Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
7.0ms	259×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 6.0 (- x 1.0))
0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.3b	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite24.0ms

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:

6.0ms	(* 6.0 (- x 1.0))
6.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
11.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series159.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(* 6.0 (- x 1.0))
35.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
79.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (40.0ms)

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

prune165.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize9.0ms

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)))

rewrite34.0ms

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:

11.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
11.0ms	(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

series199.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
41.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
80.0ms	(/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (63.0ms)

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

prune400.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 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	(/ 1 (/ (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)) 6.0))
0.0b	(/ (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)) 6.0)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

771×	`times-frac`
440×	`add-sqr-sqrt` `*-un-lft-identity`
336×	`add-cube-cbrt`
75×	`associate-/r*`
52×	`distribute-lft-out--` `difference-of-squares`
35×	`associate-/r/`
32×	`add-exp-log`
27×	`associate-/l*`
23×	`div-inv`
20×	`add-cbrt-cube`
19×	`div-exp`
17×	`flip3--` `flip--`
10×	`cbrt-undiv`
9×	`add-log-exp`
5×	`pow1`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `associate-+l+` `pow-flip` `inv-pow`

Counts

4 → 450

Calls

4 calls:

10.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
10.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
22.0ms	(/ 1 (/ (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)) 6.0))
14.0ms	(/ (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)) 6.0)

series470.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))
40.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
277.0ms	(/ 1 (/ (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)) 6.0))
84.0ms	(/ (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)) 6.0)

simplify94.0ms

Algorithm

egg-herbie

Counts

462 → 462

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1593	7412
1	5001	6855

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

25068×	`times-frac`
15405×	`*-un-lft-identity`
13777×	`add-sqr-sqrt`
12195×	`sqrt-prod`
8249×	`add-cube-cbrt`
2764×	`difference-of-squares`
2196×	`distribute-lft-out`
1382×	`distribute-lft-out--`
658×	`associate-/r/`
360×	`div-inv`
186×	`flip3-+` `flip-+`
119×	`associate-/l*`
115×	`flip3--` `flip--`
69×	`associate-/r*`
27×	`add-exp-log` `add-cbrt-cube`
16×	`cbrt-undiv` `div-exp`
14×	`add-log-exp`
6×	`sum-log`
4×	`pow1`
3×	`associate-/l/`
2×	`+-commutative` `associate-+l+` `frac-2neg` `sqrt-div` `clear-num`

Counts

4 → 7088

Calls

4 calls:

11.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
10.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
24.0ms	(/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))
195.0ms	(/ (/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (+ (sqrt x) (sqrt 1.0)))) (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0))))

series999.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
35.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
497.0ms	(/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0)))
425.0ms	(/ (/ 6.0 (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (+ (sqrt x) (sqrt 1.0)))) (/ (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))) (- (sqrt x) (sqrt 1.0))))

simplify2.7s

Algorithm

egg-herbie

Counts

7100 → 7100

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5001	322214

prune12.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes20.0ms

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	18	8
1	18	8

end0.0ms

sample627.0ms

Algorithm

intervals

Results

235.0ms	8000×	body	80	valid
214.0ms	8043×	body	80	nan