Details

sample46.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
14.0ms	243×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	39	7
2	61	7
3	80	7
4	105	7
5	114	7
6	114	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (- x 1.0))
0.1b	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
9×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `associate-r`
4×	`associate-*r/`
3×	`times-frac` `associate-l` `associate-/r*` `sum-log`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l+` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
6.0ms	(* 6.0 (- x 1.0))
10.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series148.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
39.0ms	(* 6.0 (- x 1.0))
75.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify54.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	377	495
1	1642	421
2	5001	420

prune133.0ms

Filtered

73 candidates to 53 candidates (72.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Merged error: 0b

Counts

74 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `sum-log`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l+`

Counts

3 → 154

Calls

3 calls:

10.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
6.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
13.0ms	(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

series188.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
36.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
79.0ms	(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	641	2084
1	2942	1986
2	5001	1984

prune300.0ms

Filtered

163 candidates to 126 candidates (77.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	163	3	166

Merged error: 0b

Counts

166 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(+ 1.0 (* 4.0 (sqrt x)))
0.0b	(* 6.0 (- x 1.0))
0.1b	(/ (* 6.0 (- x 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1`
5×	`associate-r`
4×	`times-frac` `associate-r/` `associate-/r` `sum-log`
3×	`flip3-+` `associate-l` `flip-+` `distribute-lft-out`
2×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/`
1×	`associate-+r+` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
2.0ms	(+ 1.0 (* 4.0 (sqrt x)))
6.0ms	(* 6.0 (- x 1.0))
9.0ms	(/ (* 6.0 (- x 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series191.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
37.0ms	(+ 1.0 (* 4.0 (sqrt x)))
41.0ms	(* 6.0 (- x 1.0))
75.0ms	(/ (* 6.0 (- x 1.0)) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	422	590
1	1779	510
2	5001	510

prune137.0ms

Filtered

90 candidates to 65 candidates (72.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	90	3	93

Merged error: 0b

Counts

93 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
0.1b	(* (* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
0.2b	(* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
16.0b	(/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
31×	`times-frac`
25×	`add-cube-cbrt`
22×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
6×	`associate-r` `add-log-exp`
5×	`associate-l/` `associate-/l`
4×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r/`
3×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-/r*` `flip--` `flip-+`
2×	`frac-times` `sub-neg` `associate-+r+` `associate-r/` `associate--l+` `-commutative` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `div-sub` `clear-num` `sum-log`

Counts

4 → 124

Calls

4 calls:

5.0ms	(+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
15.0ms	(* (* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
14.0ms	(* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
8.0ms	(/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))
121.0ms	(* (* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0) (- (+ x 1.0) (* 4.0 (sqrt x))))
58.0ms	(* (/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0)))) 6.0)
56.0ms	(/ (- x 1.0) (+ (* (- (* 4.0 4.0)) x) (* (+ x 1.0) (+ x 1.0))))

simplify91.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	679	2076
1	3109	1821
2	5001	1802

prune283.0ms

Filtered

136 candidates to 100 candidates (73.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	136	3	139

Merged error: 0b

Counts

139 → 3

regimes13.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

end0.0ms

sample834.0ms

Algorithm

intervals

Results

330.0ms	8000×	body	80	valid
303.0ms	8097×	body	80	nan