Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify10.0ms

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: 28.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(- (* b c) (* a d))
27.9b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite20.0ms

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:

4.0ms	(+ (* c c) (* d d))
3.0ms	(- (* b c) (* a d))
12.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series149.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* c c) (* d d))
37.0ms	(- (* b c) (* a d))
86.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify37.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (31.0ms)

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

prune187.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* a d))
18.4b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))

rewrite21.0ms

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:

3.0ms	(- (* b c) (* a d))
9.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b c) (* a d))
117.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(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

prune294.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.1b

localize14.0ms

Local error

Found 4 expressions with local error:

12.1b	(/ (* a d) (sqrt (+ (* c c) (* d d))))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

8.0ms	(/ (* a d) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (* a d) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))
40.0ms	(sqrt (+ (* c c) (* d d)))

simplify77.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	200	562
1	766	521
2	3168	514
3	5001	514

prune469.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.1b

localize19.0ms

Local error

Found 4 expressions with local error:

29.2b	(sqrt (+ (* c c) (* d d)))
29.2b	(sqrt (+ (* c c) (* d d)))
30.1b	(cbrt (+ (* c c) (* d d)))
30.1b	(cbrt (+ (* c c) (* d d)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(cbrt (+ (* c c) (* d d)))
4.0ms	(cbrt (+ (* c c) (* d d)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ (* c c) (* d d)))
44.0ms	(sqrt (+ (* c c) (* d d)))
99.0ms	(cbrt (+ (* c c) (* d d)))
93.0ms	(cbrt (+ (* c c) (* d d)))

simplify65.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	141	444
1	440	420
2	1470	416
3	5001	414

prune304.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.1b

regimes133.0ms

Accuracy

0% (2.0b remaining)

Error of 24.5b against oracle of 22.4b and baseline of 24.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	18
1	16	18

end0.0ms

sample533.0ms

Algorithm

intervals

Results

314.0ms

8469×

body

valid