Details

sample14.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	65×	body	80	nan

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Merged error: 20.6b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
19.1b	(sqrt (+ (* x x) y))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`fma-def`
8×	`add-cube-cbrt`
5×	`associate-l` `sqrt-prod` `hypot-def`
4×	`swap-sqr` `distribute-lft-out` `add-log-exp`
3×	`pow1` `associate-r`
2×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `*-commutative` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

2 → 54

Calls

2 calls:

9.0ms	(+ (* x x) y)
9.0ms	(sqrt (+ (* x x) y))

series65.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ (* x x) y)
46.0ms	(sqrt (+ (* x x) y))

simplify63.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	153	170
1	518	156
2	1716	146
3	5002	142

prune127.0ms

Filtered

60 candidates to 46 candidates (76.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	3	61

Merged error: 0b

Counts

61 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

19.1b	(sqrt (fma (* (cbrt (* x x)) (cbrt (* x x))) (cbrt (* x x)) y))
28.6b	(cbrt (* x x))
28.6b	(cbrt (* x x))
28.6b	(cbrt (* x x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

45×	`cbrt-prod`
27×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
9×	`swap-sqr` `associate-r` `associate-l`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 90

Calls

4 calls:

1.0ms	(sqrt (fma (* (cbrt (* x x)) (cbrt (* x x))) (cbrt (* x x)) y))
4.0ms	(cbrt (* x x))
4.0ms	(cbrt (* x x))
4.0ms	(cbrt (* x x))

series684.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(sqrt (fma (* (cbrt (* x x)) (cbrt (* x x))) (cbrt (* x x)) y))
190.0ms	(cbrt (* x x))
176.0ms	(cbrt (* x x))
177.0ms	(cbrt (* x x))

simplify113.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	177	542
1	585	507
2	3118	459
3	5002	452

prune256.0ms

Filtered

102 candidates to 78 candidates (76.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	102	3	105

Merged error: 0b

Counts

105 → 3

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune2.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Merged error: 0b

Counts

3 → 3

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 1/2 (/ y x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`associate-r`
12×	`*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`times-frac`
9×	`associate-*r/`
6×	`add-exp-log` `add-cbrt-cube`
4×	`associate-/l*`
3×	`pow1` `associate-l` `associate-/r*`
2×	`prod-exp` `clear-num` `un-div-inv` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `pow-prod-down` `*-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 44

Calls

1 calls:

8.0ms

(* 1/2 (/ y x))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(* 1/2 (/ y x))

simplify97.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	188	151
1	871	141
2	3500	141
3	5001	141

prune73.0ms

Filtered

47 candidates to 32 candidates (68.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	47	3	50

Merged error: 0b

Counts

50 → 3

regimes74.0ms

Accuracy

97.6% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 21.4b

bsearch49.0ms

Steps

Iters	Range		Point
9	8.754339875160778e+94	1.3220497141557022e+101	4.422381501037617e+97
6	-7.455282738767828e+100	-1.8066912586882657e+100	-6.282485967221723e+100

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	15
1	31	15
2	33	15
3	33	15

end0.0ms

sample368.0ms

Algorithm

intervals

Results

159.0ms	8000×	body	80	valid
44.0ms	2702×	body	80	nan