Details

sample22.0ms

Algorithm

intervals

Results

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

simplify83.0ms

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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize17.0ms

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

rewrite688.0ms

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:

65.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
177.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
264.0ms	(/ (/ (/ (+ (+ (+ 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))
149.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
141.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms	(/ (/ (/ (+ (+ (+ 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))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify137.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1513	12983
1	5002	12137

prune1.1s

Filtered

488 candidates to 299 candidates (61.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite589.0ms

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:

154.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
101.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
178.0ms	(/ (/ (/ (+ (+ (+ 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)))
133.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
41.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
158.0ms	(/ (/ (/ (+ (+ (+ 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)))
82.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify112.0ms

Algorithm

egg-herbie

Counts

409 → 409

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1492	9201
1	5001	8846

prune1.3s

Filtered

409 candidates to 307 candidates (75.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite517.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
46×	`times-frac`
45×	`sqrt-prod`
38×	`add-cube-cbrt`
25×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div` `distribute-lft-out`
8×	`pow1`
7×	`associate-l` `associate-/l*`
6×	`unswap-sqr`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `hypot-def` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 143

Calls

4 calls:

270.0ms	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
98.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
70.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
73.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series383.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))))
199.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta)))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
54.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	450	2040
1	1792	1810
2	5002	1734

prune444.0ms

Filtered

155 candidates to 104 candidates (67.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0)))
0.0b	(/ (/ (/ (+ (+ (+ 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)) 1.0) (- (+ alpha beta) (* 2.0 1.0))))
2.1b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite975.0ms

Algorithm

rewrite-expression-head

Rules

4788×	`times-frac`
2658×	`*-un-lft-identity`
1682×	`add-sqr-sqrt` `add-cube-cbrt`
488×	`distribute-lft-out`
365×	`associate-/r/`
361×	`difference-of-squares`
183×	`div-inv`
104×	`associate-/l*`
100×	`flip3--` `flip--`
84×	`flip3-+` `flip-+`
34×	`add-exp-log` `add-cbrt-cube`
28×	`associate-/r*`
20×	`cbrt-undiv` `div-exp`
6×	`associate-/l/`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`

Counts

4 → 1713

Calls

4 calls:

146.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0)))
321.0ms	(/ (/ (/ (+ (+ (+ 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)) 1.0) (- (+ alpha beta) (* 2.0 1.0))))
177.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
149.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0)))
218.0ms	(/ (/ (/ (+ (+ (+ 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)) 1.0) (- (+ alpha beta) (* 2.0 1.0))))
162.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify675.0ms

Algorithm

egg-herbie

Counts

1725 → 1725

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5001	80389

prune5.1s

Filtered

1725 candidates to 1106 candidates (64.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.9b

regimes66.0ms

Accuracy

50.6% (1.3b remaining)

Error of 2.5b against oracle of 1.2b and baseline of 3.8b

bsearch68.0ms

Steps

Iters	Range		Point
8	1.9454904414609723e+167	1.5585196027825523e+171	9.279265165473009e+169

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	43
1	42	43

end0.0ms

sample538.0ms

Algorithm

intervals

Results

291.0ms	8000×	body	80	valid
100.0ms	8000×	pre	80	true