Details

sample10.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 14.6b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

14.6b

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `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 → 31

Calls

1 calls:

6.0ms

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

series65.0ms

Counts

1 → 3

Calls

1 calls:

64.0ms

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

simplify58.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	171	215
1	589	196
2	1979	191
3	5002	186

prune72.0ms

Filtered

34 candidates to 29 candidates (85.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	30	4	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	4	35

Merged error: 0b

Counts

35 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
14.5b	(sqrt (+ (* x x) 1.0))
14.5b	(sqrt (+ (* x x) 1.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
30×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`pow1` `sqrt-div` `div-exp`
8×	`prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `pow-flip` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `associate-/l*`
2×	`rem-sqrt-square` `hypot-def`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `inv-pow`

Counts

4 → 174

Calls

4 calls:

26.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
7.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))

series236.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
73.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
50.0ms	(sqrt (+ (* x x) 1.0))
48.0ms	(sqrt (+ (* x x) 1.0))

simplify82.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	644	1786
1	3211	1573
2	5001	1404

prune284.0ms

Filtered

186 candidates to 118 candidates (63.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	186	4	190

Merged error: 0b

Counts

190 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ 1 (/ (fma x x 1.0) x))
14.5b	(/ (fma x x 1.0) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv`
3×	`pow1`
2×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

2 → 107

Calls

2 calls:

11.0ms	(/ 1 (/ (fma x x 1.0) x))
3.0ms	(/ (fma x x 1.0) x)

series164.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ 1 (/ (fma x x 1.0) x))
91.0ms	(/ (fma x x 1.0) x)

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	360	746
1	1496	655
2	5002	578

prune121.0ms

Filtered

113 candidates to 64 candidates (56.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	114	3	117

Merged error: 0b

Counts

117 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1.0 (/ 1 x) x)
0.1b	(/ 1 (fma 1.0 (/ 1 x) x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log`
4×	`add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `pow-flip` `frac-2neg` `1-exp` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

2 → 43

Calls

2 calls:

1.0ms	(fma 1.0 (/ 1 x) x)
8.0ms	(/ 1 (fma 1.0 (/ 1 x) x))

series105.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(fma 1.0 (/ 1 x) x)
48.0ms	(/ 1 (fma 1.0 (/ 1 x) x))

simplify44.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	136	257
1	415	227
2	1338	213
3	5002	211

prune57.0ms

Filtered

49 candidates to 30 candidates (61.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	49	3	52

Merged error: 0b

Counts

52 → 3

regimes12.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	3
1	8	3

end0.0ms

sample216.0ms

Algorithm

intervals

Results

133.0ms

8000×

body

valid