Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

268×

body

valid

simplify11.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* b c) (* a d))
24.2b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

8.0ms	(- (* b c) (* a d))
25.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series135.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (* b c) (* a d))
92.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify97.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	251	464
1	938	427
2	3504	426
3	5001	426

prune137.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* b c) (* a d))
14.9b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(sqrt (+ (* c c) (* d d)))

rewrite53.0ms

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:

8.0ms	(- (* b c) (* a d))
25.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b c) (* a d))
121.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
36.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify94.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

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

prune287.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.4b

localize15.0ms

Local error

Found 4 expressions with local error:

10.4b	(/ (* a d) (sqrt (+ (* c c) (* d d))))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(sqrt (+ (* c c) (* d d)))

rewrite44.0ms

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:

17.0ms	(/ (* a d) (sqrt (+ (* c c) (* d d))))
10.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series175.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (* a d) (sqrt (+ (* c c) (* d d))))
37.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify76.0ms

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

prune264.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.2b

localize18.0ms

Local error

Found 4 expressions with local error:

8.9b	(/ (* b c) (sqrt (+ (* c c) (* d d))))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(sqrt (+ (* c c) (* d d)))

rewrite41.0ms

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:

17.0ms	(/ (* b c) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series170.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (* b c) (sqrt (+ (* c c) (* d d))))
36.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify73.0ms

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

prune235.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.7b

regimes134.0ms

Accuracy

0% (0.4b remaining)

Error of 22.1b against oracle of 21.7b and baseline of 22.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	18
1	15	18

end0.0ms

sample605.0ms

Algorithm

intervals

Results

322.0ms

8478×

body

valid