Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

269×

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

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ (* a c) (* b d))
25.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

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

series117.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* a c) (* b d))
84.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify84.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2851	412
3	5003	412

prune148.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* a c) (* b d))
14.6b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.7b	(sqrt (+ (* c c) (* d d)))
31.7b	(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)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* a c) (* b d))
108.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
36.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(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

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 24.1b

localize15.0ms

Local error

Found 4 expressions with local error:

7.5b	(/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d)))))
31.7b	(sqrt (+ (* c c) (* d d)))
31.7b	(sqrt (+ (* c c) (* d d)))
31.7b	(sqrt (+ (* c c) (* d d)))

rewrite26.0ms

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:

12.0ms	(/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d)))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d)))))
40.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify80.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (23.0ms)

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

prune389.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.1b

localize16.0ms

Local error

Found 4 expressions with local error:

9.8b	(/ (+ (* a c) (* b d)) (fabs (cbrt (+ (* c c) (* d d)))))
31.7b	(sqrt (+ (* c c) (* d d)))
32.8b	(cbrt (+ (* c c) (* d d)))
32.8b	(cbrt (+ (* c c) (* d d)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

8.0ms	(/ (+ (* a c) (* b d)) (fabs (cbrt (+ (* c c) (* d d)))))
3.0ms	(sqrt (+ (* c c) (* d d)))
2.0ms	(cbrt (+ (* c c) (* d d)))
2.0ms	(cbrt (+ (* c c) (* d d)))

series341.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (* a c) (* b d)) (fabs (cbrt (+ (* c c) (* d d)))))
42.0ms	(sqrt (+ (* c c) (* d d)))
96.0ms	(cbrt (+ (* c c) (* d d)))
96.0ms	(cbrt (+ (* c c) (* d d)))

simplify139.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	300	831
1	1116	772
2	4292	767
3	5003	765

prune337.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 24.1b

regimes191.0ms

Accuracy

0% (3.0b 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

sample509.0ms

Algorithm

intervals

Results

297.0ms

8463×

body

valid