Details

sample16.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	101×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	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: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series190.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(+ 1.0 (sqrt (+ x 1.0)))
147.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify34.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	290	412
1	1095	368
2	5001	361

prune102.0ms

Filtered

58 candidates to 45 candidates (77.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	3	59

Merged error: 0b

Counts

59 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
18×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `associate-l` `flip-+` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 99

Calls

3 calls:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
12.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
8.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series302.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(+ 1.0 (sqrt (+ x 1.0)))
143.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
110.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	429	761
1	1909	654
2	5001	610

prune135.0ms

Filtered

108 candidates to 67 candidates (62.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	108	3	111

Merged error: 0b

Counts

111 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
52×	`times-frac`
38×	`add-cube-cbrt`
35×	`sqrt-prod`
30×	`associate-r`
14×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `associate-/l*` `unswap-sqr`
5×	`pow1` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 125

Calls

3 calls:

8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
17.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series480.0ms

Counts

3 → 9

Calls

3 calls:

292.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
46.0ms	(+ 1.0 (sqrt (+ x 1.0)))
141.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	511	1228
1	2196	1085
2	5001	1054

prune199.0ms

Filtered

134 candidates to 85 candidates (63.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	134	3	137

Merged error: 0b

Counts

137 → 3

regimes30.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample412.0ms

Algorithm

intervals

Results

218.0ms	7997×	body	80	valid
67.0ms	2764×	body	80	nan
0.0ms	3×	body	1280	valid