Details

Time bar (total: 19.7s)

sample36.0ms

Algorithm
intervals
Results
8.0ms196×body80valid
4.0ms256×pre80true
4.0ms20×body1280valid
3.0ms19×body640valid
2.0ms15×body320valid
0.0ms6×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

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))
2.0b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
24.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite471.0ms

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))
344.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
28.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series579.0ms

Counts
3 → 9
Calls
3 calls:
223.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
279.0ms
(+ (/ (/ (* (+ 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 (77.0ms)

IterNodesCost
07011971
137401800
250011782

prune733.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.4b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
3.2b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
10036×times-frac
6754×*-un-lft-identity
4612×add-sqr-sqrt
3458×add-cube-cbrt
1178×fma-def
1071×distribute-lft-out
577×distribute-lft-out-- difference-of-squares
400×associate-/r/
314×associate-/l*
205×div-inv
164×flip3-+ flip-+
105×associate-/r*
62×add-exp-log
43×div-exp
32×flip3-- add-cbrt-cube flip--
19×cbrt-undiv
6×rec-exp 1-exp add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
4 → 3236
Calls
4 calls:
165.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
32.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.0s
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series622.0ms

Counts
4 → 12
Calls
4 calls:
287.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
67.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
143.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
125.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify459.0ms

Algorithm
egg-herbie
Counts
3248 → 3248
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500147178

prune9.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.4b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
14.5b
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
1062×times-frac
759×*-un-lft-identity
595×add-sqr-sqrt
413×add-cube-cbrt
105×associate-/r*
91×distribute-lft-out-- difference-of-squares
82×distribute-lft-out
65×associate-/r/
34×add-exp-log
33×div-inv
27×flip3-+ flip-+
24×associate-/l*
20×div-exp add-cbrt-cube
10×cbrt-undiv
6×pow1
5×flip3-- flip--
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×pow-flip inv-pow
1×fma-udef associate-/l/
Counts
4 → 595
Calls
4 calls:
62.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
18.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
28.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
0.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series356.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
68.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
149.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
82.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify116.0ms

Algorithm
egg-herbie
Counts
607 → 607
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
017428804
150018301

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
0.4b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
2.1b
(log (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
14.5b
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
888×times-frac
604×*-un-lft-identity
484×add-sqr-sqrt
340×add-cube-cbrt
96×associate-/r*
72×distribute-lft-out-- difference-of-squares
60×distribute-lft-out
49×associate-/r/
26×add-exp-log
25×div-inv
20×flip3-+ flip-+
15×div-exp
13×add-cbrt-cube
7×pow1
6×cbrt-undiv log-prod
4×expm1-log1p-u exp-prod flip3-- flip-- log1p-expm1-u add-log-exp
3×rec-exp 1-exp exp-sum associate-/l*
2×log-pow
1×pow-flip frac-2neg rem-log-exp clear-num fma-udef rem-exp-log inv-pow
Counts
4 → 455
Calls
4 calls:
1.0ms
(exp (log (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
29.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.0ms
(log (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
0.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series424.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(exp (log (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
149.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
121.0ms
(log (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
80.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify101.0ms

Algorithm
egg-herbie
Counts
467 → 467
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015667353
150016677

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.1b

regimes365.0ms

Accuracy

18.3% (5.6b remaining)

Error of 11.4b against oracle of 5.8b and baseline of 12.7b

bsearch46.0ms

Steps
ItersRangePoint
5
2.2311381873559525e+79
6.756405221066791e+79
6.605015183417663e+79

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample852.0ms

Algorithm
intervals
Results
269.0ms6344×body80valid
129.0ms8000×pre80true
118.0ms539×body1280valid
97.0ms583×body640valid
43.0ms347×body320valid
16.0ms187×body160valid