series716.0ms (7.7%)

simplify102.0ms (1.1%)

prune203.0ms (2.2%)

localize14.0ms (0.1%)

rewrite87.0ms (0.9%)

series655.0ms (7%)

simplify70.0ms (0.8%)

prune151.0ms (1.6%)

regimes1.5s (15.6%)

bsearch61.0ms (0.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (25.1%)

Profiling