Details

sample21.0ms

Algorithm

intervals

Results

11.0ms

272×

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: 25.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(+ (* a c) (* b d))
25.0b	(/ (+ (* 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:

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

series144.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* c c) (* d d))
33.0ms	(+ (* a c) (* b d))
82.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify131.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (30.0ms)

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

prune178.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* a c) (* b d))
16.6b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite24.0ms

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))
12.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* a c) (* b d))
110.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
36.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify82.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (24.0ms)

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

prune277.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* a c) (* b d))
25.0b	(/ (+ (* a c) (* b d)) (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-div`
10×	`add-sqr-sqrt` `flip3-+` `flip-+`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity` `associate-/r/`
6×	`pow1` `sqrt-prod` `add-log-exp`
4×	`frac-times`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `div-exp` `associate-l/` `associate-/l/`
1×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv`

Counts

4 → 72

Calls

4 calls:

3.0ms	(+ (* a c) (* b d))
18.0ms	(/ (+ (* a c) (* b d)) (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series193.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* a c) (* b d))
83.0ms	(/ (+ (* a c) (* b d)) (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))))
36.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(sqrt (+ (* c c) (* d d)))

simplify90.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	294	782
1	994	686
2	3181	667
3	5002	667

prune250.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.6b

localize14.0ms

Local error

Found 4 expressions with local error:

16.6b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`add-exp-log` `associate-/r*` `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 → 88

Calls

4 calls:

12.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
36.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))

simplify72.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	242	919
1	758	870
2	2276	857
3	5001	857

prune315.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.6b

regimes209.0ms

Accuracy

25.4% (2.2b remaining)

Error of 25.7b against oracle of 23.5b and baseline of 26.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	26
1	28	26
2	28	26

end0.0ms

sample493.0ms

Algorithm

intervals

Results

284.0ms

8482×

body

valid