Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	33	17
1	122	15
2	598	13
3	4475	13
4	5001	13

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.3b

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))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
587×	`*-un-lft-identity`
341×	`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` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`fma-def` `frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 476

Calls

4 calls:

122.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
336.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
487.0ms	(/ (/ (/ (+ (+ (+ 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))
287.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
127.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
135.0ms	(/ (/ (/ (+ (+ (+ 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))
72.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify133.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1513	12983
1	5002	12137

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.8b

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) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

618×	`times-frac`
402×	`*-un-lft-identity`
290×	`add-sqr-sqrt` `add-cube-cbrt`
77×	`associate-/l*`
56×	`distribute-lft-out`
24×	`div-inv`
22×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
12×	`associate-/r/`
11×	`cbrt-undiv` `div-exp`
6×	`flip3--` `flip--` `associate-/l/`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `flip-+`
1×	`div-sub`

Counts

4 → 397

Calls

4 calls:

190.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
297.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
331.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
259.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
113.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
142.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
75.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify115.0ms

Algorithm

egg-herbie

Counts

409 → 409

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1492	9201
1	5002	8846

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

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))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
0.1b	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite6.8s

Algorithm

rewrite-expression-head

Rules

98889×	`times-frac`
64792×	`*-un-lft-identity`
38820×	`sqrt-prod`
32650×	`add-sqr-sqrt` `add-cube-cbrt`
18119×	`distribute-lft-out`
5246×	`associate-/r/`
2656×	`div-inv`
2593×	`flip3-+` `flip-+`
389×	`associate-/r*`
76×	`associate-/l*`
66×	`sqrt-div`
15×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`

Counts

4 → 21035

Calls

4 calls:

960.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
266.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
286.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
288.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series543.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
253.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
69.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify12.3s

Algorithm

egg-herbie

Counts

21047 → 21047

Iterations

Useful iterations: 0 (160.0ms)

Iter	Nodes	Cost
0	16693	1402916

prune1.1m

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.3b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite979.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
206×	`*-un-lft-identity`
136×	`add-sqr-sqrt` `add-cube-cbrt`
75×	`sqrt-prod`
41×	`associate-/l*`
35×	`distribute-lft-out`
18×	`associate-/r*`
17×	`add-exp-log`
16×	`associate-/r/`
15×	`add-cbrt-cube`
12×	`sqrt-div`
10×	`flip3-+` `flip-+`
8×	`div-inv`
7×	`div-exp`
6×	`pow1` `cbrt-undiv`
5×	`associate-/l/`
4×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip`
1×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `inv-pow`

Counts

4 → 280

Calls

4 calls:

38.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
344.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
291.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
292.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
190.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
90.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
74.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify124.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	924	5166
1	4109	4735
2	5002	4724

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

regimes99.0ms

Accuracy

56.4% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.6b

bsearch63.0ms

Steps

Iters	Range		Point
8	4.647991296681607e+170	1.7887515913112942e+173	9.72193149300398e+170

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	40
1	34	40

end0.0ms

sample564.0ms

Algorithm

intervals

Results

297.0ms	8000×	body	80	valid
86.0ms	8000×	pre	80	true