Details

analyze13.0ms

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

sample25.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify263.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (255.0ms)

Iter	Nodes	Cost
0	5007	22

prune1.0ms

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: 17.1b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
16.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/_binary64_656`
7×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
5×	`flip-+_binary64_615` `flip3-+_binary64_588`
4×	`add-cube-cbrt_binary64_561` `frac-times_binary64_582` `add-log-exp_binary64_555` `*-un-lft-identity_binary64_590` `add-sqr-sqrt_binary64_575`
3×	`flip--_binary64_616` `times-frac_binary64_585` `flip3--_binary64_589` `associate-/r*_binary64_653`
2×	`cbrt-undiv_binary64_560` `pow1_binary64_532` `associate-/r/_binary64_655` `associate-l/_binary64_652` `associate-r/_binary64_651` `div-exp_binary64_539`
1×	`cbrt-unprod_binary64_559` `+-commutative_binary64_657` `div-inv_binary64_591` `prod-exp_binary64_537` `frac-2neg_binary64_583` `associate-/l*_binary64_654` `clear-num_binary64_593` `sum-log_binary64_500`

Counts

2 → 42

Calls

2 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
12.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series60.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+.f64 (.f64 x x) (.f64 y y))
40.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

simplify43.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5124	969

prune41.0ms

Filtered

39 candidates to 48 candidates (-23.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	5	49

Merged error: 0.7b

Counts

49 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3))
0.0b	(pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3)
16.8b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac_binary64_585`
47×	`add-cube-cbrt_binary64_561` `*-un-lft-identity_binary64_590` `add-sqr-sqrt_binary64_575`
42×	`cbrt-prod_binary64_557`
36×	`unpow-prod-down_binary64_521` `cube-prod_binary64_563`
17×	`difference-of-squares_binary64_619`
10×	`associate-/r/_binary64_655`
9×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
6×	`add-log-exp_binary64_555`
5×	`flip-+_binary64_615` `div-inv_binary64_591` `pow1_binary64_532` `flip3-+_binary64_588`
4×	`associate-/l*_binary64_654`
3×	`pow-unpow_binary64_519` `associate-/r*_binary64_653`
2×	`rem-cube-cbrt_binary64_566` `flip--_binary64_616` `cbrt-undiv_binary64_560` `cube-div_binary64_564` `cube-mult_binary64_565` `sqr-pow_binary64_622` `flip3--_binary64_589` `associate-/l/_binary64_656` `unpow3_binary64_530` `pow-exp_binary64_510` `div-exp_binary64_539`
1×	`pow1/3_binary64_524` `pow-to-exp_binary64_511` `sub-neg_binary64_594` `frac-2neg_binary64_583` `div-sub_binary64_584` `pow-pow_binary64_514` `cbrt-div_binary64_558` `clear-num_binary64_593` `diff-log_binary64_501` `rem-cbrt-cube_binary64_567`

Counts

4 → 156

Calls

4 calls:

4.0ms	(-.f64 (.f64 x x) (.f64 y y))
12.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3))
11.0ms	(pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3)
9.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(-.f64 (.f64 x x) (.f64 y y))
40.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3))
50.0ms	(pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3)
43.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

simplify81.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5171	5215

prune88.0ms

Filtered

96 candidates to 168 candidates (-75.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	168	5	173

Merged error: 0.7b

Counts

173 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
16.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
16.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

115×	`add-sqr-sqrt_binary64_575`
96×	`times-frac_binary64_585`
95×	`*-un-lft-identity_binary64_590`
57×	`add-cube-cbrt_binary64_561` `sqrt-prod_binary64_569`
36×	`associate-l_binary64_650`
30×	`associate-r_binary64_649`
18×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
13×	`difference-of-squares_binary64_619` `distribute-lft-out--_binary64_635`
10×	`sqrt-div_binary64_570`
9×	`unswap-sqr_binary64_618`
8×	`pow1_binary64_532`
6×	`distribute-lft-out_binary64_634` `associate-/r/_binary64_655` `associate-/r*_binary64_653`
5×	`flip-+_binary64_615` `cbrt-undiv_binary64_560` `associate-/l*_binary64_654` `flip3-+_binary64_588` `div-exp_binary64_539`
4×	`cbrt-unprod_binary64_559` `prod-exp_binary64_537` `add-log-exp_binary64_555`
3×	`div-inv_binary64_591`
2×	`rem-sqrt-square_binary64_578` `pow1/2_binary64_522` `associate-/l/_binary64_656` `sqrt-pow1_binary64_571`
1×	`pow-prod-down_binary64_513` `flip--_binary64_616` `frac-times_binary64_582` `-commutative_binary64_658` `frac-2neg_binary64_583` `div-sub_binary64_584` `flip3--_binary64_589` `associate-l/_binary64_652` `clear-num_binary64_593` `associate-*r/_binary64_651`

