Details

sample89.0ms

Algorithm

intervals

Results

24.0ms	337×	body	80	valid
23.0ms	45×	body	1280	valid
17.0ms	45×	body	640	valid
4.0ms	57×	body	80	overflowed
4.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 27.2b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (+ 1.0 eps) x)
1.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
31×	`flip3--` `flip3-+` `flip--` `flip-+`
21×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
14×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out--`

Counts

4 → 172

Calls

4 calls:

12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
13.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
6.0ms	(* (+ 1.0 eps) x)
19.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series316.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
47.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
30.0ms	(* (+ 1.0 eps) x)
189.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify149.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1257	4061
1	4772	3783
2	5001	3783

prune401.0ms

Filtered

184 candidates to 94 candidates (51.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	2	185

Merged error: 0.2b

Counts

185 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
7.0b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 45

Calls

2 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series78.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(* 0.6666666666666667 (pow x 3))
38.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify35.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	207	270
1	894	242
2	5002	238

prune87.0ms

Filtered

51 candidates to 31 candidates (60.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	50	3	53

Merged error: 0.2b

Counts

53 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
1.0b	(exp (log (* 0.6666666666666667 (pow x 3))))
7.0b	(- (+ (exp (log (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
47.5b	(log (* 0.6666666666666667 (pow x 3)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`add-exp-log`
12×	`associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`pow1` `prod-exp` `add-cbrt-cube`
4×	`unpow-prod-down` `exp-prod` `cube-prod` `rem-log-exp` `unswap-sqr`
3×	`associate-l`
2×	`pow-to-exp` `log-prod` `diff-log` `pow-exp` `log-pow` `sqr-pow`
1×	`cube-mult` `sub-neg` `flip3--` `unpow3` `exp-sum` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log`

Counts

4 → 71

Calls

4 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
4.0ms	(exp (log (* 0.6666666666666667 (pow x 3))))
10.0ms	(- (+ (exp (log (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
4.0ms	(log (* 0.6666666666666667 (pow x 3)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 0.6666666666666667 (pow x 3))
41.0ms	(exp (log (* 0.6666666666666667 (pow x 3))))
38.0ms	(- (+ (exp (log (* 0.6666666666666667 (pow x 3)))) 2.0) (* 1.0 (pow x 2)))
150.0ms	(log (* 0.6666666666666667 (pow x 3)))

simplify40.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	262	413
1	1064	355
2	5002	346

prune305.0ms

Filtered

83 candidates to 49 candidates (59.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	83	3	86

Merged error: 0.2b

Counts

86 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
0.0b	(* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x)))))
3.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x))))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

384×	`frac-times`
360×	`sqrt-div`
284×	`exp-neg`
258×	`neg-sub0` `exp-diff`
234×	`frac-sub`
196×	`associate-*l/`
132×	`associate-*r/`
91×	`flip3--` `flip--`
80×	`flip3-+` `flip-+`
26×	`un-div-inv`
14×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
10×	`add-cube-cbrt`
9×	`associate-l`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sqrt-prod` `*-commutative`
2×	`distribute-lft-out` `unswap-sqr`
1×	`sub-neg` `diff-log`

Counts

4 → 335

Calls

4 calls:

6.0ms	(* (+ 1.0 eps) x)
6.0ms	(* (+ 1.0 eps) x)
21.0ms	(* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x)))))
25.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x))))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ 1.0 eps) x)
30.0ms	(* (+ 1.0 eps) x)
48.0ms	(* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x)))))
196.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (- (/ 1.0 eps) 1.0) (sqrt (exp (- (* (+ 1.0 eps) x))))) (sqrt (exp (- (* (+ 1.0 eps) x))))))

simplify142.0ms

Algorithm

egg-herbie

Counts

347 → 347

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2200	12136
1	5001	11742

prune549.0ms

Filtered

347 candidates to 109 candidates (31.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	347	0	347
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	347	3	350

Merged error: 0.2b

Counts

350 → 3

regimes72.0ms

Accuracy

97.2% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.6b

bsearch126.0ms

Steps

Iters	Range		Point
8	14.716166499582775	53889.47736569451	377.3254080657518

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	30
1	59	30
2	59	30

end0.0ms

sample2.6s

Algorithm

intervals

Results

859.0ms	1699×	body	1280	valid
716.0ms	10167×	body	80	valid
389.0ms	1241×	body	640	valid
143.0ms	657×	body	320	valid
136.0ms	1978×	body	80	overflowed
44.0ms	320×	body	160	valid