Details

Time bar (total: 14.6s)

sample35.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
3.0ms256×pre80true

simplify84.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize15.0ms

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)))

rewrite1.3s

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:
121.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
339.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
487.0ms
(/ (/ (/ (+ (+ (+ 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))
280.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
131.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
141.0ms
(/ (/ (/ (+ (+ (+ 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))
68.0ms
(/ (+ (+ (+ 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

prune3.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite952.0ms

Algorithm
rewrite-expression-head
Rules
121×times-frac
108×*-un-lft-identity
72×add-sqr-sqrt add-cube-cbrt
42×add-exp-log add-cbrt-cube
24×associate-/l*
21×cbrt-undiv div-exp
18×distribute-lft-out
13×associate-/r*
8×div-inv associate-/l/
6×prod-exp associate-/r/ cbrt-unprod
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×flip3-- flip--
1×frac-times div-sub associate-*r/ associate-*l/
Counts
4 → 195
Calls
4 calls:
99.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
284.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
310.0ms
(/ (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
250.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
116.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))
161.0ms
(/ (* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
76.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify58.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09863910
150023318

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
244×times-frac
170×*-un-lft-identity
154×add-exp-log
104×div-exp
102×add-sqr-sqrt
97×add-cube-cbrt
61×add-cbrt-cube
40×distribute-lft-out
34×associate-/l*
31×cbrt-undiv
30×1-exp prod-exp
21×associate-*l*
16×div-inv
12×rec-exp associate-/r/
10×associate-/r* cbrt-unprod
7×associate-*l/
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ associate-*r* clear-num flip-+
2×fma-udef associate-/l/ unswap-sqr
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative
Counts
4 → 289
Calls
4 calls:
62.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
30.0ms
(/ (/ 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
152.0ms
(/ (/ (/ 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
29.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

series503.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
132.0ms
(/ (/ 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta))))
146.0ms
(/ (/ (/ 1 1) (* (/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0)))) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
90.0ms
(/ (fma 1.0 2.0 (+ alpha beta)) (+ beta (+ alpha (fma alpha beta 1.0))))

simplify71.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011494784
150024155

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.9b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite646.0ms

Algorithm
rewrite-expression-head
Rules
126×*-un-lft-identity
84×sqrt-prod
77×times-frac
62×add-sqr-sqrt
56×add-cube-cbrt
39×distribute-lft-out
13×associate-/r*
12×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
1×sqrt-undiv
Counts
4 → 177
Calls
4 calls:
181.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
205.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
125.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
128.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series393.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
104.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
43.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify68.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05272718
119402545
250012473

prune1.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes133.0ms

Accuracy

71.9% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.9b

bsearch161.0ms

Steps
ItersRangePoint
10
2.0135024651821765e+153
2.140923875068213e+164
1.5559448905417946e+156

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04539
14539

end0.0ms

sample795.0ms

Algorithm
intervals
Results
549.0ms8000×body80valid
100.0ms8000×pre80true