Details

sample130.0ms

Algorithm

intervals

Results

32.0ms	59×	body	10240	exit
32.0ms	52×	body	1280	valid
27.0ms	320×	body	80	valid
11.0ms	34×	body	640	valid
5.0ms	20×	body	320	valid
1.0ms	9×	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: 26.9b

Counts

2 → 1

localize18.0ms

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)
2.1b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite59.0ms

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:

11.0ms	(* (+ 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)))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
49.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
28.0ms	(* (+ 1.0 eps) x)
188.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify152.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (26.0ms)

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

prune446.0ms

Filtered

184 candidates to 94 candidates (51.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	180	4	184
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	4	185

Merged error: 0.4b

Counts

185 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
6.8b	(- (+ (* 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)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(* 0.6666666666666667 (pow x 3))
42.0ms	(- (+ (* 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

prune119.0ms

Filtered

51 candidates to 31 candidates (60.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Merged error: 0.4b

Counts

55 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
0.1b	(* 0.6666666666666667 (pow x 3))
2.4b	(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
6.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

8.0ms	(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
6.0ms	(* 0.6666666666666667 (pow x 3))
8.0ms	(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series185.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3)
36.0ms	(* 0.6666666666666667 (pow x 3))
43.0ms	(cbrt (pow (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) 3))
39.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify54.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	346	869
1	1520	811
2	5001	802

prune239.0ms

Filtered

105 candidates to 60 candidates (57.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Merged error: 0.4b

Counts

109 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp (- (* (- 1.0 eps) x))))
0.0b	(cbrt (exp (- (* (- 1.0 eps) x))))
0.1b	(* (cbrt (exp (- (* (- 1.0 eps) x)))) (cbrt (exp (- (* (- 1.0 eps) x)))))
3.3b	(- (* (* (+ 1.0 (/ 1.0 eps)) (* (cbrt (exp (- (* (- 1.0 eps) x)))) (cbrt (exp (- (* (- 1.0 eps) x)))))) (cbrt (exp (- (* (- 1.0 eps) x))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

1548×	`frac-times`
1474×	`cbrt-div`
1057×	`exp-neg`
977×	`neg-sub0` `exp-diff`
720×	`frac-sub`
612×	`associate-*l/`
558×	`associate-*r/`
243×	`flip3-+` `flip-+`
241×	`flip3--` `flip--`
80×	`un-div-inv`
22×	`cbrt-prod` `add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l` `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 → 806

Calls

4 calls:

3.0ms	(cbrt (exp (- (* (- 1.0 eps) x))))
3.0ms	(cbrt (exp (- (* (- 1.0 eps) x))))
8.0ms	(* (cbrt (exp (- (* (- 1.0 eps) x)))) (cbrt (exp (- (* (- 1.0 eps) x)))))
56.0ms	(- (* (* (+ 1.0 (/ 1.0 eps)) (* (cbrt (exp (- (* (- 1.0 eps) x)))) (cbrt (exp (- (* (- 1.0 eps) x)))))) (cbrt (exp (- (* (- 1.0 eps) x))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series412.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(cbrt (exp (- (* (- 1.0 eps) x))))
50.0ms	(cbrt (exp (- (* (- 1.0 eps) x))))
109.0ms	(* (cbrt (exp (- (* (- 1.0 eps) x)))) (cbrt (exp (- (* (- 1.0 eps) x)))))
200.0ms	(- (* (* (+ 1.0 (/ 1.0 eps)) (* (cbrt (exp (- (* (- 1.0 eps) x)))) (cbrt (exp (- (* (- 1.0 eps) x)))))) (cbrt (exp (- (* (- 1.0 eps) x))))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify384.0ms

Algorithm

egg-herbie

Counts

818 → 818

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5001	45143

prune961.0ms

Filtered

818 candidates to 156 candidates (19.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	814	4	818
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	817	5	822

Merged error: 0.4b

Counts

822 → 5

regimes95.0ms

Accuracy

96.1% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 17.0b

bsearch158.0ms

Steps

Iters	Range		Point
10	4.278730963433957e-11	13.656696832425032	12.312429890800345

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	97
1	66	97
2	66	97

end0.0ms

sample3.0s

Algorithm

intervals

Results

804.0ms	1843×	body	10240	exit
765.0ms	1711×	body	1280	valid
590.0ms	9938×	body	80	valid
342.0ms	1274×	body	640	valid
114.0ms	636×	body	320	valid
37.0ms	324×	body	160	valid