Details

analyze18.0ms

Algorithm

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

sample20.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify140.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4897	15
1	4897	15

prune2.0ms

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

Merged error: 20.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
20.6b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `flip3--_binary64` `times-frac_binary64` `flip--_binary64`
2×	`pow1_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-/r/_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 42

Calls

2 calls:

5.0ms	(+.f64 (.f64 x x) (.f64 y y))
14.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series18.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(+.f64 (.f64 x x) (.f64 y y))
12.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

simplify26.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5103	655

prune33.0ms

Filtered

39 candidates to 48 candidates (-23.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Merged error: 0.6b

Counts

49 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) (+.f64 x y))
0.0b	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
19.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
19.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
62×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
40×	`sqrt-prod_binary64`
36×	`associate-l_binary64`
13×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `sqrt-div_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `associate-/r/_binary64`
3×	`unswap-sqr_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 151

Calls

4 calls:

18.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) (+.f64 x y))
10.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) (+.f64 x y))
13.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5881	2655

prune63.0ms

Filtered

114 candidates to 163 candidates (-43.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	163	4	167

Merged error: 0.6b

Counts

167 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (log.f64 (exp.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))) (+.f64 x y))
0.0b	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
19.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
19.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
44×	`add-cube-cbrt_binary64`
40×	`associate-l_binary64`
39×	`sqrt-prod_binary64`
37×	`log-pow_binary64`
36×	`exp-prod_binary64`
13×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`pow1_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
6×	`associate-/r*_binary64`
5×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `associate-r_binary64` `associate-/r/_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `associate-*r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 148

Calls

4 calls:

22.0ms	(.f64 (log.f64 (exp.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))) (+.f64 x y))
10.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 (log.f64 (exp.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))) (+.f64 x y))
13.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify64.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	6259	2489

prune62.0ms

Filtered

110 candidates to 160 candidates (-45.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	160	4	164

Merged error: 0.6b

Counts

164 → 4

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify5.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune2.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Merged error: 0.6b

Counts

4 → 4

regimes68.0ms

Accuracy

73.5% (5.2b remaining)

Error of 5.7b against oracle of 0.5b and baseline of 20.0b

bsearch24.0ms

Steps

Iters	Range	Point
2	1.8871331990306155e-168	2.0970867028428884e-168	2.070842514866354e-168
7	-1.2025400738261047e-140	-2.8453063763646958e-142	-2.8799716158898233e-142
8	-6.669835681073004e+154	-2.348927082170636e+152	-1.349908665709368e+154

Iters

Range

Point

1.8871331990306155e-168

2.0970867028428884e-168

2.070842514866354e-168

-1.2025400738261047e-140

-2.8453063763646958e-142

-2.8799716158898233e-142

-6.669835681073004e+154

-2.348927082170636e+152

-1.349908665709368e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	31
1	63	31

end0.0ms

sample580.0ms

Algorithm

intervals

Results

295.0ms	8000×	body	80	valid
148.0ms	8000×	pre	80	true

Details

analyze18.0ms

sample20.0ms

simplify140.0ms

prune2.0ms

localize9.0ms

rewrite19.0ms

series18.0ms

simplify26.0ms

prune33.0ms

localize11.0ms

rewrite45.0ms

series41.0ms

simplify56.0ms

prune63.0ms

localize14.0ms

rewrite51.0ms

series41.0ms

simplify64.0ms

prune62.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify5.0ms

prune2.0ms

regimes68.0ms

bsearch24.0ms

simplify3.0ms

end0.0ms

sample580.0ms

Profiling