Details

sample26.0ms

Algorithm

intervals

Results

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

simplify81.0ms

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: 1.8b

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))
1.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite640.0ms

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:

60.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
163.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
247.0ms	(/ (/ (/ (+ (+ (+ 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))
136.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
134.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
145.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify139.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1513	12983
1	5002	12137

prune1.1s

Filtered

488 candidates to 299 candidates (61.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.8b

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)))
0.1b	(/ (/ (/ (+ (+ (+ 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)))
1.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite571.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
831×	`*-un-lft-identity`
384×	`add-sqr-sqrt` `add-cube-cbrt`
254×	`distribute-lft-out`
82×	`associate-/l*`
62×	`associate-/r/`
33×	`flip3-+` `flip-+`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 536

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
166.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
208.0ms	(/ (/ (/ (+ (+ (+ 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)))
140.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ (+ alpha beta) (* beta alpha))
140.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
162.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
81.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify156.0ms

Algorithm

egg-herbie

Counts

548 → 548

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1536	14467
1	5001	13533

prune1.2s

Filtered

548 candidates to 295 candidates (53.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)))
0.1b	(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
1.7b	(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))

rewrite445.0ms

Algorithm

rewrite-expression-head

Rules

4992×	`times-frac`
3969×	`*-un-lft-identity`
1844×	`add-sqr-sqrt` `add-cube-cbrt`
1275×	`distribute-lft-out`
284×	`associate-/l*`
181×	`associate-/r/`
102×	`div-inv`
79×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`associate-/r*` `add-cbrt-cube`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1`
4×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 1741

Calls

4 calls:

62.0ms	(/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)))
139.0ms	(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
17.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))

series521.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
82.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0)))
177.0ms	(/ (/ (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (fma 2.0 1.0 1.0)))
101.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (+ (+ (fma alpha beta beta) alpha) 1.0))

simplify509.0ms

Algorithm

egg-herbie

Counts

1753 → 1753

Iterations

Useful iterations: 1 (64.0ms)

Iter	Nodes	Cost
0	3886	47902
1	5001	45048

prune3.4s

Filtered

1753 candidates to 704 candidates (40.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 1) (fma 1.0 2.0 (+ alpha beta)))
0.0b	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (fma alpha beta beta) alpha) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (/ (/ (sqrt 1) (fma 1.0 2.0 (+ alpha beta))) 1) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (fma alpha beta beta) alpha) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
1.7b	(/ (+ (+ (fma alpha beta beta) alpha) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

34028×	`times-frac`
24744×	`*-un-lft-identity`
11744×	`add-sqr-sqrt` `add-cube-cbrt`
7800×	`distribute-lft-out`
3009×	`sqrt-prod`
880×	`div-inv`
797×	`associate-/r/`
364×	`flip3-+` `flip-+`
137×	`associate-/r*`
86×	`associate-/l*`
70×	`add-exp-log`
53×	`div-exp`
49×	`add-cbrt-cube`
32×	`cbrt-undiv`
6×	`1-exp`
5×	`associate-/l/`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`

Counts

4 → 8150

Calls

4 calls:

3.0ms	(/ (sqrt 1) (fma 1.0 2.0 (+ alpha beta)))
68.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (fma alpha beta beta) alpha) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
239.0ms	(/ (/ (/ (sqrt 1) (fma 1.0 2.0 (+ alpha beta))) 1) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (fma alpha beta beta) alpha) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
46.0ms	(/ (+ (+ (fma alpha beta beta) alpha) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (sqrt 1) (fma 1.0 2.0 (+ alpha beta)))
129.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (fma alpha beta beta) alpha) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
172.0ms	(/ (/ (/ (sqrt 1) (fma 1.0 2.0 (+ alpha beta))) 1) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (/ (+ (+ (fma alpha beta beta) alpha) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
79.0ms	(/ (+ (+ (fma alpha beta beta) alpha) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify3.2s

Algorithm

egg-herbie

Counts

8162 → 8162

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5773	320193

prune19.3s

Filtered

8162 candidates to 3355 candidates (41.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes75.0ms

Accuracy

72% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 3.6b

bsearch88.0ms

Steps

Iters	Range		Point
11	7.8512521379903e+159	1.3123977658214608e+188	8.012177184264198e+159

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	27
1	39	27

end0.0ms

sample528.0ms

Algorithm

intervals

Results

291.0ms	8000×	body	80	valid
95.0ms	8000×	pre	80	true