Details

sample22.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

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))
2.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite687.0ms

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)
176.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
263.0ms	(/ (/ (/ (+ (+ (+ 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))
150.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
139.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
154.0ms	(/ (/ (/ (+ (+ (+ 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))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify137.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1513	12983
1	5002	12137

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
0.1b	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))

rewrite464.0ms

Algorithm

rewrite-expression-head

Rules

205×	`times-frac`
134×	`add-exp-log`
131×	`*-un-lft-identity`
123×	`add-sqr-sqrt`
104×	`add-cube-cbrt`
82×	`div-exp`
52×	`add-cbrt-cube`
44×	`associate-r`
30×	`prod-exp`
25×	`cbrt-undiv`
24×	`1-exp`
20×	`associate-/r*`
16×	`associate-/r/` `div-inv`
13×	`associate-/l*`
12×	`rec-exp`
11×	`flip3-+` `flip-+` `distribute-lft-out`
9×	`cbrt-unprod`
7×	`pow1` `associate-/l/` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `associate-l` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-*r/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 289

Calls

4 calls:

95.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0)))
6.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
166.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
182.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0)))
39.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
166.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
82.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))

simplify74.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1213	4435
1	5001	3747

prune719.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize22.0ms

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)))) (/ (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))))
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)))
2.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

1777×	`times-frac`
1545×	`*-un-lft-identity`
761×	`add-sqr-sqrt`
747×	`sqrt-prod`
678×	`add-cube-cbrt`
497×	`distribute-lft-out`
321×	`associate-r`
104×	`associate-/r/`
71×	`associate-/l*`
63×	`associate-l`
54×	`flip3-+` `flip-+`
52×	`div-inv`
20×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
6×	`pow1`
5×	`associate-/l/`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `sqrt-div` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 896

Calls

4 calls:

764.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (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))))
187.0ms	(/ (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)))
149.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (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))))
136.0ms	(/ (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)))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
73.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify277.0ms

Algorithm

egg-herbie

Counts

908 → 908

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1974	28172
1	5001	27040

prune2.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.8b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
1.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite521.0ms

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:

19.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
184.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
151.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
205.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
105.0ms	(/ (+ (+ (+ 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)))

simplify116.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	924	5167
1	4109	4735
2	5002	4724

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.7b

regimes79.0ms

Accuracy

59.3% (1.0b remaining)

Error of 2.1b against oracle of 1.1b and baseline of 3.6b

bsearch54.0ms

Steps

Iters	Range		Point
8	2.3564981589069093e+172	2.7685158948624654e+175	2.0414729809724826e+175

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	23
1	32	23

end0.0ms

sample754.0ms

Algorithm

intervals

Results

509.0ms	8000×	body	80	valid
95.0ms	8000×	pre	80	true