Details

sample32.0ms

Algorithm

intervals

Results

21.0ms

274×

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: 24.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
23.8b	(/ (- (* 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:

3.0ms	(+ (* c c) (* d d))
2.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series164.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* c c) (* d d))
43.0ms	(- (* b c) (* a d))
92.0ms	(/ (- (* 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

prune189.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.7b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.7b	(sqrt (+ (* c c) (* d d)))
28.7b	(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

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

series227.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* b c) (* a d))
112.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(sqrt (+ (* c c) (* d d)))

simplify97.0ms

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

prune292.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.8b	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
28.7b	(sqrt (+ (* c c) (* d d)))
28.7b	(sqrt (+ (* c c) (* d d)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

2.0ms	(- (* b c) (* a d))
25.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b c) (* a d))
120.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
35.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))

simplify50.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	378	916
1	1785	831
2	5001	807

prune312.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
0.7b	(/ 1 (+ (* c c) (* d d)))
23.4b	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `flip3-+` `associate-l` `associate-/r` `flip--` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 98

Calls

4 calls:

2.0ms	(+ (* c c) (* d d))
2.0ms	(- (* b c) (* a d))
5.0ms	(/ 1 (+ (* c c) (* d d)))
20.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* c c) (* d d))
43.0ms	(- (* b c) (* a d))
37.0ms	(/ 1 (+ (* c c) (* d d)))
87.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

simplify50.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	384	857
1	1929	753
2	5002	724

prune223.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 21.0b

regimes150.0ms

Accuracy

0% (3.2b remaining)

Error of 26.1b against oracle of 22.9b and baseline of 26.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

end0.0ms

sample861.0ms

Algorithm

intervals

Results

638.0ms

8450×

body

valid