Details

sample26.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite700.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

60.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
183.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
270.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
152.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
141.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
71.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify143.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))

2.8b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite618.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
827×	`*-un-lft-identity`
382×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
66×	`associate-/r/`
36×	`flip3-+` `flip-+`
31×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`frac-add` `associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 515

Calls

3 calls:

185.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

241.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))

154.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series365.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

148.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))

78.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify162.0ms

Algorithm

egg-herbie

Counts

524 → 524

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1562	15016
1	5002	14467

prune947.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))))
0.6b	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))))
2.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

4022×	`times-frac`
2814×	`*-un-lft-identity`
1796×	`add-sqr-sqrt`
1628×	`sqrt-prod`
1578×	`add-cube-cbrt`
709×	`distribute-lft-out`
706×	`associate-r`
154×	`associate-/r/`
87×	`associate-/l*`
85×	`flip3-+` `flip-+`
71×	`div-inv`
66×	`associate-l`
45×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
22×	`cbrt-undiv` `sqrt-div` `div-exp`
12×	`frac-add`
8×	`pow1` `prod-exp` `associate-/r*` `cbrt-unprod`
4×	`add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 1691

Calls

4 calls:

217.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))))
1.2s	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))))
65.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series625.0ms

Counts

4 → 12

Calls

4 calls:

376.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))))
149.0ms	(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))))
44.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
54.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify586.0ms

Algorithm

egg-herbie

Counts

1703 → 1703

Iterations

Useful iterations: 1 (66.0ms)

Iter	Nodes	Cost
0	4473	60416
1	5001	58327

prune3.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b	(/ (* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))))
2.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
30×	`sqrt-prod`
27×	`add-sqr-sqrt`
26×	`times-frac`
25×	`add-cube-cbrt`
23×	`add-exp-log`
16×	`sqrt-div`
15×	`add-cbrt-cube`
14×	`associate-/r*`
10×	`flip3-+` `flip-+`
9×	`div-exp`
8×	`pow1` `associate-/r/` `distribute-lft-out`
6×	`associate-/l/`
5×	`cbrt-undiv`
4×	`frac-add` `prod-exp` `associate-/l*` `add-log-exp`
3×	`pow-flip` `sqrt-pow1` `pow1/2`
2×	`frac-times` `rem-sqrt-square` `rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `cbrt-unprod` `div-inv`
1×	`associate-*r/` `un-div-inv` `inv-pow`

Counts

4 → 126

Calls

4 calls:

19.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
84.0ms	(/ (* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))))
66.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
67.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series332.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
169.0ms	(/ (* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	663	1785
1	2855	1579
2	5001	1550

prune424.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.7b

regimes63.0ms

Accuracy

59.6% (1.0b remaining)

Error of 2.1b against oracle of 1.1b and baseline of 3.6b

bsearch51.0ms

Steps

Iters	Range		Point
8	2.3564981589069093e+172	2.7685158948624654e+175	2.0414729809724826e+175

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	17
1	27	17

end0.0ms

sample548.0ms

Algorithm

intervals

Results

309.0ms	8000×	body	80	valid
95.0ms	8000×	pre	80	true