Details

sample31.0ms

Algorithm

intervals

Results

19.0ms

270×

body

valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
27.5b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

2.0ms	(+ (* c c) (* d d))
3.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series158.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* c c) (* d d))
39.0ms	(- (* b c) (* a d))
88.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify40.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	292	541
1	1273	493
2	5002	491

prune193.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
17.9b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.6b	(sqrt (+ (* c c) (* d d)))
28.6b	(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

2.0ms	(- (* b c) (* a d))
11.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b c) (* a d))
115.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify102.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845

prune292.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.0b

localize13.0ms

Local error

Found 4 expressions with local error:

11.2b	(/ (* a d) (sqrt (+ (* c c) (* d d))))
28.6b	(sqrt (+ (* c c) (* d d)))
28.6b	(sqrt (+ (* c c) (* d d)))
28.6b	(sqrt (+ (* c c) (* d d)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-div`
7×	`pow1`
6×	`times-frac` `associate-/r*`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

7.0ms	(/ (* a d) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series183.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (* a d) (sqrt (+ (* c c) (* d d))))
36.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(sqrt (+ (* c c) (* d d)))
51.0ms	(sqrt (+ (* c c) (* d d)))

simplify78.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	200	562
1	766	521
2	3168	514
3	5001	514

prune269.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.6b

localize13.0ms

Local error

Found 4 expressions with local error:

10.7b	(/ (* b c) (sqrt (+ (* c c) (* d d))))
28.6b	(sqrt (+ (* c c) (* d d)))
28.6b	(sqrt (+ (* c c) (* d d)))
28.6b	(sqrt (+ (* c c) (* d d)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-div`
7×	`pow1`
6×	`times-frac` `associate-/r*`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

7.0ms	(/ (* b c) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* b c) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify75.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	199	562
1	770	521
2	3194	514
3	5001	514

prune265.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.9b

regimes177.0ms

Accuracy

0% (0.4b remaining)

Error of 22.2b against oracle of 21.8b and baseline of 22.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	18
1	17	18

end0.0ms

sample756.0ms

Algorithm

intervals

Results

535.0ms

8488×

body

valid