Details

sample23.0ms

Algorithm

intervals

Results

9.0ms	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: 2.7b

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))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

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:

107.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
331.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
482.0ms	(/ (/ (/ (+ (+ (+ 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))
284.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
132.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
143.0ms	(/ (/ (/ (+ (+ (+ 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))
66.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify134.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune973.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.4b

localize13.0ms

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)))

2.4b

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

rewrite1.1s

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:

335.0ms

(/ (/ (+ (+ (+ 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)))

285.0ms

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

series343.0ms

Counts

3 → 9

Calls

3 calls:

132.0ms

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

138.0ms

(/ (/ (/ (+ (+ (+ 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)))

73.0ms

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

simplify149.0ms

Algorithm

egg-herbie

Counts

524 → 524

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1562	15016
1	5002	14467

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.4b

localize18.0ms

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)))
0.4b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.4b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite682.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
84×	`sqrt-prod`
77×	`times-frac`
58×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
39×	`distribute-lft-out`
13×	`associate-/r*`
12×	`associate-/l*`
10×	`flip3-+` `sqrt-div` `flip-+`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l/`
6×	`pow1`
4×	`frac-add` `associate-/r/` `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 → 171

Calls

4 calls:

232.0ms	(/ (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
209.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
116.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
117.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series363.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
93.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
41.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	580	2800
1	2301	2626
2	5001	2567

prune462.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (/ 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))))
0.5b	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.4b	(/ (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite655.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 636

Calls

4 calls:

250.0ms	(/ (/ (/ 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))))
92.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
38.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
228.0ms	(/ (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series322.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (/ (/ 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))))
34.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
61.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
85.0ms	(/ (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify168.0ms

Algorithm

egg-herbie

Counts

648 → 648

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	2039	16002
1	5002	14680

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

69.7% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 4.0b

bsearch60.0ms

Steps

Iters	Range		Point
8	2.2183211114809943e+158	3.233563472897972e+161	2.2630609713050934e+158

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	51
1	47	51

end0.0ms

sample553.0ms

Algorithm

intervals

Results

292.0ms	8000×	body	80	valid
82.0ms	8000×	pre	80	true