Details

sample23.0ms

Algorithm

intervals

Results

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

simplify76.0ms

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

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
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)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 463

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
37.0ms	(/ (/ (/ (+ (+ (+ 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))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ alpha beta) (* beta alpha))
133.0ms	(/ (/ (+ (+ (+ 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))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify138.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* beta alpha) (+ alpha beta))
0.0b	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 463

Calls

4 calls:

6.0ms	(+ (* beta alpha) (+ alpha beta))
22.0ms	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
44.0ms	(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
15.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (* beta alpha) (+ alpha beta))
131.0ms	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
147.0ms	(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
73.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify143.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1517	13008
1	5001	12540

prune984.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)))
0.5b	(/ (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))
2.9b	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))

rewrite60.0ms

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:

19.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)))
19.0ms	(/ (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
8.0ms	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))
8.0ms	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))

series410.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)))
104.0ms	(/ (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
53.0ms	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))
48.0ms	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	508	2617
1	1945	2448
2	5001	2394

prune434.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

1471×	`times-frac`
1040×	`*-un-lft-identity`
673×	`add-sqr-sqrt`
627×	`sqrt-prod`
590×	`add-cube-cbrt`
258×	`associate-r`
225×	`distribute-lft-out`
88×	`associate-/r/`
71×	`associate-/l*`
63×	`associate-l`
46×	`flip3-+` `flip-+`
44×	`div-inv`
20×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`pow1`
5×	`associate-/l/`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `sqrt-div` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 761

Calls

4 calls:

41.0ms	(/ (sqrt (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
284.0ms	(* (sqrt (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
15.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
16.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (sqrt (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
149.0ms	(* (sqrt (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
74.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
82.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify252.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1953	24980
1	5001	24018

prune2.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.2b

regimes73.0ms

Accuracy

55.7% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch55.0ms

Steps

Iters	Range		Point
8	4.294153376568447e+165	1.2685709578037348e+169	1.3924787671773796e+167

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	33
1	40	33

end0.0ms

sample538.0ms

Algorithm

intervals

Results

311.0ms	8000×	body	80	valid
89.0ms	8000×	pre	80	true