Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

269×

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: 25.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.4b	(- (* b c) (* a d))
24.7b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite16.0ms

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:

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

series158.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* c c) (* d d))
39.0ms	(- (* b c) (* a d))
88.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify39.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (33.0ms)

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

prune180.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b c) (* a d))
15.2b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
27.3b	(sqrt (+ (* c c) (* d d)))
27.3b	(sqrt (+ (* c c) (* d d)))

rewrite26.0ms

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))))
7.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b c) (* a d))
117.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
40.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify98.0ms

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

prune479.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
14.8b	(/ (* a d) (+ (* c c) (* d d)))
18.3b	(/ (* b c) (+ (* c c) (* d d)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `associate-/r/` `add-log-exp`
6×	`times-frac` `associate-/r*`
5×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `div-exp` `div-inv`
3×	`distribute-rgt-out--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l*`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

3.0ms	(+ (* c c) (* d d))
33.0ms	(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
6.0ms	(/ (* a d) (+ (* c c) (* d d)))
6.0ms	(/ (* b c) (+ (* c c) (* d d)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* c c) (* d d))
121.0ms	(- (/ (* b c) (+ (* c c) (* d d))) (/ (* a d) (+ (* c c) (* d d))))
45.0ms	(/ (* a d) (+ (* c c) (* d d)))
50.0ms	(/ (* b c) (+ (* c c) (* d d)))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	385	746
1	1875	664
2	5002	660

prune222.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ a (sqrt (+ (* c c) (* d d)))) (/ d (sqrt (+ (* c c) (* d d)))))
18.3b	(/ (* b c) (+ (* c c) (* d d)))
27.3b	(sqrt (+ (* c c) (* d d)))
27.3b	(sqrt (+ (* c c) (* d d)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
51×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
30×	`sqrt-prod`
24×	`associate-r` `associate-l`
21×	`add-exp-log` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`pow1` `sqrt-div`
6×	`cbrt-undiv` `div-exp` `associate-/r/`
5×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
4×	`add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 130

Calls

4 calls:

41.0ms	(* (/ a (sqrt (+ (* c c) (* d d)))) (/ d (sqrt (+ (* c c) (* d d)))))
6.0ms	(/ (* b c) (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (/ a (sqrt (+ (* c c) (* d d)))) (/ d (sqrt (+ (* c c) (* d d)))))
45.0ms	(/ (* b c) (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify65.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	576	1547
1	2594	1391
2	5001	1322

prune366.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.4b

regimes112.0ms

Accuracy

0% (1.1b remaining)

Error of 22.9b against oracle of 21.8b and baseline of 22.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	23
1	18	23

end0.0ms

sample498.0ms

Algorithm

intervals

Results

289.0ms

8514×

body

valid