Counts

4 → 183

Calls

4 calls:

12.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
34.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.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)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
42.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
23.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
26.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify105.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4978	5945
1	4978	5945

prune109.0ms

Filtered

124 candidates to 195 candidates (-57.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	195	5	200

Merged error: 0.7b

Counts

200 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(/.f64 (-.f64 x y) (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y)))
16.5b	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac_binary64_585`
161×	`*-un-lft-identity_binary64_590`
117×	`add-sqr-sqrt_binary64_575`
79×	`add-cube-cbrt_binary64_561`
22×	`distribute-lft-out_binary64_634` `associate-/r*_binary64_653`
19×	`difference-of-squares_binary64_619` `distribute-lft-out--_binary64_635`
15×	`associate-/r/_binary64_655`
10×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
9×	`flip-+_binary64_615` `flip3-+_binary64_588`
8×	`div-inv_binary64_591` `associate-/l*_binary64_654`
5×	`add-log-exp_binary64_555`
4×	`cbrt-undiv_binary64_560` `associate-/l/_binary64_656` `div-exp_binary64_539`
3×	`pow1_binary64_532`
2×	`frac-2neg_binary64_583` `clear-num_binary64_593`
1×	`+-commutative_binary64_657` `flip--_binary64_616` `div-sub_binary64_584` `flip3--_binary64_589` `sum-log_binary64_500`

Counts

3 → 177

Calls

3 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
13.0ms	(/.f64 (-.f64 x y) (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y)))
9.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y))

series103.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+.f64 (.f64 x x) (.f64 y y))
43.0ms	(/.f64 (-.f64 x y) (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y)))
40.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 x y))

simplify111.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5198	6506

prune98.0ms

Filtered

124 candidates to 186 candidates (-50.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	186	5	191

Merged error: 0.7b

Counts

191 → 5

regimes44.0ms

Accuracy

75.8% (4.6b remaining)

Error of 5.1b against oracle of 0.5b and baseline of 19.6b

bsearch49.0ms

Steps

Iters	Range	Point
9	5.4987918040985985e-167	1.3409831727452555e-160	1.5861413695832953e-162
7	-1.2733248278336006e-161	-1.216331656383701e-163	-1.5902636281828094e-162
10	-2.682978585628977e+160	-5.749057462488708e+149	-1.3302442616326837e+154

Iters

Range

Point

5.4987918040985985e-167

1.3409831727452555e-160

1.5861413695832953e-162

-1.2733248278336006e-161

-1.216331656383701e-163

-1.5902636281828094e-162

-2.682978585628977e+160

-5.749057462488708e+149

-1.3302442616326837e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	49
1	45	49

end0.0ms

sample582.0ms

Algorithm

intervals

Results

289.0ms	8000×	body	80	valid
148.0ms	8000×	pre	80	true

Details

analyze13.0ms

sample25.0ms

simplify263.0ms

prune1.0ms

localize9.0ms

rewrite18.0ms

series60.0ms

simplify43.0ms

prune41.0ms

localize12.0ms

rewrite43.0ms

series156.0ms

simplify81.0ms

prune88.0ms

localize12.0ms

rewrite62.0ms

series142.0ms

simplify105.0ms

prune109.0ms

localize9.0ms

rewrite36.0ms

series103.0ms

simplify111.0ms

prune98.0ms

regimes44.0ms

bsearch49.0ms

simplify3.0ms

end0.0ms

sample582.0ms

Profiling