Details

sample104.0ms

Algorithm

intervals

Results

36.0ms	60×	body	1280	valid
26.0ms	338×	body	80	valid
11.0ms	34×	body	640	valid
5.0ms	71×	body	80	overflowed
5.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (33.0ms)

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

prune10.0ms

Filtered

1 candidates to 1 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: 28.2b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
1.5b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

122×	`*-un-lft-identity`
106×	`times-frac`
96×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
27×	`distribute-lft-out--`
18×	`difference-of-squares`
10×	`add-cbrt-cube` `distribute-lft-out` `associate-/l*`
8×	`add-exp-log`
6×	`pow1` `associate-/r*` `add-log-exp`
5×	`associate-l`
4×	`div-inv` `associate-/l/`
3×	`flip3--` `div-sub` `associate-r` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-*l/` `clear-num`
1×	`sub-neg` `distribute-rgt-out--` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `sub-div` `associate--r-` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

6.0ms	(* (- 1.0 eps) x)
11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
11.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
195.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series85.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (- 1.0 eps) x)
12.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
15.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
53.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	684	1993
1	2176	1881
2	5002	1880

prune363.0ms

Filtered

150 candidates to 107 candidates (28.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	150	2	152

Merged error: 0.2b

Counts

152 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
0.2b	(* 0.5 (pow x 2))
6.0b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp` `unswap-sqr`
7×	`add-cbrt-cube`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`cube-mult` `sub-neg` `flip3--` `unpow3` `associate--l+` `sum-log` `flip--`

Counts

3 → 72

Calls

3 calls:

6.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(* 0.5 (pow x 2))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series11.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* 0.33333333333333337 (pow x 3))
3.0ms	(* 0.5 (pow x 2))
4.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	281	367
1	1207	327
2	5001	314

prune104.0ms

Filtered

81 candidates to 48 candidates (40.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	80	3	83

Merged error: 0.2b

Counts

83 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
0.2b	(* 0.5 (pow x 2))
1.7b	(log (exp (* 0.5 (pow x 2))))
10.5b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`associate-r`
16×	`*-un-lft-identity`
14×	`add-exp-log`
13×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
6×	`pow1` `log-prod` `associate-l` `prod-exp`
4×	`cube-prod` `log-pow` `sqr-pow`
3×	`associate--r+`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `unpow2`
1×	`cube-mult` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `unpow3` `rem-log-exp` `associate--l+` `sum-log` `flip--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

6.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(* 0.5 (pow x 2))
2.0ms	(log (exp (* 0.5 (pow x 2))))
9.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))

series15.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 0.33333333333333337 (pow x 3))
3.0ms	(* 0.5 (pow x 2))
3.0ms	(log (exp (* 0.5 (pow x 2))))
5.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (log (exp (* 0.5 (pow x 2)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	318	516
1	1268	447
2	5001	433

prune165.0ms

Filtered

104 candidates to 63 candidates (39.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	103	4	107

Merged error: 0.2b

Counts

107 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

5.4b	(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
5.4b	(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
35.6b	(sqrt (* 0.5 (pow x 2)))
35.6b	(sqrt (* 0.5 (pow x 2)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-sqr-sqrt` `sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+`

Counts

4 → 50

Calls

4 calls:

4.0ms	(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
4.0ms	(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
3.0ms	(sqrt (* 0.5 (pow x 2)))
3.0ms	(sqrt (* 0.5 (pow x 2)))

series16.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
4.0ms	(sqrt (+ (* 0.33333333333333337 (pow x 3)) 1.0))
4.0ms	(sqrt (* 0.5 (pow x 2)))
4.0ms	(sqrt (* 0.5 (pow x 2)))

simplify76.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	167	336
1	478	324
2	2323	324
3	5001	322

prune195.0ms

Filtered

62 candidates to 52 candidates (16.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	62	4	66

Merged error: 0.2b

Counts

66 → 4

regimes102.0ms

Accuracy

96.9% (0.5b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 16.0b

bsearch91.0ms

Steps

Iters	Range		Point
9	0.0005128181360460238	127140.91663662092	1.5711212170237787

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	26
1	41	26

end0.0ms

sample3.0s

Algorithm

intervals

Results

981.0ms	1782×	body	1280	valid
772.0ms	9927×	body	80	valid
451.0ms	1292×	body	640	valid
151.0ms	1960×	body	80	overflowed
147.0ms	628×	body	320	valid
53.0ms	339×	body	160	valid

Details

sample104.0ms

simplify34.0ms

prune10.0ms

localize18.0ms

rewrite229.0ms

series85.0ms

simplify64.0ms

prune363.0ms

localize9.0ms

rewrite19.0ms

series11.0ms

simplify45.0ms

prune104.0ms

localize12.0ms

rewrite25.0ms

series15.0ms

simplify46.0ms

prune165.0ms

localize14.0ms

rewrite16.0ms

series16.0ms

simplify76.0ms

prune195.0ms

regimes102.0ms

bsearch91.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling