Details

sample9.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune1.0ms

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: 13.8b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

13.8b

(/ x (+ (* x x) 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
15×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`distribute-lft-out`
5×	`associate-/r*`
4×	`associate-l`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 39

Calls

1 calls:

9.0ms

(/ x (+ (* x x) 1.0))

series64.0ms

Counts

1 → 3

Calls

1 calls:

63.0ms

(/ x (+ (* x x) 1.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	168	245
1	565	224
2	1921	218
3	5002	212

prune54.0ms

Filtered

42 candidates to 29 candidates (69.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	2	43

Merged error: 0b

Counts

43 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ 1 (+ (* x x) 1.0))
13.0b	(* x (/ 1 (+ (* x x) 1.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
32×	`times-frac`
31×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
21×	`associate-r`
16×	`distribute-lft-out`
15×	`add-exp-log`
11×	`associate-r/` `associate-l*`
10×	`associate-/r*`
9×	`add-cbrt-cube`
7×	`associate-/l*`
5×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`clear-num` `un-div-inv` `unswap-sqr`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `frac-2neg` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

2 → 101

Calls

2 calls:

10.0ms	(/ 1 (+ (* x x) 1.0))
19.0ms	(* x (/ 1 (+ (* x x) 1.0)))

series106.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ 1 (+ (* x x) 1.0))
64.0ms	(* x (/ 1 (+ (* x x) 1.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	330	538
1	1446	456
2	5001	388

prune110.0ms

Filtered

107 candidates to 61 candidates (57.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	107	2	109

Merged error: 0b

Counts

109 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (pow x 5))
0.3b	(/ 1 (pow x 3))
19.7b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

1344×	`times-frac`
1014×	`add-sqr-sqrt`
954×	`*-un-lft-identity`
902×	`add-cube-cbrt`
700×	`prod-diff`
619×	`unpow-prod-down`
225×	`sqr-pow`
217×	`associate-/r*`
182×	`frac-sub`
92×	`unpow3`
87×	`associate-/l*`
60×	`div-inv`
49×	`difference-of-squares`
29×	`frac-2neg` `clear-num`
25×	`fma-neg`
21×	`add-exp-log`
12×	`pow-flip` `div-exp`
7×	`pow1` `add-cbrt-cube` `distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `pow-unpow` `1-exp` `pow-exp`
5×	`add-log-exp`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-pow` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 1101

Calls

3 calls:

5.0ms	(/ 1 (pow x 5))
6.0ms	(/ 1 (pow x 3))
64.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series188.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ 1 (pow x 5))
33.0ms	(/ 1 (pow x 3))
104.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify288.0ms

Algorithm

egg-herbie

Counts

1110 → 1110

Iterations

Useful iterations: 1 (65.0ms)

Iter	Nodes	Cost
0	3803	25736
1	5001	16976

prune799.0ms

Filtered

1110 candidates to 186 candidates (16.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	1110	0	1110
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	1110	2	1112

Merged error: 0b

Counts

1112 → 2

regimes19.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.3b

bsearch54.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	458.0651429950271
7	-5.001954329178871e+47	-2.6517802389952764e+46	-7.41750500238859e+46

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample221.0ms

Algorithm

intervals

Results

136.0ms

8000×

body

valid