Details

sample41.0ms

Algorithm

intervals

Results

10.0ms	213×	body	160	nan
10.0ms	438×	body	80	nan
7.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

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: 28.1b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
26.2b	(sqrt (- (* x x) 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod` `sqrt-prod`
3×	`add-cbrt-cube`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `flip--` `difference-of-squares`

Counts

3 → 43

Calls

3 calls:

10.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
7.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(sqrt (- (* x x) 1.0))

series319.0ms

Counts

3 → 9

Calls

3 calls:

198.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
69.0ms	(+ x (sqrt (- (* x x) 1.0)))
51.0ms	(sqrt (- (* x x) 1.0))

simplify132.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (127.0ms)

Iter	Nodes	Cost
0	316	408
1	1042	379
2	4663	366
3	5002	365

prune133.0ms

Filtered

52 candidates to 43 candidates (82.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	2	53

Merged error: 0b

Counts

53 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x)))))
0.0b	(* 0.5 (/ 1 x))
0.0b	(+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x))))
0.5b	(/ 0.125 (pow x 3))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

47×	`times-frac`
45×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
38×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`associate-r` `add-log-exp`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
11×	`add-cbrt-cube`
7×	`pow1`
5×	`div-exp`
4×	`cube-mult` `associate-+r+` `log-prod` `unpow3` `prod-exp` `sqr-pow`
3×	`diff-log` `associate-l` `sum-log` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `log-div` `flip3-+` `associate--l+` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `rec-exp` `frac-2neg` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `un-div-inv` `-commutative`

Counts

4 → 135

Calls

4 calls:

21.0ms	(log (+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x)))))
7.0ms	(* 0.5 (/ 1 x))
17.0ms	(+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x))))
5.0ms	(/ 0.125 (pow x 3))

series428.0ms

Counts

4 → 12

Calls

4 calls:

328.0ms	(log (+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x)))))
15.0ms	(* 0.5 (/ 1 x))
49.0ms	(+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x))))
35.0ms	(/ 0.125 (pow x 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	530	877
1	2644	781
2	5003	776

prune291.0ms

Filtered

147 candidates to 90 candidates (61.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	147	2	149

Merged error: 0b

Counts

149 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
26.2b	(sqrt (- (* x x) 1.0))
26.2b	(sqrt (- (* x x) 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
2×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

8.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(sqrt (- (* x x) 1.0))
4.0ms	(sqrt (- (* x x) 1.0))

series231.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ x (sqrt (- (* x x) 1.0)))
65.0ms	(+ x (sqrt (- (* x x) 1.0)))
53.0ms	(sqrt (- (* x x) 1.0))
50.0ms	(sqrt (- (* x x) 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	217	442
1	657	422
2	2555	410
3	5001	408

prune236.0ms

Filtered

68 candidates to 58 candidates (85.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	68	2	70

Merged error: 0b

Counts

70 → 2

regimes26.0ms

Accuracy

0% (0.1b 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	17	8
1	17	8

end0.0ms

sample1.4s

Algorithm

intervals

Results

388.0ms	17075×	body	80	nan
361.0ms	7816×	body	160	nan
233.0ms	8000×	body	80	valid