Details

Time bar (total: 8.9s)

sample32.0ms

Algorithm
intervals
Results
8.0ms211×body80valid
4.0ms256×pre80true
4.0ms18×body1280valid
2.0ms14×body640valid
1.0ms10×body320valid
0.0ms3×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize18.0ms

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))
1.3b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite474.0ms

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:
92.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
348.0ms
(+ (/ (/ (* (+ 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)))

series590.0ms

Counts
3 → 9
Calls
3 calls:
233.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
278.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
79.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify100.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07011971
137401800
250011782

prune547.0ms

Filtered
168 candidates to 131 candidates (78.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))
0.1b
(* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
1.3b
(+ (/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))) 1.0)
1.8b
(/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))))

rewrite413.0ms

Algorithm
rewrite-expression-head
Rules
111×*-un-lft-identity
109×times-frac
74×add-sqr-sqrt
51×add-cube-cbrt
41×add-exp-log
32×add-cbrt-cube
26×associate-*r*
21×fma-def distribute-lft-out
20×div-exp associate-/l*
13×cbrt-undiv
9×distribute-lft-out-- difference-of-squares
8×prod-exp
7×div-inv
6×pow1 associate-/r* associate-/r/ cbrt-unprod add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×1-exp associate-*r/ associate-*l* associate-/l/
2×flip3-- frac-2neg flip3-+ clear-num flip-- flip-+ unswap-sqr
1×+-commutative pow-prod-down sum-log *-commutative
Counts
4 → 191
Calls
4 calls:
131.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))
158.0ms
(* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
71.0ms
(+ (/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))) 1.0)
46.0ms
(/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))))

series763.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))
137.0ms
(* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
292.0ms
(+ (/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))) 1.0)
233.0ms
(/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))))

simplify110.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
08122355
141162007
250011985

prune605.0ms

Filtered
203 candidates to 138 candidates (68.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
0.1b
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (fma (fma i 2.0 (+ alpha beta)) 1 2.0))
1.8b
(* (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (fma (fma i 2.0 (+ alpha beta)) 1 2.0)) (- beta alpha))
2.5b
(+ (* (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (fma (fma i 2.0 (+ alpha beta)) 1 2.0)) (- beta alpha)) 1.0)

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
195×times-frac
180×*-un-lft-identity
139×add-sqr-sqrt
128×add-cube-cbrt
52×associate-*l*
36×prod-diff
25×distribute-lft-out
22×distribute-rgt-in associate-+l+ distribute-lft-in
20×add-exp-log add-cbrt-cube associate-/l*
10×div-inv
7×cbrt-undiv div-exp
6×pow1 associate-/r* add-log-exp
5×associate-*r*
4×expm1-log1p-u sub-neg log1p-expm1-u
3×prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times flip3-- frac-2neg flip3-+ associate-*r/ clear-num flip-- flip-+
1×+-commutative fma-def pow-prod-down associate-*l/ sum-log *-commutative distribute-lft-out-- difference-of-squares
Counts
4 → 259
Calls
4 calls:
8.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
12.0ms
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (fma (fma i 2.0 (+ alpha beta)) 1 2.0))
42.0ms
(* (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (fma (fma i 2.0 (+ alpha beta)) 1 2.0)) (- beta alpha))
15.0ms
(+ (* (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (fma (fma i 2.0 (+ alpha beta)) 1 2.0)) (- beta alpha)) 1.0)

series785.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
168.0ms
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (fma (fma i 2.0 (+ alpha beta)) 1 2.0))
240.0ms
(* (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (fma (fma i 2.0 (+ alpha beta)) 1 2.0)) (- beta alpha))
308.0ms
(+ (* (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (fma (fma i 2.0 (+ alpha beta)) 1 2.0)) (- beta alpha)) 1.0)

simplify130.0ms

Algorithm
egg-herbie
Counts
271 → 271
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
09733829
143743471
250013468

prune987.0ms

Filtered
271 candidates to 193 candidates (71.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
1.3b
(+ (/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))) 1.0)
1.8b
(/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))))
4.4b
(log (+ (/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))) 1.0))

rewrite342.0ms

Algorithm
rewrite-expression-head
Rules
89×times-frac
81×*-un-lft-identity
54×add-sqr-sqrt
41×add-cube-cbrt
40×add-exp-log
30×add-cbrt-cube
26×associate-*r*
21×fma-def
19×div-exp
16×distribute-lft-out associate-/l*
12×cbrt-undiv
8×prod-exp
7×pow1
6×cbrt-unprod div-inv add-log-exp
4×expm1-log1p-u log-prod associate-/r/ log1p-expm1-u distribute-lft-out-- difference-of-squares
3×1-exp associate-*r/ associate-*l*
2×log-div flip3-+ flip-+ unswap-sqr
1×+-commutative flip3-- frac-2neg rem-log-exp pow-prod-down clear-num associate-/r* sum-log log-pow *-commutative flip-- associate-/l/
Counts
4 → 161
Calls
4 calls:
159.0ms
(* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
71.0ms
(+ (/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))) 1.0)
46.0ms
(/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))))
57.0ms
(log (+ (/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))) 1.0))

series923.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
282.0ms
(+ (/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))) 1.0)
228.0ms
(/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))))
278.0ms
(log (+ (/ (/ (+ alpha beta) 1) (* (fma i 2.0 (+ alpha beta)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))) 1.0))

simplify105.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08042268
139191912
250031847

prune566.0ms

Filtered
173 candidates to 118 candidates (68.2%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

regimes250.0ms

Accuracy

12.4% (7.1b remaining)

Error of 11.5b against oracle of 4.4b and baseline of 12.5b

bsearch82.0ms

Steps
ItersRangePoint
9
1.1943555489229326e+215
2.002666651560134e+223
1.7246601237522257e+223

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04031
14031

end0.0ms

sample835.0ms

Algorithm
intervals
Results
257.0ms6342×body80valid
132.0ms8000×pre80true
112.0ms535×body1280valid
86.0ms557×body640valid
48.0ms386×body320valid
14.0ms180×body160valid