Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

273×

body

valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	36	7
2	48	7
3	66	7
4	72	7
5	72	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (* b c) (* a d))
28.7b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite13.0ms

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×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

2.0ms	(- (* b c) (* a d))
9.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series127.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (* b c) (* a d))
88.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify104.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	251	464
1	938	427
2	3504	426
3	5001	426

prune148.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b c) (* a d))
17.3b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(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`
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))
10.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
7.0ms	(sqrt (+ (* c c) (* d d)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b c) (* a d))
111.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
39.0ms	(sqrt (+ (* c c) (* d d)))
35.0ms	(sqrt (+ (* c c) (* d d)))

simplify96.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	304	910
1	990	857
2	3354	845
3	5001	845

prune291.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 25.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b c) (* a d))
17.4b	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite36.0ms

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))
24.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b c) (* a d))
114.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
35.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify46.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (37.0ms)

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

prune301.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(- (* b c) (* a d))
0.5b	(/ 1 (+ (* c c) (* d d)))
28.5b	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 87

Calls

3 calls:

2.0ms	(- (* b c) (* a d))
5.0ms	(/ 1 (+ (* c c) (* d d)))
23.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

series166.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(- (* b c) (* a d))
37.0ms	(/ 1 (+ (* c c) (* d d)))
87.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

simplify46.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	343	780
1	1563	687
2	5002	659

prune381.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.2b

regimes154.0ms

Accuracy

0% (3.2b remaining)

Error of 26.2b against oracle of 23.0b and baseline of 26.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

end0.0ms

sample531.0ms

Algorithm

intervals

Results

314.0ms

8485×

body

valid