Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

264×

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: 25.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.2b	(- (* b c) (* a d))
25.0b	(/ (- (* 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))
9.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series364.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (* c c) (* d d))
38.0ms	(- (* b c) (* a d))
292.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify40.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (34.0ms)

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

prune183.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.8b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b c) (* a d))
15.9b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.3b	(sqrt (+ (* c c) (* d d)))
29.3b	(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))))
3.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b c) (* a d))
114.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
40.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))

simplify98.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	304	912
1	990	857
2	3354	845
3	5001	845

prune288.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.0b

localize17.0ms

Local error

Found 4 expressions with local error:

14.2b	(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
16.5b	(cbrt (- (* b c) (* a d)))
16.5b	(cbrt (- (* b c) (* a d)))
16.5b	(cbrt (- (* b c) (* a d)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
25×	`add-sqr-sqrt`
24×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
19×	`cbrt-prod`
16×	`add-exp-log` `frac-times`
15×	`flip3--` `flip--`
12×	`associate-*l/`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+` `div-inv`

Counts

4 → 102

Calls

4 calls:

49.0ms	(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
2.0ms	(cbrt (- (* b c) (* a d)))
2.0ms	(cbrt (- (* b c) (* a d)))
2.0ms	(cbrt (- (* b c) (* a d)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (* (cbrt (- (* b c) (* a d))) (cbrt (- (* b c) (* a d)))) (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
116.0ms	(cbrt (- (* b c) (* a d)))
118.0ms	(cbrt (- (* b c) (* a d)))
121.0ms	(cbrt (- (* b c) (* a d)))

simplify67.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	619	1928
1	2363	1739
2	5001	1650

prune390.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.0b

localize19.0ms

Local error

Found 4 expressions with local error:

16.5b	(cbrt (- (* b c) (* a d)))
21.6b	(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
21.6b	(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
21.6b	(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

102×	`cbrt-prod`
54×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-/r/`
5×	`cbrt-div`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `div-inv`
1×	`flip3--` `flip--`

Counts

4 → 112

Calls

4 calls:

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

series918.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (- (* b c) (* a d)))
267.0ms	(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
270.0ms	(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))
265.0ms	(cbrt (/ (cbrt (- (* b c) (* a d))) (+ (* c c) (* d d))))

simplify118.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	432	2151
1	1205	2085
2	4263	2061
3	5002	2038

prune551.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 23.0b

regimes205.0ms

Accuracy

0% (2.8b remaining)

Error of 25.7b against oracle of 22.9b and baseline of 25.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	13
1	16	13

end0.0ms

sample514.0ms

Algorithm

intervals

Results

299.0ms

8495×

body

valid