Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	149×	body	80	valid
4.0ms	248×	body	80	nan
3.0ms	39×	body	1280	valid
3.0ms	46×	body	640	valid
1.0ms	19×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

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: 25.8b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

1.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 70

Calls

1 calls:

10.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series75.0ms

Counts

1 → 3

Calls

1 calls:

75.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify142.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (132.0ms)

Iter	Nodes	Cost
0	252	1065
1	759	733
2	4363	623
3	5001	593

prune84.0ms

Filtered

73 candidates to 27 candidates (37.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Merged error: 0.1b

Counts

74 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 75

Calls

2 calls:

8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
16.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series202.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
138.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	356	693
1	1446	627
2	5001	586

prune146.0ms

Filtered

81 candidates to 51 candidates (63.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	78	6	84

Merged error: 0.0b

Counts

84 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
10.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (+ x 1.0))
91.0ms	(cbrt (+ x 1.0))
86.0ms	(cbrt (+ x 1.0))
122.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify151.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (141.0ms)

Iter	Nodes	Cost
0	321	818
1	1071	769
2	4756	694
3	5001	692

prune353.0ms

Filtered

115 candidates to 83 candidates (72.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	4	4
Picked	0	1	1
Done	1	0	1
Total	114	7	121

Merged error: 0.0b

Counts

121 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

42×	`cbrt-prod`
37×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
18×	`cbrt-div`
17×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
8×	`sqrt-prod`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (sqrt (+ x 1.0)))
4.0ms	(cbrt (sqrt (+ x 1.0)))
10.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (+ x 1.0))
85.0ms	(cbrt (sqrt (+ x 1.0)))
92.0ms	(cbrt (sqrt (+ x 1.0)))
100.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	443	914
1	1476	857
2	5001	801

prune388.0ms

Filtered

121 candidates to 85 candidates (70.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	121	7	128

Merged error: 0.0b

Counts

128 → 7

regimes33.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	13
1	18	13
2	18	13

end0.0ms

sample641.0ms

Algorithm

intervals

Results

138.0ms	1688×	body	1280	valid
127.0ms	7900×	body	80	nan
84.0ms	1248×	body	640	valid
73.0ms	4119×	body	80	valid
33.0ms	641×	body	320	valid
10.0ms	304×	body	160	valid