Details

Time bar (total: 15.9s)

sample52.0ms

Algorithm
intervals
Results
19.0ms202×body80valid
6.0ms21×body640valid
6.0ms16×body1280valid
6.0ms256×pre80true
3.0ms13×body320valid
1.0ms4×body160valid

simplify54.0ms

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: 21.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite461.0ms

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:
91.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
337.0ms
(+ (/ (/ (* (+ 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)))

series562.0ms

Counts
3 → 9
Calls
3 calls:
220.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
264.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
78.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify95.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07011971
137401800
250011782

prune521.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta))))
0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.5b
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta)))) 1.0)

rewrite586.0ms

Algorithm
rewrite-expression-head
Rules
342×times-frac
302×*-un-lft-identity
259×add-sqr-sqrt
154×add-cube-cbrt
127×associate-*r* sqrt-prod
45×distribute-lft-out
34×associate-*l*
29×add-exp-log add-cbrt-cube distribute-lft-out-- difference-of-squares
14×associate-/r*
12×sqrt-div associate-/r/ unswap-sqr
11×cbrt-undiv div-exp
9×associate-/l*
8×flip3-+ flip-+
7×div-inv
6×pow1 prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u log1p-expm1-u associate-/l/
2×frac-2neg clear-num
1×+-commutative frac-times flip3-- fma-def div-sub associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative flip--
Counts
4 → 336
Calls
4 calls:
347.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta))))
69.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
68.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
80.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta)))) 1.0)

series756.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta))))
127.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
132.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
275.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta)))) 1.0)

simplify87.0ms

Algorithm
egg-herbie
Counts
348 → 348
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
014956352
150015917

prune972.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.9b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.9b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0b
(* (* (/ (cbrt (- beta alpha)) (/ (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (- beta alpha)))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (fma i 2.0 (+ alpha beta))))
8.5b
(+ (* (* (/ (cbrt (- beta alpha)) (/ (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (- beta alpha)))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (fma i 2.0 (+ alpha beta)))) 1.0)

rewrite752.0ms

Algorithm
rewrite-expression-head
Rules
498×times-frac
340×*-un-lft-identity
288×add-sqr-sqrt
262×associate-*r*
254×cbrt-prod
228×add-cube-cbrt
168×sqrt-prod
112×add-exp-log
87×add-cbrt-cube
48×cbrt-undiv div-exp
39×prod-exp cbrt-unprod
30×distribute-lft-out-- difference-of-squares
26×distribute-lft-out
10×cbrt-div
9×pow1
6×flip3-+ sqrt-div associate-/r/ flip-+ add-log-exp
5×frac-times associate-*l/
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-*r/ pow-prod-down
2×pow1/3
1×+-commutative fma-def associate-*l* sum-log *-commutative
Counts
4 → 370
Calls
4 calls:
29.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
382.0ms
(* (* (/ (cbrt (- beta alpha)) (/ (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (- beta alpha)))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (fma i 2.0 (+ alpha beta))))
275.0ms
(+ (* (* (/ (cbrt (- beta alpha)) (/ (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (- beta alpha)))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (fma i 2.0 (+ alpha beta)))) 1.0)

series4.9s

Counts
4 → 12
Calls
4 calls:
174.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
172.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
3.5s
(* (* (/ (cbrt (- beta alpha)) (/ (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (- beta alpha)))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (fma i 2.0 (+ alpha beta))))
1.1s
(+ (* (* (/ (cbrt (- beta alpha)) (/ (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (- beta alpha)))) (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (fma i 2.0 (+ alpha beta)))) 1.0)

simplify152.0ms

Algorithm
egg-herbie
Counts
382 → 382
Iterations

Useful iterations: 1 (49.0ms)

IterNodesCost
0263713586
1500112591

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (- beta alpha))
0.9b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.9b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.5b
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (/ (cbrt (- beta alpha)) (/ (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (- beta alpha)))) (/ (cbrt (- beta alpha)) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (fma i 2.0 (+ alpha beta)))) 1.0)

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
13×cbrt-prod *-un-lft-identity
9×add-sqr-sqrt
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×flip3-+ pow1/3 flip-+
2×distribute-lft-out
1×+-commutative flip3-- fma-def sum-log flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 63
Calls
4 calls:
2.0ms
(cbrt (- beta alpha))
29.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
216.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (/ (cbrt (- beta alpha)) (/ (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (- beta alpha)))) (/ (cbrt (- beta alpha)) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (fma i 2.0 (+ alpha beta)))) 1.0)

series1.6s

Counts
4 → 12
Calls
4 calls:
151.0ms
(cbrt (- beta alpha))
174.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
171.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.1s
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (/ (cbrt (- beta alpha)) (/ (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (- beta alpha)))) (/ (cbrt (- beta alpha)) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (fma i 2.0 (+ alpha beta)))) 1.0)

simplify50.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05381290
116141174
250021157

prune456.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.2b

regimes304.0ms

Accuracy

19.2% (5.2b remaining)

Error of 11.2b against oracle of 6.0b and baseline of 12.4b

bsearch60.0ms

Steps
ItersRangePoint
5
3.749479162223782e+181
1.156670155801419e+182
1.0395626917288666e+182

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05346
15346

end0.0ms

sample1.3s

Algorithm
intervals
Results
502.0ms6369×body80valid
196.0ms523×body1280valid
179.0ms8000×pre80true
166.0ms554×body640valid
82.0ms366×body320valid
28.0ms188×body160valid