Details

sample20.0ms

Algorithm

intervals

Results

10.0ms

277×

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.8b	(- (* b c) (* a d))
26.6b	(/ (- (* 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)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* c c) (* d d))
38.0ms	(- (* b c) (* a d))
87.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify42.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (32.0ms)

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

prune176.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 26.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b c) (* a d))
15.5b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(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)))
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)) (sqrt (+ (* c c) (* d d))))
35.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify94.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	304	912
1	990	857
2	3354	845
3	5001	845

prune277.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.1b

localize15.0ms

Local error

Found 4 expressions with local error:

9.2b	(/ (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d)))))
29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(sqrt (+ (* c c) (* d d)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

585×	`sqrt-prod`
567×	`times-frac`
302×	`add-sqr-sqrt`
299×	`add-cube-cbrt` `*-un-lft-identity`
50×	`sqrt-div`
33×	`associate-/l*`
22×	`associate-/r/`
14×	`flip3-+` `flip-+`
11×	`div-inv`
9×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
7×	`pow1`
4×	`add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp`
2×	`div-sub`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 402

Calls

4 calls:

33.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d)))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (sqrt (+ (* c c) (* d d))))) (sqrt (sqrt (+ (* c c) (* d d)))))
39.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(sqrt (+ (* c c) (* d d)))

simplify130.0ms

Algorithm

egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	1021	11198
1	4133	10155
2	5002	10139

prune851.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.1b

localize19.0ms

Local error

Found 4 expressions with local error:

29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(sqrt (+ (* c c) (* d d)))
29.7b	(sqrt (+ (* c c) (* d d)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series144.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ (* c c) (* d d)))
34.0ms	(sqrt (+ (* c c) (* d d)))
37.0ms	(sqrt (+ (* c c) (* d d)))
33.0ms	(sqrt (+ (* c c) (* d d)))

simplify139.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 5 (134.0ms)

Iter	Nodes	Cost
0	89	400
1	215	388
2	503	388
3	1265	388
4	4227	388
5	5002	384

prune296.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.1b

regimes146.0ms

Accuracy

-5.8% (3.1b remaining)

Error of 26.8b against oracle of 23.7b and baseline of 26.7b

bsearch47.0ms

Steps

Iters	Range		Point
10	6.409730244873951e+265	3.5402997186520582e+277	2.966297851011323e+277

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	19
1	26	19
2	26	19

end0.0ms

sample504.0ms

Algorithm

intervals

Results

300.0ms

8494×

body

valid