Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

276×

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.9b	(+ (* a c) (* b d))
29.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite49.0ms

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:

7.0ms	(+ (* c c) (* d d))
7.0ms	(+ (* a c) (* b d))
33.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series131.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* c c) (* d d))
29.0ms	(+ (* a c) (* b d))
74.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify129.0ms

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

prune166.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 28.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (* a c) (* b d))
19.1b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.0b	(sqrt (+ (* c c) (* d d)))
30.0b	(sqrt (+ (* c c) (* d d)))

rewrite59.0ms

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:

7.0ms	(+ (* a c) (* b d))
34.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
8.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* a c) (* b d))
98.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
32.0ms	(sqrt (+ (* c c) (* d d)))

simplify79.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

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

prune277.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 25.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(/ 1 (+ (* c c) (* d d)))
0.9b	(+ (* a c) (* b d))
28.6b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `1-exp` `associate-*l/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 97

Calls

4 calls:

8.0ms	(+ (* c c) (* d d))
13.0ms	(/ 1 (+ (* c c) (* d d)))
7.0ms	(+ (* a c) (* b d))
48.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* c c) (* d d))
33.0ms	(/ 1 (+ (* c c) (* d d)))
29.0ms	(+ (* a c) (* b d))
74.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

simplify52.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	393	853
1	2037	749
2	5003	720

prune237.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 25.5b

localize19.0ms

Local error

Found 4 expressions with local error:

19.8b	(cbrt (+ (* a c) (* b d)))
30.0b	(sqrt (+ (* c c) (* d d)))
30.0b	(sqrt (+ (* c c) (* d d)))
30.0b	(sqrt (+ (* c c) (* d d)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 58

Calls

4 calls:

4.0ms	(cbrt (+ (* a c) (* b d)))
7.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (+ (* a c) (* b d)))
31.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))
32.0ms	(sqrt (+ (* c c) (* d d)))

simplify118.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 4 (112.0ms)

Iter	Nodes	Cost
0	255	440
1	654	422
2	1696	416
3	4112	412
4	5001	411

prune275.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 25.5b

regimes259.0ms

Accuracy

37.9% (1.9b remaining)

Error of 25.3b against oracle of 23.3b and baseline of 26.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	38
1	31	38
2	31	38

end0.0ms

sample549.0ms

Algorithm

intervals

Results

278.0ms

8493×

body

valid