Details

Time bar (total: 11.8s)

sample23.0ms

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: 4.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b
(+ (+ alpha beta) (* beta alpha))
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))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite597.0ms

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
10×cbrt-undiv div-exp associate-/r*
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 → 475
Calls
4 calls:
164.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
15.0ms
(+ (+ alpha beta) (* beta alpha))
246.0ms
(/ (/ (/ (+ (+ (+ 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))
141.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms
(+ (+ alpha beta) (* beta alpha))
159.0ms
(/ (/ (/ (+ (+ (+ 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))
83.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify138.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0153413079
1500112129

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b
(+ (+ alpha beta) (* beta alpha))
0.1b
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite590.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
119×*-un-lft-identity
104×add-sqr-sqrt
74×add-cube-cbrt
60×associate-*l*
49×add-exp-log
29×add-cbrt-cube
21×div-exp distribute-lft-out
18×associate-*r*
14×associate-/r/
12×prod-exp
11×cbrt-undiv
9×flip3-+ flip-+ add-log-exp unswap-sqr
7×pow1 associate-/r* div-inv associate-/l*
6×cbrt-unprod
4×expm1-log1p-u rec-exp fma-def 1-exp log1p-expm1-u
3×sum-log
2×frac-2neg clear-num associate-/l/
1×+-commutative frac-times associate-+l+ pow-flip associate-*r/ pow-prod-down associate-*l/ un-div-inv *-commutative inv-pow
Counts
4 → 215
Calls
4 calls:
61.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
14.0ms
(+ (+ alpha beta) (* beta alpha))
367.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
139.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
15.0ms
(+ (+ alpha beta) (* beta alpha))
160.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify118.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010603544
149772900
250012900

prune584.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.5b
(* (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))
3.8b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
3058×times-frac
2200×*-un-lft-identity
1591×add-sqr-sqrt
1159×sqrt-prod
1118×add-cube-cbrt
786×associate-*r*
599×distribute-lft-out
148×associate-*l*
95×add-exp-log
88×unswap-sqr
63×add-cbrt-cube
57×div-exp
48×div-inv
33×cbrt-undiv
25×associate-/l*
22×sqrt-div
20×prod-exp associate-/r/
12×flip3-+ cbrt-unprod flip-+
8×pow1 1-exp
6×associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 1306
Calls
4 calls:
120.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.7s
(* (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))
67.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
68.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series767.0ms

Counts
4 → 12
Calls
4 calls:
468.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
193.0ms
(* (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ beta (+ alpha (fma 1.0 2.0 1.0)))))
47.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
58.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify404.0ms

Algorithm
egg-herbie
Counts
1318 → 1318
Iterations

Useful iterations: 1 (68.0ms)

IterNodesCost
0422439865
1500138307

prune2.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
2.3b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
3.9b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite310.0ms

Algorithm
rewrite-expression-head
Rules
59×*-un-lft-identity
52×times-frac
34×add-sqr-sqrt
32×add-cube-cbrt
20×add-exp-log add-cbrt-cube associate-/l*
14×distribute-lft-out
9×add-log-exp
7×cbrt-undiv div-exp
6×pow1
5×associate-*l*
4×expm1-log1p-u fma-def flip3-+ associate-*l/ associate-/r* flip-+ log1p-expm1-u div-inv
3×associate-*r* prod-exp sum-log cbrt-unprod associate-/l/
2×frac-2neg clear-num associate-/r/ fma-udef
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
4 → 136
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
29.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
137.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
126.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
38.0ms
(* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
168.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ beta (+ alpha (fma 1.0 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))))
85.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify91.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06121863
130061619
250011609

prune409.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.1b

regimes62.0ms

Accuracy

56.9% (1.1b remaining)

Error of 2.5b against oracle of 1.3b and baseline of 3.9b

bsearch76.0ms

Steps
ItersRangePoint
9
4.46568626735839e+154
1.7309518057475715e+164
2.7674997282640276e+163

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04428
14628
24628

end0.0ms

sample528.0ms

Algorithm
intervals
Results
295.0ms8000×body80valid
91.0ms8000×pre80true