Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

265×

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: 29.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(- (* b c) (* a d))
28.6b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite17.0ms

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))
11.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* c c) (* d d))
41.0ms	(- (* b c) (* a d))
87.0ms	(/ (- (* 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

prune179.0ms

Filtered

64 candidates to 50 candidates (78.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 28.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* a d))
16.2b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
31.3b	(sqrt (+ (* c c) (* d d)))
31.3b	(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))
12.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b c) (* a d))
111.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
37.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(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

prune290.0ms

Filtered

98 candidates to 75 candidates (76.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(- (* b c) (* a d))
28.6b	(/ (- (* b c) (* a d)) (* 1 (+ (* c c) (* d d))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow1` `times-frac` `div-exp` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `flip3-+` `associate-*r/` `prod-exp` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `frac-2neg` `diff-log` `1-exp` `div-sub` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv`

Counts

3 → 50

Calls

3 calls:

3.0ms	(+ (* c c) (* d d))
2.0ms	(- (* b c) (* a d))
11.0ms	(/ (- (* b c) (* a d)) (* 1 (+ (* c c) (* d d))))

series152.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* c c) (* d d))
38.0ms	(- (* b c) (* a d))
85.0ms	(/ (- (* b c) (* a d)) (* 1 (+ (* c c) (* d d))))

simplify49.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	346	451
1	1900	382
2	5003	380

prune146.0ms

Filtered

59 candidates to 42 candidates (71.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.8b

localize11.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ a (/ (+ (* c c) (* d d)) d))
3.8b	(/ b (/ (+ (* c c) (* d d)) c))
18.1b	(/ (+ (* c c) (* d d)) d)
20.6b	(/ (+ (* c c) (* d d)) c)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
104×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
12×	`div-inv` `associate-/l*`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
2×	`flip3-+` `associate-/r/` `flip-+`

Counts

4 → 198

Calls

4 calls:

8.0ms	(/ a (/ (+ (* c c) (* d d)) d))
8.0ms	(/ b (/ (+ (* c c) (* d d)) c))
9.0ms	(/ (+ (* c c) (* d d)) d)
9.0ms	(/ (+ (* c c) (* d d)) c)

series181.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ a (/ (+ (* c c) (* d d)) d))
45.0ms	(/ b (/ (+ (* c c) (* d d)) c))
40.0ms	(/ (+ (* c c) (* d d)) d)
51.0ms	(/ (+ (* c c) (* d d)) c)

simplify82.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	717	2042
1	3290	1930
2	5001	1930

prune570.0ms

Filtered

210 candidates to 170 candidates (81.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.2b

regimes203.0ms

Accuracy

86.4% (1.1b remaining)

Error of 8.8b against oracle of 7.7b and baseline of 15.7b

bsearch96.0ms

Steps

Iters	Range		Point
8	5.96376719448995e+152	1.5700055992880228e+155	1.3361970456774806e+154
10	-5.423750125877881e+166	-4.210667097524952e+153	-1.3273326724633925e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms

sample531.0ms

Algorithm

intervals

Results

314.0ms

8422×

body

valid