Details

sample24.0ms

Algorithm

intervals

Results

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

simplify79.0ms

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: 3.9b

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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite690.0ms

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:

58.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
177.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
266.0ms	(/ (/ (/ (+ (+ (+ 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)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
139.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
154.0ms	(/ (/ (/ (+ (+ (+ 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))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify140.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

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)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite631.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
833×	`*-un-lft-identity`
383×	`add-sqr-sqrt` `add-cube-cbrt`
256×	`distribute-lft-out`
82×	`associate-/l*`
66×	`associate-/r/`
41×	`flip3-+` `flip-+`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
16×	`add-log-exp`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
8×	`frac-add` `sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+` `associate-+r+`

Counts

4 → 537

Calls

4 calls:

20.0ms	(+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))
180.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
235.0ms	(/ (/ (/ (+ (+ (+ 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)))
149.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))
145.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms	(/ (/ (/ (+ (+ (+ 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)))
81.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify159.0ms

Algorithm

egg-herbie

Counts

549 → 549

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1642	15242
1	5001	14684

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ 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))))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite444.0ms

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:

198.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
114.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
61.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
65.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series416.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (+ (+ (+ 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))))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify205.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	507	2617
1	1942	2448
2	5003	2394

prune445.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize19.0ms

Local error

Found 4 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))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))))
0.6b	(/ (/ (/ (+ (+ (+ 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))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

16124×	`times-frac`
12690×	`*-un-lft-identity`
5740×	`add-sqr-sqrt` `add-cube-cbrt`
5460×	`sqrt-prod`
4021×	`distribute-lft-out`
726×	`associate-/r/`
572×	`associate-/l*`
386×	`flip3-+` `flip-+`
341×	`div-inv`
66×	`sqrt-div`
44×	`frac-add`
34×	`add-exp-log` `add-cbrt-cube`
22×	`associate-/r*`
20×	`cbrt-undiv` `div-exp`
5×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 5141

Calls

4 calls:

190.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
446.0ms	(/ (/ (/ (/ (+ (+ (+ 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)))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))))
241.0ms	(/ (/ (/ (+ (+ (+ 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))))
148.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
153.0ms	(/ (/ (/ (/ (+ (+ (+ 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)))) (sqrt (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0))))
156.0ms	(/ (/ (/ (+ (+ (+ 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))))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.0s

Algorithm

egg-herbie

Counts

5153 → 5153

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5001	237190

prune9.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.7b

regimes81.0ms

Accuracy

44.6% (1.4b remaining)

Error of 2.5b against oracle of 1.1b and baseline of 3.7b

bsearch162.0ms

Steps

Iters	Range		Point
8	8.87684895593605e+202	1.112373966613911e+206	9.033818313421002e+202
7	3.0378422936948995e+125	1.866677400288751e+127	6.921240179554494e+125
5	9.28359310650799e+76	2.4961067465364225e+77	2.442757479764143e+77

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	79
1	61	79

end0.0ms

sample526.0ms

Algorithm

intervals

Results

296.0ms	8000×	body	80	valid
90.0ms	8000×	pre	80	true