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: 3.9b

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

rewrite123.0ms

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:

8.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
41.0ms	(/ (/ (/ (+ (+ (+ 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))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
138.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
148.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify140.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1513	12983
1	5002	12137

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
10.6b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

88×	`times-frac`
74×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
48×	`sqrt-prod`
36×	`add-exp-log`
28×	`associate-/l*`
27×	`add-cbrt-cube`
19×	`div-exp`
12×	`cbrt-undiv` `distribute-lft-out`
8×	`associate-/r*`
6×	`pow1` `sqrt-div` `prod-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3-+` `1-exp` `associate-/r/` `flip-+`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `hypot-def`
1×	`associate-*l/` `associate-/l/`

Counts

4 → 165

Calls

4 calls:

11.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
27.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
146.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))

simplify80.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	676	2861
1	3075	2427
2	5001	2287

prune478.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.4b

localize20.0ms

Local error

Found 4 expressions with local error:

3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
10.6b	(/ (/ (* (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
40×	`add-cbrt-cube`
32×	`div-exp`
20×	`add-sqr-sqrt`
18×	`cbrt-undiv`
17×	`*-un-lft-identity`
16×	`prod-exp`
13×	`times-frac`
12×	`sqrt-prod`
11×	`add-cube-cbrt`
9×	`cbrt-unprod`
7×	`pow1` `associate-/l*`
6×	`sqrt-div` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `hypot-def` `div-inv` `distribute-lft-out`
1×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

8.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
36.0ms	(/ (/ (* (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
151.0ms	(/ (/ (* (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))) 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))

simplify76.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	512	2005
1	2666	1467
2	5001	1345

prune393.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.4b

localize17.0ms

Local error

Found 4 expressions with local error:

3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
14.2b	(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

149×	`times-frac`
101×	`*-un-lft-identity`
87×	`associate-r`
86×	`add-sqr-sqrt`
77×	`add-cube-cbrt`
49×	`cbrt-prod`
30×	`cbrt-div`
25×	`add-exp-log`
19×	`flip3-+` `flip-+`
17×	`add-cbrt-cube`
16×	`frac-times`
12×	`associate-*l/` `distribute-lft-out`
9×	`pow1` `prod-exp` `cbrt-unprod`
8×	`associate-/r/`
6×	`cbrt-undiv` `div-exp`
5×	`associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`pow1/3` `pow-prod-down`
1×	`associate-l` `*-commutative`

Counts

4 → 181

Calls

4 calls:

7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
56.0ms	(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
60.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
147.0ms	(* (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify69.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1230	4669
1	5002	4249

prune703.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.4b

regimes99.0ms

Accuracy

58.5% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 4.1b

bsearch44.0ms

Steps

Iters	Range		Point
6	3.3069971847189657e+170	3.354978332984879e+171	5.976763221550627e+170

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	36
1	35	36

end0.0ms

sample537.0ms

Algorithm

intervals

Results

301.0ms	8000×	body	80	valid
98.0ms	8000×	pre	80	true