Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

270×

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
27.3b	(/ (- (* 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)))

series153.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* c c) (* d d))
40.0ms	(- (* b c) (* a d))
85.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify39.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (32.0ms)

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

prune168.0ms

Filtered

64 candidates to 50 candidates (78.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 26.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.8b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
32.2b	(sqrt (+ (* c c) (* d d)))
32.2b	(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))
10.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b c) (* a d))
111.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
38.0ms	(sqrt (+ (* c c) (* d d)))
36.0ms	(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

prune274.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
16.9b	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
32.2b	(sqrt (+ (* c c) (* d d)))
32.2b	(sqrt (+ (* c c) (* d d)))

rewrite37.0ms

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

series226.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* b c) (* a d))
111.0ms	(* (- (* b c) (* a d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
36.0ms	(sqrt (+ (* c c) (* d d)))
38.0ms	(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

prune280.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 24.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(+ (* c c) (* d d))
15.3b	(/ (* b c) (+ (* c c) (* d d)))
18.4b	(/ (* a d) (+ (* c c) (* d d)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`times-frac` `associate-/r*`
4×	`pow1` `cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+`
2×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

2.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* c c) (* d d))
6.0ms	(/ (* b c) (+ (* c c) (* d d)))
6.0ms	(/ (* a d) (+ (* c c) (* d d)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* c c) (* d d))
28.0ms	(+ (* c c) (* d d))
43.0ms	(/ (* b c) (+ (* c c) (* d d)))
46.0ms	(/ (* a d) (+ (* c c) (* d d)))

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	309	530
1	1570	442
2	5001	438

prune188.0ms

Filtered

80 candidates to 60 candidates (75.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 23.7b

regimes116.0ms

Accuracy

40% (1.5b remaining)

Error of 23.7b against oracle of 22.1b and baseline of 24.7b

bsearch106.0ms

Steps

Iters	Range		Point
9	6.632739157271252e+62	1.647935043894467e+68	3.4366687886863465e+63
10	-1.1492159344471653e-16	-6.899281251030229e-31	-4.002330886974353e-17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	28
1	37	28

end0.0ms

sample500.0ms

Algorithm

intervals

Results

290.0ms

8451×

body

valid