Details

Time bar (total: 13.7s)

sample24.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify84.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

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

rewrite658.0ms

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:
62.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
169.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
251.0ms
(/ (/ (/ (+ (+ (+ 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))
144.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
137.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
152.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify135.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0151312983
1500212137

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.1b

localize23.0ms

Local error

Found 4 expressions with local error:

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))) (- (+ 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)))
13.2b
(* (/ (/ (/ (+ (+ (+ 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))) (- (+ alpha beta) (* 2.0 1.0)))

rewrite798.0ms

Algorithm
rewrite-expression-head
Rules
934×times-frac
557×*-un-lft-identity
429×add-sqr-sqrt
415×add-cube-cbrt
166×associate-*l*
71×distribute-lft-out
59×associate-/l*
49×add-exp-log add-cbrt-cube
32×div-inv
24×cbrt-undiv div-exp
16×associate-/r/
11×flip3-- flip--
10×associate-/r*
8×prod-diff prod-exp cbrt-unprod associate-/l/
7×distribute-rgt-in distribute-lft-in
6×pow1
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u add-log-exp unswap-sqr
3×frac-2neg associate-*r* clear-num
2×sub-neg flip3-+ associate-*l/ associate--l+ flip-+
1×pow-prod-down *-commutative
Counts
4 → 522
Calls
4 calls:
174.0ms
(/ (* (/ (/ (/ (+ (+ (+ 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))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
172.0ms
(/ (/ (/ (+ (+ (+ 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)))
127.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
287.0ms
(* (/ (/ (/ (+ (+ (+ 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))) (- (+ alpha beta) (* 2.0 1.0)))

series733.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ (* (/ (/ (/ (+ (+ (+ 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))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
349.0ms
(/ (/ (/ (+ (+ (+ 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)))
80.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
150.0ms
(* (/ (/ (/ (+ (+ (+ 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))) (- (+ alpha beta) (* 2.0 1.0)))

simplify149.0ms

Algorithm
egg-herbie
Counts
534 → 534
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0205412731
1500212127

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

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

rewrite1.3s

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:
179.0ms
(/ (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)))
709.0ms
(* (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))))
143.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
144.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ (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)))
160.0ms
(* (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))))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
79.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify276.0ms

Algorithm
egg-herbie
Counts
908 → 908
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0197428172
1500127040

prune2.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
1.5b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.5b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite522.0ms

Algorithm
rewrite-expression-head
Rules
756×times-frac
594×*-un-lft-identity
419×sqrt-prod
372×add-sqr-sqrt add-cube-cbrt
111×distribute-lft-out
61×associate-/l*
40×sqrt-div associate-/r/
26×associate-/r*
24×add-exp-log
21×flip3-+ flip-+
20×div-inv
18×add-cbrt-cube
12×div-exp
8×cbrt-undiv
6×pow1
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
3×pow-flip
2×rec-exp 1-exp
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 587
Calls
4 calls:
18.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
96.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
225.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
143.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
103.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
169.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
101.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify157.0ms

Algorithm
egg-herbie
Counts
599 → 599
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0136913739
1500112934

prune1.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.1b

regimes77.0ms

Accuracy

31.7% (1.6b remaining)

Error of 2.6b against oracle of 1.1b and baseline of 3.4b

bsearch90.0ms

Steps
ItersRangePoint
9
4.3222540007457085e+189
2.958753465288834e+197
2.9207371840511997e+197

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05455
15455

end0.0ms

sample543.0ms

Algorithm
intervals
Results
299.0ms8000×body80valid
101.0ms8000×pre80true