Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite643.0ms

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:

53.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
164.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
250.0ms	(/ (/ (/ (+ (+ (+ 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))
142.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
140.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
149.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify140.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune961.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.1b

localize14.0ms

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))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

5500×	`times-frac`
3741×	`*-un-lft-identity`
2185×	`add-sqr-sqrt` `add-cube-cbrt`
1821×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
778×	`distribute-lft-out`
450×	`associate-/l*`
302×	`neg-mul-1`
260×	`associate-/r/`
132×	`flip3-+` `flip-+`
130×	`div-inv`
17×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube` `distribute-neg-frac` `add-log-exp`
6×	`sum-log`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `div-sub` `distribute-frac-neg` `clear-num`
2×	`neg-sub0`
1×	`+-commutative` `associate-+l+`

Counts

4 → 2570

Calls

4 calls:

54.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
272.0ms	(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
427.0ms	(/ (/ (- (/ (+ (+ (+ 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))
139.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
223.0ms	(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
228.0ms	(/ (/ (- (/ (+ (+ (+ 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))
83.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify746.0ms

Algorithm

egg-herbie

Counts

2582 → 2582

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5001	84724

prune6.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
80×	`sqrt-prod`
70×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`associate-/r*`
11×	`associate-/l*`
10×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 159

Calls

4 calls:

183.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
107.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
59.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
57.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series417.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
113.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	507	2619
1	1928	2448
2	5001	2394

prune622.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
0.2b	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite450.0ms

Algorithm

rewrite-expression-head

Rules

958×	`times-frac`
444×	`*-un-lft-identity`
424×	`add-sqr-sqrt` `add-cube-cbrt`
402×	`sqrt-prod`
181×	`associate-/l*`
79×	`add-exp-log`
53×	`associate-/r/`
49×	`add-cbrt-cube`
47×	`div-exp`
46×	`sqrt-div`
27×	`flip3-+` `flip-+`
26×	`cbrt-undiv`
25×	`div-inv`
17×	`associate-/r*`
13×	`pow1`
10×	`prod-exp` `distribute-lft-out`
8×	`pow-flip`
6×	`cbrt-unprod` `pow-div`
5×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
4×	`frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
2×	`frac-times` `associate-*r/` `inv-pow`
1×	`associate-*l/`

Counts

4 → 627

Calls

4 calls:

152.0ms	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
49.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
18.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
184.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series354.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
37.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
69.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
94.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify167.0ms

Algorithm

egg-herbie

Counts

639 → 639

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1960	15887
1	5002	14379

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

69.6% (1.0b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.4b

bsearch66.0ms

Steps

Iters	Range		Point
9	5.7510599805381075e+158	7.599981289786604e+167	3.1020071240454246e+159

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	40
1	66	40
2	69	40
3	73	40
4	73	40

end0.0ms

sample520.0ms

Algorithm

intervals

Results

293.0ms	8000×	body	80	valid
94.0ms	8000×	pre	80	true