Details

sample99.0ms

Algorithm

intervals

Results

29.0ms	58×	body	1280	valid
23.0ms	58×	body	10240	exit
16.0ms	295×	body	80	valid
8.0ms	33×	body	640	valid
4.0ms	25×	body	320	valid
0.0ms	4×	body	160	valid

simplify35.0ms

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

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: 28.0b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
76×	`exp-neg` `frac-times`
57×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
38×	`associate-*r/`
32×	`flip3--` `flip--`
28×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
19×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log` `associate-r`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out`

Counts

4 → 166

Calls

4 calls:

14.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
7.0ms	(* (- 1.0 eps) x)
7.0ms	(* (+ 1.0 eps) x)
20.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
30.0ms	(* (- 1.0 eps) x)
31.0ms	(* (+ 1.0 eps) x)
199.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify146.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1251	3880
1	4783	3607
2	5002	3607

prune396.0ms

Filtered

178 candidates to 90 candidates (50.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	2	179

Merged error: 0.2b

Counts

179 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
0.1b	(* 0.6666666666666667 (pow x 3))
8.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

5.0ms	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
6.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series168.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
38.0ms	(* 0.6666666666666667 (pow x 3))
46.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify44.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	251	336
1	1024	311
2	5002	307

prune123.0ms

Filtered

65 candidates to 41 candidates (63.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	3	67

Merged error: 0.2b

Counts

67 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
0.5b	(exp (log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))))
8.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
12.2b	(log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
9.0ms	(exp (log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
11.0ms	(log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 0.6666666666666667 (pow x 3))
46.0ms	(exp (log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))))
41.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
95.0ms	(log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	330	691
1	1352	626
2	5001	602

prune216.0ms

Filtered

88 candidates to 58 candidates (65.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	88	3	91

Merged error: 0.2b

Counts

91 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (- (/ 1.0 eps) 1.0))
0.4b	(cbrt (- (/ 1.0 eps) 1.0))
0.4b	(* (cbrt (- (/ 1.0 eps) 1.0)) (cbrt (- (/ 1.0 eps) 1.0)))
18.9b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (cbrt (- (/ 1.0 eps) 1.0)) (cbrt (- (/ 1.0 eps) 1.0))) (* (cbrt (- (/ 1.0 eps) 1.0)) (exp (- (* (+ 1.0 eps) x))))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

1692×	`frac-times`
1582×	`cbrt-div`
801×	`frac-sub`
792×	`flip3--` `flip--`
680×	`exp-neg`
603×	`associate-*r/`
594×	`associate-*l/`
510×	`neg-sub0` `exp-diff`
267×	`flip3-+` `flip-+`
170×	`un-div-inv`
52×	`add-sqr-sqrt`
44×	`cbrt-prod`
32×	`*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`pow1` `swap-sqr`
9×	`associate-r` `associate-l`
8×	`pow1/3` `distribute-lft-out--`
6×	`add-exp-log` `times-frac` `add-log-exp`
4×	`add-cbrt-cube` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 904

Calls

4 calls:

6.0ms	(cbrt (- (/ 1.0 eps) 1.0))
6.0ms	(cbrt (- (/ 1.0 eps) 1.0))
18.0ms	(* (cbrt (- (/ 1.0 eps) 1.0)) (cbrt (- (/ 1.0 eps) 1.0)))
61.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (cbrt (- (/ 1.0 eps) 1.0)) (cbrt (- (/ 1.0 eps) 1.0))) (* (cbrt (- (/ 1.0 eps) 1.0)) (exp (- (* (+ 1.0 eps) x))))))

series882.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(cbrt (- (/ 1.0 eps) 1.0))
152.0ms	(cbrt (- (/ 1.0 eps) 1.0))
205.0ms	(* (cbrt (- (/ 1.0 eps) 1.0)) (cbrt (- (/ 1.0 eps) 1.0)))
241.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (cbrt (- (/ 1.0 eps) 1.0)) (cbrt (- (/ 1.0 eps) 1.0))) (* (cbrt (- (/ 1.0 eps) 1.0)) (exp (- (* (+ 1.0 eps) x))))))

simplify511.0ms

Algorithm

egg-herbie

Counts

916 → 916

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5002	57830

prune2.6s

Filtered

916 candidates to 357 candidates (39.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	916	0	916
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	916	3	919

Merged error: 0.2b

Counts

919 → 3

regimes75.0ms

Accuracy

96.7% (0.5b remaining)

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

bsearch127.0ms

Steps

Iters	Range		Point
8	108.10498260228141	57946.35045805707	163.11371107757716

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	34
1	62	34
2	62	34

end0.0ms

sample3.0s

Algorithm

intervals

Results

863.0ms	1999×	body	10240	exit
770.0ms	1693×	body	1280	valid
579.0ms	10017×	body	80	valid
336.0ms	1279×	body	640	valid
112.0ms	644×	body	320	valid
33.0ms	294×	body	160	valid

Details

sample99.0ms

simplify35.0ms

prune6.0ms

localize17.0ms

rewrite57.0ms

series313.0ms

simplify146.0ms

prune396.0ms

localize10.0ms

rewrite20.0ms

series168.0ms

simplify44.0ms

prune123.0ms

localize14.0ms

rewrite35.0ms

series223.0ms

simplify47.0ms

prune216.0ms

localize27.0ms

rewrite252.0ms

series882.0ms

simplify511.0ms

prune2.6s

regimes75.0ms

bsearch127.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling