Details

Time bar (total: 10.9s)

sample34.0ms

Algorithm
intervals
Results
8.0ms201×body80valid
4.0ms256×pre80true
4.0ms19×body1280valid
2.0ms13×body640valid
2.0ms14×body320valid
1.0ms9×body160valid

simplify52.0ms

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: 23.3b

localize13.0ms

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))
2.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.3b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite852.0ms

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:
173.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
616.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
56.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series633.0ms

Counts
3 → 9
Calls
3 calls:
246.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
300.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
86.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify97.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07011971
137401800
250011782

prune541.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 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
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.3b
(+ (* (/ 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))))) 1.0)

rewrite1.0s

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:
472.0ms
(* (/ 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)))))
130.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
120.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
290.0ms
(+ (* (/ 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)

series835.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(* (/ 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)))))
134.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
129.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
311.0ms
(+ (* (/ 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)

simplify117.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
09503691
149253156
250013155

prune761.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.3b
(log (exp (+ (* (/ 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)))
8.3b
(+ (* (/ 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))))) 1.0)

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
58×add-sqr-sqrt
56×times-frac
42×add-cube-cbrt
40×sqrt-prod
14×associate-/r*
10×add-exp-log distribute-lft-out
8×add-cbrt-cube associate-/l* distribute-lft-out-- difference-of-squares
7×pow1
6×add-log-exp
4×expm1-log1p-u log-prod sqrt-div associate-/r/ log-pow log1p-expm1-u
3×exp-prod pow-flip flip3-+ div-exp flip-+
2×cbrt-undiv frac-2neg clear-num div-inv associate-/l/
1×+-commutative rec-exp flip3-- fma-def sqrt-pow1 pow1/2 1-exp div-sub rem-log-exp exp-sum sum-log flip-- inv-pow
Counts
4 → 151
Calls
4 calls:
129.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
120.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.1s
(log (exp (+ (* (/ 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)))
296.0ms
(+ (* (/ 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)

series861.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
125.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
298.0ms
(log (exp (+ (* (/ 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)))
298.0ms
(+ (* (/ 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)

simplify67.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05942406
122792147
250012082

prune536.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
13.1b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite229.0ms

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:
174.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
46.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series545.0ms

Counts
3 → 9
Calls
3 calls:
172.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
85.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
288.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify94.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07273112
132592892
250012876

prune596.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 6.0b

regimes286.0ms

Accuracy

14.9% (5.5b remaining)

Error of 11.3b against oracle of 5.8b and baseline of 12.2b

bsearch76.0ms

Steps
ItersRangePoint
8
1.0980023513866943e+148
5.636643246150371e+152
4.038875915762912e+148

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04732
14732

end0.0ms

sample880.0ms

Algorithm
intervals
Results
247.0ms6376×body80valid
132.0ms8000×pre80true
97.0ms509×body1280valid
89.0ms596×body640valid
42.0ms321×body320valid
15.0ms198×body160valid