Details

sample37.0ms

Algorithm

intervals

Results

26.0ms

270×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* a c) (* b d))
27.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite15.0ms

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:

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

series118.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ (* a c) (* b d))
82.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify86.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (24.0ms)

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

prune130.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 27.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
15.9b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
33.4b	(sqrt (+ (* c c) (* d d)))
33.4b	(sqrt (+ (* c c) (* d d)))

rewrite25.0ms

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))))
4.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a c) (* b d))
106.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify84.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (25.0ms)

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

prune271.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 25.9b

localize15.0ms

Local error

Found 4 expressions with local error:

13.7b	(* (/ 1 (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d))))) (/ (+ (* a c) (* b d)) (cbrt (+ (* c c) (* d d)))))
34.4b	(cbrt (+ (* c c) (* d d)))
34.4b	(cbrt (+ (* c c) (* d d)))
34.4b	(cbrt (+ (* c c) (* d d)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
43×	`add-sqr-sqrt`
33×	`times-frac`
25×	`*-un-lft-identity`
24×	`associate-r`
22×	`add-cube-cbrt`
21×	`cbrt-prod`
20×	`cbrt-div` `prod-exp`
18×	`add-cbrt-cube`
15×	`div-exp` `associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1`
5×	`frac-times`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 119

Calls

4 calls:

80.0ms	(* (/ 1 (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d))))) (/ (+ (* a c) (* b d)) (cbrt (+ (* c c) (* d d)))))
2.0ms	(cbrt (+ (* c c) (* d d)))
2.0ms	(cbrt (+ (* c c) (* d d)))
5.0ms	(cbrt (+ (* c c) (* d d)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (/ 1 (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d))))) (/ (+ (* a c) (* b d)) (cbrt (+ (* c c) (* d d)))))
96.0ms	(cbrt (+ (* c c) (* d d)))
97.0ms	(cbrt (+ (* c c) (* d d)))
94.0ms	(cbrt (+ (* c c) (* d d)))

simplify89.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	614	2237
1	3263	1929
2	5001	1759

prune360.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 25.9b

localize22.0ms

Local error

Found 4 expressions with local error:

34.4b	(cbrt (+ (* c c) (* d d)))
34.4b	(cbrt (+ (* c c) (* d d)))
34.4b	(cbrt (+ (* c c) (* d d)))
34.4b	(cbrt (+ (* c c) (* d d)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (+ (* c c) (* d d)))
2.0ms	(cbrt (+ (* c c) (* d d)))
2.0ms	(cbrt (+ (* c c) (* d d)))
2.0ms	(cbrt (+ (* c c) (* d d)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ (* c c) (* d d)))
91.0ms	(cbrt (+ (* c c) (* d d)))
92.0ms	(cbrt (+ (* c c) (* d d)))
97.0ms	(cbrt (+ (* c c) (* d d)))

simplify51.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	123	488
1	408	452
2	1387	444
3	5002	444

prune286.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 25.9b

regimes165.0ms

Accuracy

0% (3.0b remaining)

Error of 26.6b against oracle of 23.6b and baseline of 26.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample1.0s

Algorithm

intervals

Results

825.0ms

8533×

body

valid