Details

sample24.0ms

Algorithm

intervals

Results

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

simplify77.0ms

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: 3.8b

localize12.0ms

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

rewrite591.0ms

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:

13.0ms	(+ (+ alpha beta) (* beta alpha))
163.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
246.0ms	(/ (/ (/ (+ (+ (+ 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))
139.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* beta alpha))
138.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify135.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune981.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.8b

localize20.0ms

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))

rewrite405.0ms

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:

180.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
105.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
58.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
56.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series398.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
104.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (44.0ms)

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

prune435.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.8b

localize14.0ms

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

rewrite727.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
269×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
130×	`add-cube-cbrt`
78×	`associate-r`
68×	`distribute-lft-out`
50×	`add-exp-log`
32×	`add-cbrt-cube`
26×	`associate-/r/`
22×	`div-exp` `associate-/l*`
15×	`flip3-+` `associate-l` `flip-+`
13×	`cbrt-undiv` `div-inv`
12×	`prod-exp`
9×	`add-log-exp` `unswap-sqr`
7×	`associate-/r*`
6×	`pow1` `cbrt-unprod`
3×	`rec-exp` `1-exp` `sum-log` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `frac-times` `associate-+l+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 291

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* beta alpha))
206.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
352.0ms	(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
138.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
119.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
153.0ms	(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

303 → 303

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1189	6034
1	5001	5626

prune670.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.7b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
16.9b	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0)))

rewrite762.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
192×	`*-un-lft-identity`
135×	`add-sqr-sqrt`
126×	`add-cube-cbrt`
78×	`associate-l`
37×	`difference-of-squares`
34×	`add-exp-log` `add-cbrt-cube`
33×	`distribute-lft-out`
26×	`associate-/r/`
23×	`associate-/l*`
14×	`cbrt-undiv` `div-exp`
13×	`div-inv`
12×	`flip3-+` `flip-+`
11×	`associate-/r*`
8×	`associate-/l/`
6×	`pow1` `flip3--` `prod-exp` `flip--` `cbrt-unprod`
4×	`frac-times` `associate-*r/` `add-log-exp`
3×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-r` `clear-num` `unswap-sqr`
2×	`sub-neg` `associate-*l/` `associate--l+`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 290

Calls

4 calls:

161.0ms	(/ (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
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))))
137.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
282.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0)))

series725.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(/ (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
165.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
73.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
258.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (- (+ alpha beta) (* 2.0 1.0)))

simplify94.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1248	7238
1	5002	6527

prune883.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.8b

regimes56.0ms

Accuracy

55.2% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.8b

bsearch74.0ms

Steps

Iters	Range		Point
8	4.8266542845792594e+173	1.0069133071674746e+178	1.967831461911932e+174

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	51
1	47	51

end0.0ms

sample547.0ms

Algorithm

intervals

Results

295.0ms	8000×	body	80	valid
99.0ms	8000×	pre	80	true