Details

Time bar (total: 16.6s)

sample28.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
3.0ms256×pre80true

simplify87.0ms

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: 3.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.1b
(/ (/ (+ (+ (+ 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))
3.4b
(/ (+ (+ (+ 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:
120.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
331.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
483.0ms
(/ (/ (/ (+ (+ (+ 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))
285.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
146.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
155.0ms
(/ (/ (/ (+ (+ (+ 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)))

simplify127.0ms

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: 0.9b

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)))) (/ (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)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.1s

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:
1.1s
(* (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))))
322.0ms
(/ (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)))
279.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
281.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(* (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))))
133.0ms
(/ (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)))
83.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
85.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify256.0ms

Algorithm
egg-herbie
Counts
908 → 908
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0197428172
1500127040

prune2.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* (sqrt (/ 1 (+ (+ 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))))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
1.7b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.3b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
2949×times-frac
2558×*-un-lft-identity
1932×sqrt-prod
1147×add-sqr-sqrt add-cube-cbrt
951×associate-*r*
800×distribute-lft-out
96×sqrt-div
92×associate-/r/
48×flip3-+ flip-+
46×div-inv
38×associate-/l*
25×add-exp-log add-cbrt-cube
15×associate-/r*
9×pow1
7×cbrt-undiv div-exp
6×prod-exp cbrt-unprod
5×frac-times associate-*l/ associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*r/ pow-prod-down clear-num
1×associate-*l* *-commutative
Counts
4 → 1303
Calls
4 calls:
1.1s
(* (* (sqrt (/ 1 (+ (+ 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))))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
344.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
290.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
286.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series421.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(* (* (sqrt (/ 1 (+ (+ 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))))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ alpha beta) (fma 2.0 1.0 1.0))))
76.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
96.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
82.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify421.0ms

Algorithm
egg-herbie
Counts
1315 → 1315
Iterations

Useful iterations: 1 (60.0ms)

IterNodesCost
0363247115
1500245379

prune2.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
1.2b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))))
3.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite656.0ms

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:
31.0ms
(+ (+ alpha beta) (* beta alpha))
80.0ms
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
282.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))))
259.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ (+ alpha beta) (* beta alpha))
38.0ms
(* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta)))
170.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (* (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (fma 1.0 2.0 (+ alpha beta))))
84.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify88.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06001864
129801619
250021609

prune398.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.9b

regimes73.0ms

Accuracy

53.5% (1.1b remaining)

Error of 2.2b against oracle of 1.1b and baseline of 3.5b

bsearch42.0ms

Steps
ItersRangePoint
6
1.809709784161149e+161
2.5652737557520484e+162
3.046720525631589e+161

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04141
14341
24341

end0.0ms

sample563.0ms

Algorithm
intervals
Results
289.0ms8000×body80valid
86.0ms8000×pre80true