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: 3.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.1b	(/ (/ (+ (+ (+ 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))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

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:

115.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
356.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
515.0ms	(/ (/ (/ (+ (+ (+ 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))
307.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
155.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
159.0ms	(/ (/ (/ (+ (+ (+ 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))
86.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify130.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.9b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

7742×	`times-frac`
4062×	`*-un-lft-identity`
3062×	`add-sqr-sqrt`
3060×	`add-cube-cbrt`
2004×	`sqrt-prod`
501×	`distribute-lft-out`
193×	`div-inv`
185×	`associate-/r/`
89×	`associate-/r*`
82×	`flip3-+` `flip-+`
36×	`add-exp-log`
32×	`associate-/l*`
27×	`add-cbrt-cube`
25×	`div-exp`
16×	`cbrt-undiv`
6×	`pow1` `sqrt-div`
4×	`add-log-exp`
3×	`1-exp` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 2367

Calls

4 calls:

220.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
123.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
123.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
447.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
49.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
150.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

simplify792.0ms

Algorithm

egg-herbie

Counts

2379 → 2379

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5001	98865

prune5.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
1.2b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
54×	`times-frac`
33×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
22×	`associate-/l*`
20×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
14×	`associate-/r/`
13×	`add-log-exp`
12×	`distribute-lft-out`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `sum-log`
4×	`associate-r/` `associate-l` `associate-l/` `associate-/r*` `div-inv`
3×	`associate-r` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 143

Calls

4 calls:

115.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
392.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
416.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
308.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
37.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
163.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
84.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify110.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	732	2482
1	3919	2257
2	5002	2257

prune381.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize26.0ms

Local error

Found 4 expressions with local error:

3.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
15.5b	(* (* (/ (sqrt (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (sqrt 1)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (/ (sqrt (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt 1)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))))

rewrite4.0s

Algorithm

rewrite-expression-head

Rules

10808×	`times-frac`
4932×	`*-un-lft-identity`
4326×	`add-sqr-sqrt` `add-cube-cbrt`
3600×	`sqrt-prod`
3205×	`associate-r`
1212×	`cbrt-prod`
449×	`associate-/r/`
307×	`div-inv`
303×	`distribute-lft-out`
199×	`flip3-+` `flip-+`
178×	`add-exp-log`
112×	`add-cbrt-cube`
92×	`div-exp`
55×	`prod-exp`
52×	`cbrt-undiv`
35×	`cbrt-unprod`
9×	`pow1` `frac-times`
8×	`sqrt-div`
7×	`associate-*l/`
6×	`rec-exp` `cbrt-div` `1-exp`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down`
1×	`associate-l` `*-commutative`

Counts

4 → 3323

Calls

4 calls:

63.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
62.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
67.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3s	(* (* (/ (sqrt (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (sqrt 1)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (/ (sqrt (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt 1)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
64.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
310.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
163.0ms	(* (* (/ (sqrt (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) (sqrt 1)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (/ (sqrt (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt 1)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))))

simplify1.1s

Algorithm

egg-herbie

Counts

3335 → 3335

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5001	141743

prune13.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.9b

regimes57.0ms

Accuracy

53.4% (1.1b remaining)

Error of 2.3b against oracle of 1.1b and baseline of 3.6b

bsearch45.0ms

Steps

Iters	Range		Point
6	1.809709784161149e+161	2.5652737557520484e+162	3.046720525631589e+161

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	38
1	43	38

end0.0ms

sample572.0ms

Algorithm

intervals

Results

287.0ms	8000×	body	80	valid
93.0ms	8000×	pre	80	true