Details

sample92.0ms

Algorithm

intervals

Results

30.0ms	58×	body	1280	valid
22.0ms	295×	body	80	valid
13.0ms	33×	body	640	valid
5.0ms	25×	body	320	valid
4.0ms	58×	body	80	overflowed
1.0ms	4×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

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)))))

rewrite60.0ms

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))))
9.0ms	(* (- 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)))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
33.0ms	(* (- 1.0 eps) x)
27.0ms	(* (+ 1.0 eps) x)
197.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify157.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 1 (27.0ms)

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

prune387.0ms

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)))

series156.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(+ (* 0.6666666666666667 (pow x 3)) 2.0)
36.0ms	(* 0.6666666666666667 (pow x 3))
42.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify38.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (32.0ms)

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

prune120.0ms

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))))

rewrite33.0ms

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:

7.0ms	(* 0.6666666666666667 (pow x 3))
8.0ms	(exp (log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))))
8.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
7.0ms	(log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 0.6666666666666667 (pow x 3))
37.0ms	(exp (log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))))
43.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
84.0ms	(log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

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

prune198.0ms

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

localize21.0ms

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))))))

rewrite320.0ms

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:

7.0ms	(cbrt (- (/ 1.0 eps) 1.0))
10.0ms	(cbrt (- (/ 1.0 eps) 1.0))
19.0ms	(* (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))))))

series700.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (- (/ 1.0 eps) 1.0))
142.0ms	(cbrt (- (/ 1.0 eps) 1.0))
188.0ms	(* (cbrt (- (/ 1.0 eps) 1.0)) (cbrt (- (/ 1.0 eps) 1.0)))
231.0ms	(- (* (+ 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))))))

simplify667.0ms

Algorithm

egg-herbie

Counts

916 → 916

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5002	57830

prune2.4s

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

regimes74.0ms

Accuracy

96.7% (0.5b remaining)

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

bsearch130.0ms

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

sample2.6s

Algorithm

intervals

Results

867.0ms	1693×	body	1280	valid
710.0ms	10017×	body	80	valid
398.0ms	1279×	body	640	valid
139.0ms	1999×	body	80	overflowed
135.0ms	644×	body	320	valid
42.0ms	294×	body	160	valid