Details

sample105.0ms

Algorithm

intervals

Results

30.0ms	68×	body	10240	exit
26.0ms	60×	body	1280	valid
18.0ms	343×	body	80	valid
9.0ms	35×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	11×	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: 29.6b

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	(exp (- (* (- 1.0 eps) x)))
0.0b	(exp (- (* (+ 1.0 eps) x)))
2.6b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
78×	`exp-neg`
76×	`frac-times`
59×	`neg-sub0` `exp-diff`
38×	`associate-r/` `associate-l/`
30×	`flip3-+` `flip-+`
28×	`flip3--` `flip--`
19×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube`
5×	`add-exp-log`
4×	`associate-l` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 155

Calls

4 calls:

12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
7.0ms	(exp (- (* (- 1.0 eps) x)))
3.0ms	(exp (- (* (+ 1.0 eps) x)))
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
31.0ms	(exp (- (* (- 1.0 eps) x)))
25.0ms	(exp (- (* (+ 1.0 eps) x)))
190.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify145.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	1163	3849
1	4237	3585
2	5001	3574

prune408.0ms

Filtered

167 candidates to 86 candidates (51.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	4	168

Merged error: 0.2b

Counts

168 → 4

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
5.0b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite15.0ms

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)))

series76.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(* 0.6666666666666667 (pow x 3))
37.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (29.0ms)

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

prune115.0ms

Filtered

51 candidates to 31 candidates (60.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	50	5	55

Merged error: 0.2b

Counts

55 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
0.1b	(* 0.6666666666666667 (pow x 3))
9.0b	(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
10.2b	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))) (* 1.0 (* 1.0 (pow x 4)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `difference-of-squares`
39×	`times-frac`
34×	`sqr-pow`
30×	`add-cube-cbrt`
24×	`associate-r`
18×	`unpow-prod-down` `cube-prod`
16×	`add-exp-log`
13×	`associate-/l*`
10×	`add-cbrt-cube`
8×	`unswap-sqr`
6×	`associate-l` `prod-exp` `add-log-exp`
5×	`difference-cubes` `distribute-lft-out--`
4×	`pow1`
3×	`associate-/r*`
2×	`cube-mult` `pow-to-exp` `flip3--` `unpow3` `pow-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 156

Calls

4 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
6.0ms	(* 0.6666666666666667 (pow x 3))
14.0ms	(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
35.0ms	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))) (* 1.0 (* 1.0 (pow x 4)))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 0.6666666666666667 (pow x 3))
41.0ms	(* 0.6666666666666667 (pow x 3))
95.0ms	(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
147.0ms	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))) (* 1.0 (* 1.0 (pow x 4)))))

simplify241.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	586	3473
1	2661	3317
2	5001	3316

prune602.0ms

Filtered

168 candidates to 116 candidates (69.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	0	3	3
Picked	0	1	1
Done	1	0	1
Total	167	6	173

Merged error: 0.2b

Counts

173 → 6

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666665 (pow x 3))
5.0b	(- (+ (* 0.6666666666666665 (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	(* 0.6666666666666665 (pow x 3))
7.0ms	(- (+ (* 0.6666666666666665 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series73.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(* 0.6666666666666665 (pow x 3))
40.0ms	(- (+ (* 0.6666666666666665 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (29.0ms)

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

prune96.0ms

Filtered

51 candidates to 31 candidates (60.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	51	6	57

Merged error: 0.2b

Counts

57 → 6

regimes85.0ms

Accuracy

96.8% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 16.8b

bsearch111.0ms

Steps

Iters	Range		Point
7	0.045867437731835374	3.2840724432267394	1.846133170564842

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	51
1	74	51
2	74	51

end0.0ms

sample2.8s

Algorithm

intervals

Results

814.0ms	2020×	body	10240	exit
728.0ms	1701×	body	1280	valid
556.0ms	10110×	body	80	valid
310.0ms	1230×	body	640	valid
111.0ms	679×	body	320	valid
31.0ms	295×	body	160	valid