Details

sample64.0ms

Algorithm

intervals

Results

46.0ms

478×

body

valid

simplify108.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	42
1	231	42
2	900	42
3	3753	42
4	5001	42

prune5.0ms

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: 0.2b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-exp-log` `add-cbrt-cube`
48×	`associate-l`
44×	`prod-exp` `cbrt-unprod`
42×	`add-sqr-sqrt`
38×	`times-frac`
36×	`pow1`
33×	`add-cube-cbrt` `*-un-lft-identity`
22×	`pow-prod-down`
15×	`associate-*l/`
13×	`sqrt-prod`
12×	`frac-add`
9×	`cbrt-undiv` `div-exp`
6×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
5×	`associate-r`
4×	`add-log-exp`
3×	`*-commutative` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 155

Calls

4 calls:

23.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
24.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
12.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms	(sqrt PI)

series464.0ms

Counts

4 → 10

Calls

4 calls:

65.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
342.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
57.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify67.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1196	4518
1	5002	3785

prune646.0ms

Filtered

165 candidates to 108 candidates (65.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	159	6	165
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	159	7	166

Merged error: 0.0b

Counts

166 → 7

localize36.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt PI)
1.0b	(* (cbrt PI) (cbrt PI))
1.0b	(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
1.0b	(sqrt (* (cbrt PI) (cbrt PI)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`pow1`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`cbrt-prod` `pow1/3`
18×	`sqrt-pow1`
12×	`times-frac`
11×	`pow-flip`
10×	`add-exp-log`
6×	`swap-sqr` `associate-r` `associate-l` `pow-prod-down` `pow-sqr` `pow-prod-up` `add-cbrt-cube`
5×	`sqrt-prod`
4×	`associate-/r*` `add-log-exp` `unswap-sqr`
3×	`pow2` `pow-plus` `associate-/l*`
2×	`pow1/2` `div-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `frac-2neg` `1-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow`

Counts

4 → 115

Calls

4 calls:

1.0ms	(cbrt PI)
6.0ms	(* (cbrt PI) (cbrt PI))
7.0ms	(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
4.0ms	(sqrt (* (cbrt PI) (cbrt PI)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt PI)
0.0ms	(* (cbrt PI) (cbrt PI))
0.0ms	(/ 1 (sqrt (* (cbrt PI) (cbrt PI))))
0.0ms	(sqrt (* (cbrt PI) (cbrt PI)))

simplify145.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	247	706
1	876	647
2	4260	542
3	5002	537

prune436.0ms

Filtered

119 candidates to 69 candidates (58.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	119	7	126

Merged error: 0.0b

Counts

126 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* (cbrt PI) (cbrt PI)))
1.0b	(cbrt PI)
1.0b	(cbrt PI)
1.0b	(cbrt PI)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 52

Calls

4 calls:

4.0ms	(sqrt (* (cbrt PI) (cbrt PI)))
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt (* (cbrt PI) (cbrt PI)))
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)

simplify61.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	113	274
1	370	262
2	1503	256
3	5002	253

prune245.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	56	7	63

Merged error: 0.0b

Counts

63 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 5.0) (pow (fabs x) 3))
0.2b	(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
0.3b	(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) 1.0) (sqrt PI))
1.0b	(sqrt PI)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
34×	`add-exp-log`
29×	`times-frac`
26×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `add-cbrt-cube`
16×	`associate-*l/`
13×	`associate-r` `prod-exp`
10×	`pow1` `unswap-sqr`
9×	`sqrt-prod` `cbrt-unprod`
8×	`frac-add` `associate-/l/`
7×	`div-exp`
6×	`flip3-+` `associate-r/` `associate-/r` `flip-+`
5×	`cbrt-undiv` `unpow-prod-down` `cube-prod`
4×	`add-log-exp`
3×	`pow-prod-down` `div-inv` `sqr-pow`
2×	`pow-to-exp` `pow-exp` `*-commutative`
1×	`cube-mult` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `unpow3` `clear-num` `associate-/l*`

Counts

4 → 133

Calls

4 calls:

10.0ms	(* (/ 1.0 5.0) (pow (fabs x) 3))
8.0ms	(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
28.0ms	(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) 1.0) (sqrt PI))
1.0ms	(sqrt PI)

series424.0ms

Counts

4 → 10

Calls

4 calls:

45.0ms	(* (/ 1.0 5.0) (pow (fabs x) 3))
38.0ms	(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
341.0ms	(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) 1.0) (sqrt PI))
0.0ms	(sqrt PI)

simplify113.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	796	2153
1	4010	1806
2	5001	1725

prune576.0ms

Filtered

143 candidates to 100 candidates (69.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	3	0	3
Picked	0	1	1
Done	0	3	3
Total	145	5	150

Merged error: 0b

Counts

150 → 5

regimes211.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	42
1	41	42

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.3s

14088×

body

valid