Details

Time bar (total: 10.2s)

sample49.0ms

Algorithm
intervals
Results
14.0ms197×body80valid
7.0ms256×pre80true
7.0ms14×body1280valid
4.0ms21×body640valid
2.0ms14×body320valid
1.0ms10×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
3.1b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite473.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-exp-log add-cbrt-cube
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r*
5×add-log-exp
4×frac-times
3×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 159
Calls
3 calls:
93.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
346.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
27.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series592.0ms

Counts
3 → 9
Calls
3 calls:
233.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
277.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
81.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify95.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07011971
137401800
250011782

prune668.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))))
0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.7b
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))))) 1.0)

rewrite569.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
87×add-exp-log
77×times-frac
70×add-sqr-sqrt
54×add-cube-cbrt
52×sqrt-prod
49×add-cbrt-cube
36×prod-exp
29×div-exp
27×associate-*l*
18×cbrt-unprod
15×cbrt-undiv
14×associate-/r*
13×distribute-lft-out
11×pow1
8×associate-/l* distribute-lft-out-- difference-of-squares
6×rec-exp sqrt-div 1-exp associate-/r/ add-log-exp
5×frac-times associate-*r/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×pow-flip pow-prod-down associate-*l/ div-inv
2×frac-2neg clear-num associate-/l/
1×+-commutative flip3-- fma-def sqrt-pow1 pow1/2 div-sub associate-*r* sum-log *-commutative flip-- inv-pow
Counts
4 → 210
Calls
4 calls:
263.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))))
66.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
71.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
160.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))))) 1.0)

series763.0ms

Counts
4 → 12
Calls
4 calls:
232.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))))
123.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
130.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
279.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))))) 1.0)

simplify123.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
09503691
149253156
250013155

prune579.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.2b
(+ (cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
10.7b
(cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

rewrite688.0ms

Algorithm
rewrite-expression-head
Rules
94×*-un-lft-identity
75×times-frac
64×cbrt-prod add-sqr-sqrt
48×add-cube-cbrt
40×sqrt-prod
35×fma-def
26×unpow-prod-down cube-prod
15×distribute-lft-out
10×sqrt-div associate-/r* associate-/r/
9×associate-/l*
8×add-exp-log add-cbrt-cube distribute-lft-out-- difference-of-squares
7×flip3-+ flip-+
6×div-inv add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
2×cbrt-undiv cube-mult frac-2neg unpow3 div-exp clear-num sqr-pow
1×+-commutative cube-div cbrt-div flip3-- pow1/3 div-sub sum-log flip-- rem-cbrt-cube
Counts
4 → 194
Calls
4 calls:
8.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
73.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
532.0ms
(+ (cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
68.0ms
(cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

series746.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
135.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
250.0ms
(+ (cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
290.0ms
(cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

simplify92.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
08062820
135292632
250022609

prune688.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.2b
(+ (cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
10.7b
(cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

rewrite691.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
152×*-un-lft-identity
106×add-sqr-sqrt
90×add-cube-cbrt
64×cbrt-prod
40×sqrt-prod
35×fma-def
26×unpow-prod-down cube-prod
25×associate-/r*
23×distribute-lft-out
19×associate-/r/
17×add-exp-log
11×add-cbrt-cube
10×flip3-+ sqrt-div flip-+ div-inv
8×div-exp associate-/l* distribute-lft-out-- difference-of-squares
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u
2×cube-mult rec-exp frac-2neg 1-exp unpow3 clear-num associate-/l/ sqr-pow
1×+-commutative cube-div cbrt-div flip3-- pow-flip pow1/3 div-sub sum-log flip-- rem-cbrt-cube inv-pow
Counts
4 → 257
Calls
4 calls:
9.0ms
(/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
72.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
530.0ms
(+ (cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
68.0ms
(cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

series817.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
131.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
268.0ms
(+ (cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
300.0ms
(cbrt (pow (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

simplify126.0ms

Algorithm
egg-herbie
Counts
269 → 269
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010453576
149643271
250013271

prune782.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

regimes252.0ms

Accuracy

16.9% (5.2b remaining)

Error of 11.2b against oracle of 5.9b and baseline of 12.2b

bsearch90.0ms

Steps
ItersRangePoint
9
1.4193065318071646e+196
6.027709900080744e+203
6.749818875677078e+202

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04225
14425
24425

end0.0ms

sample1.2s

Algorithm
intervals
Results
478.0ms6367×body80valid
212.0ms8000×pre80true
134.0ms507×body1280valid
121.0ms550×body640valid
60.0ms373×body320valid
24.0ms203×body160valid