Details

sample96.0ms

Algorithm

intervals

Results

31.0ms	57×	body	1280	valid
24.0ms	355×	body	80	valid
11.0ms	38×	body	640	valid
4.0ms	18×	body	320	valid
4.0ms	56×	body	80	overflowed
1.0ms	5×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (37.0ms)

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip--`
27×	`flip3-+` `flip-+`
18×	`un-div-inv`
12×	`add-sqr-sqrt` `exp-prod`
10×	`*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`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--` `difference-of-squares` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

3.0ms	(exp (neg (* (+ 1.0 eps) x)))
4.0ms	(exp (neg (* (- 1.0 eps) x)))
6.0ms	(* (- 1.0 eps) x)
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(exp (neg (* (+ 1.0 eps) x)))
27.0ms	(exp (neg (* (- 1.0 eps) x)))
33.0ms	(* (- 1.0 eps) x)
200.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify144.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	1175	3668
1	4323	3407
2	5002	3396

prune361.0ms

Filtered

161 candidates to 82 candidates (50.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	3	162

Merged error: 0.3b

Counts

162 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
7.4b	(- (+ (* 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)))

series82.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(* 0.6666666666666667 (pow x 3))
39.0ms	(- (+ (* 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

prune92.0ms

Filtered

51 candidates to 31 candidates (60.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Merged error: 0.3b

Counts

54 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 0.6666666666666667 x) x)
0.7b	(cbrt x)
0.7b	(pow (cbrt x) 3)
7.4b	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (* 0.6666666666666667 x) x)
1.0ms	(cbrt x)
7.0ms	(pow (cbrt x) 3)
11.0ms	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 0.6666666666666667 x) x)
177.0ms	(cbrt x)
362.0ms	(pow (cbrt x) 3)
51.0ms	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

simplify75.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	311	379
1	1784	317
2	5003	303

prune158.0ms

Filtered

85 candidates to 49 candidates (57.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Merged error: 0.3b

Counts

88 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

7.4b	(- (+ (* (* (* (cbrt (* (* 0.6666666666666667 x) x)) (cbrt (* (* 0.6666666666666667 x) x))) (cbrt (* (* 0.6666666666666667 x) x))) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))
36.6b	(cbrt (* (* 0.6666666666666667 x) x))
36.6b	(cbrt (* (* 0.6666666666666667 x) x))
36.6b	(cbrt (* (* 0.6666666666666667 x) x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

4 → 41

Calls

4 calls:

20.0ms	(- (+ (* (* (* (cbrt (* (* 0.6666666666666667 x) x)) (cbrt (* (* 0.6666666666666667 x) x))) (cbrt (* (* 0.6666666666666667 x) x))) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))
4.0ms	(cbrt (* (* 0.6666666666666667 x) x))
4.0ms	(cbrt (* (* 0.6666666666666667 x) x))
4.0ms	(cbrt (* (* 0.6666666666666667 x) x))

series731.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (+ (* (* (* (cbrt (* (* 0.6666666666666667 x) x)) (cbrt (* (* 0.6666666666666667 x) x))) (cbrt (* (* 0.6666666666666667 x) x))) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))
217.0ms	(cbrt (* (* 0.6666666666666667 x) x))
216.0ms	(cbrt (* (* 0.6666666666666667 x) x))
211.0ms	(cbrt (* (* 0.6666666666666667 x) x))

simplify197.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (190.0ms)

Iter	Nodes	Cost
0	145	548
1	596	474
2	4005	427
3	5001	391

prune151.0ms

Filtered

53 candidates to 39 candidates (73.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	53	3	56

Merged error: 0.3b

Counts

56 → 3

regimes74.0ms

Accuracy

92.2% (1.3b remaining)

Error of 1.7b against oracle of 0.4b and baseline of 16.9b

bsearch88.0ms

Steps

Iters	Range		Point
5	1.0776744539577754e-18	2.9147887557317638e-18	2.8758174537974977e-18

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	53
1	76	53
2	76	53

end0.0ms

sample2.6s

Algorithm

intervals

Results

904.0ms	1739×	body	1280	valid
712.0ms	10024×	body	80	valid
404.0ms	1269×	body	640	valid
140.0ms	632×	body	320	valid
135.0ms	1957×	body	80	overflowed
40.0ms	273×	body	160	valid

Details

sample96.0ms

simplify39.0ms

prune10.0ms

localize17.0ms

rewrite39.0ms

series286.0ms

simplify144.0ms

prune361.0ms

localize10.0ms

rewrite15.0ms

series82.0ms

simplify35.0ms

prune92.0ms

localize14.0ms

rewrite26.0ms

series622.0ms

simplify75.0ms

prune158.0ms

localize18.0ms

rewrite33.0ms

series731.0ms

simplify197.0ms

prune151.0ms

regimes74.0ms

bsearch88.0ms

simplify2.0ms

end0.0ms

sample2.6s

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