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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
24.6b	(/ (+ (* a c) (* b 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`
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:

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

series138.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* c c) (* d d))
32.0ms	(+ (* a c) (* b d))
79.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify128.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (28.0ms)

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

prune162.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 24.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
14.7b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.8b	(sqrt (+ (* c c) (* d d)))
28.8b	(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`
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))
11.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* a c) (* b d))
104.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify82.0ms

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

prune267.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.6b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
0.7b	(+ (* a c) (* b d))
24.4b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite31.0ms

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:

2.0ms	(+ (* c c) (* d d))
11.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
2.0ms	(+ (* a c) (* b d))
10.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* c c) (* d d))
130.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
32.0ms	(+ (* a c) (* b d))
53.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify69.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (51.0ms)

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

prune282.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 22.1b

localize16.0ms

Local error

Found 4 expressions with local error:

14.7b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.8b	(sqrt (+ (* c c) (* d d)))
28.8b	(sqrt (+ (* c c) (* d d)))
40.6b	(cbrt (pow (sqrt (+ (* c c) (* d d))) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
18×	`cbrt-prod` `times-frac`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `unpow-prod-down` `cube-prod` `associate-/r*` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`associate-/l*`
2×	`cube-div` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `frac-2neg` `pow1/3` `unpow3` `div-exp` `clear-num` `rem-cbrt-cube` `div-inv` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

11.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))
5.0ms	(cbrt (pow (sqrt (+ (* c c) (* d d))) 3))

series210.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(cbrt (pow (sqrt (+ (* c c) (* d d))) 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	340	1014
1	1338	937
2	5001	934

prune322.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 22.1b

regimes136.0ms

Accuracy

0% (2.9b remaining)

Error of 26.3b against oracle of 23.3b and baseline of 26.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample495.0ms

Algorithm

intervals

Results

290.0ms

8472×

body

valid