Details

sample30.0ms

Algorithm

intervals

Results

19.0ms

263×

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(- (* b c) (* a d))
23.0b	(/ (- (* 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:

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

series152.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* c c) (* d d))
38.0ms	(- (* b c) (* a d))
88.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify42.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (31.0ms)

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

prune178.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* a d))
13.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
26.4b	(sqrt (+ (* c c) (* d d)))
26.4b	(sqrt (+ (* c c) (* d d)))

rewrite23.0ms

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))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b c) (* a d))
114.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

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

prune289.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* a d))
13.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
26.4b	(sqrt (+ (* c c) (* d d)))
26.4b	(sqrt (+ (* c c) (* d d)))

rewrite27.0ms

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))
15.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b c) (* a d))
120.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(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

prune302.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* a d))
13.1b	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
26.4b	(sqrt (+ (* c c) (* d d)))
26.4b	(sqrt (+ (* c c) (* d d)))

rewrite23.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

2.0ms	(- (* b c) (* a d))
10.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b c) (* a d))
79.0ms	(/ (sqrt (+ (* c c) (* d d))) (- (* b c) (* a d)))
39.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify67.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	264	889
1	808	842
2	2357	837
3	5001	837

prune276.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.0b

regimes168.0ms

Accuracy

0% (3.1b remaining)

Error of 26.4b against oracle of 23.3b and baseline of 26.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	15
1	21	15

end0.0ms

sample862.0ms

Algorithm

intervals

Results

645.0ms

8480×

body

valid