Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

278×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(+ (* a c) (* b d))
22.1b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite18.0ms

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`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

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

series142.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* c c) (* d d))
31.0ms	(+ (* a c) (* b d))
79.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify132.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4451	477
3	5003	477

prune180.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* a c) (* b d))
12.9b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))

rewrite28.0ms

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

Counts

4 → 84

Calls

4 calls:

2.0ms	(+ (* a c) (* b d))
15.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* a c) (* b d))
108.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
33.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))

simplify80.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2693	828
3	5001	828

prune294.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(+ (* a c) (* b d))
0.9b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
21.3b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

3.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* a c) (* b d))
12.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
15.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* c c) (* d d))
31.0ms	(+ (* a c) (* b d))
132.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
49.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify65.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	518	1821
1	2632	1656
2	5001	1569

prune489.0ms

Filtered

149 candidates to 86 candidates (57.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.6b

localize18.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d)))))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

13.0ms	(/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d)))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d)))))
33.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))

simplify81.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	296	1227
1	871	1172
2	2543	1144
3	5001	1144

prune344.0ms

Filtered

112 candidates to 82 candidates (73.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.6b

regimes251.0ms

Accuracy

0% (3.0b remaining)

Error of 26.6b against oracle of 23.5b and baseline of 26.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample497.0ms

Algorithm

intervals

Results

292.0ms

8480×

body

valid