Details

Time bar (total: 7.1s)

sample36.0ms

Algorithm
intervals
Results
8.0ms213×body80valid
8.0ms256×pre80true
3.0ms17×body1280valid
2.0ms13×body640valid
1.0ms11×body320valid
0.0ms2×body160valid

simplify53.0ms

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: 20.2b

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))
0.4b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite77.0ms

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:
23.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
32.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
15.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series570.0ms

Counts
3 → 9
Calls
3 calls:
218.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
269.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
82.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify100.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07011971
137401800
250011782

prune534.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
0.4b
(+ (/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
3.9b
(* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i)))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log add-cbrt-cube
52×*-un-lft-identity
46×add-sqr-sqrt
39×times-frac
28×add-cube-cbrt
24×associate-*r*
22×prod-exp cbrt-unprod
19×frac-times
18×cbrt-undiv div-exp
17×associate-*l*
13×associate-*l/
11×pow1 associate-*r/ associate-/l/
10×fma-def
9×flip3-- flip-- distribute-lft-out
8×prod-diff
7×distribute-rgt-in distribute-lft-in
6×associate-/r/ add-log-exp
4×expm1-log1p-u pow-prod-down associate-/r* log1p-expm1-u div-inv unswap-sqr
3×flip3-+ flip-+ distribute-lft-out-- difference-of-squares
2×sub-neg associate--l+ *-commutative
1×+-commutative frac-2neg clear-num sum-log associate-/l*
Counts
4 → 184
Calls
4 calls:
35.0ms
(/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
21.0ms
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
30.0ms
(+ (/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
26.0ms
(* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i)))

series711.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
119.0ms
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
275.0ms
(+ (/ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
85.0ms
(* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (- (+ alpha beta) (* 2.0 i)))

simplify55.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010273537
150012963

prune585.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
10.3b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
162×*-un-lft-identity
118×add-sqr-sqrt
80×add-cube-cbrt
26×associate-/l*
22×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
10×add-exp-log add-cbrt-cube
7×flip3-+ associate-/r* flip-+ div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/ add-log-exp
2×frac-2neg clear-num
1×flip3-- flip-- fma-udef
Counts
3 → 181
Calls
3 calls:
10.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
19.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series496.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
157.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
264.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify98.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07273112
132592892
250022876

prune608.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
0.3b
(/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.5b
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
10.2b
(fma (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
59×add-sqr-sqrt times-frac
41×add-cube-cbrt
36×add-exp-log add-cbrt-cube
24×sqrt-prod
21×associate-*r*
16×associate-*l*
14×cbrt-undiv div-exp associate-/r*
9×distribute-lft-out
8×prod-exp cbrt-unprod
6×pow1 associate-/r/
5×associate-/l/
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv associate-/l* add-log-exp unswap-sqr
3×distribute-lft-out-- difference-of-squares
2×frac-times flip3-- frac-2neg flip3-+ associate-*r/ associate-*l/ clear-num flip-- flip-+
1×div-sub pow-prod-down *-commutative fma-udef
Counts
4 → 165
Calls
4 calls:
21.0ms
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
24.0ms
(/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
15.0ms
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.0ms
(fma (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
485.0ms
(/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
155.0ms
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
313.0ms
(fma (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify120.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09432926
147872556
250012556

prune597.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

regimes267.0ms

Accuracy

11.1% (5.6b remaining)

Error of 11.5b against oracle of 5.9b and baseline of 12.2b

bsearch76.0ms

Steps
ItersRangePoint
9
3.088617839269422e+142
1.495088011218417e+148
1.4714840476837656e+148

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04427
14627
24627

end0.0ms

sample795.0ms

Algorithm
intervals
Results
250.0ms6396×body80valid
122.0ms8000×pre80true
98.0ms499×body1280valid
91.0ms574×body640valid
38.0ms341×body320valid
14.0ms190×body160valid