Details

sample22.0ms

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: 3.6b

localize15.0ms

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

rewrite631.0ms

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:

14.0ms	(+ (+ alpha beta) (* beta alpha))
176.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
262.0ms	(/ (/ (/ (+ (+ (+ 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))
148.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
144.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
156.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify134.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune990.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (* 1 (+ (+ 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	(/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
523×	`*-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:

13.0ms	(+ (+ alpha beta) (* beta alpha))
81.0ms	(/ (/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
165.0ms	(/ (/ (/ (+ (* 1 (+ (+ 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))
54.0ms	(/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
145.0ms	(/ (/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
155.0ms	(/ (/ (/ (+ (* 1 (+ (+ 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	(/ (+ (* 1 (+ (+ alpha beta) (* beta alpha))) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify141.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1631	13491
1	5001	12958

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.6b

localize17.0ms

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))))
3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite442.0ms

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:

196.0ms	(/ (+ (+ (+ 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))
64.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series402.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
102.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (47.0ms)

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

prune433.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b	(* (+ alpha beta) (+ alpha beta))
2.3b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite452.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
145×	`*-un-lft-identity`
87×	`add-sqr-sqrt`
85×	`add-cube-cbrt`
29×	`distribute-lft-out`
25×	`associate-/l*`
19×	`difference-of-squares`
16×	`associate-/r/`
15×	`add-exp-log` `add-cbrt-cube`
14×	`flip3-+` `flip-+`
11×	`pow1` `associate-/r*`
8×	`div-inv`
6×	`swap-sqr`
5×	`cbrt-undiv` `div-exp` `associate-/l/`
4×	`frac-times` `associate-r` `associate-l` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3--` `associate-r/` `associate-l/` `flip--`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `div-sub` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 222

Calls

4 calls:

97.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
17.0ms	(* (+ alpha beta) (+ alpha beta))
178.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
151.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
15.0ms	(* (+ alpha beta) (+ alpha beta))
164.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify62.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1039	4291
1	5002	4105

prune621.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.6b

regimes64.0ms

Accuracy

56% (1.1b remaining)

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

bsearch66.0ms

Steps

Iters	Range		Point
8	6.080532357857461e+175	3.1725731237402986e+178	1.4955754255315103e+178

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	39
1	49	39
2	49	39

end0.0ms

sample520.0ms

Algorithm

intervals

Results

294.0ms	8000×	body	80	valid
91.0ms	8000×	pre	80	true