Details

Time bar (total: 8.6m)

sample36.0ms

Algorithm
intervals
Results
11.0ms204×body80valid
5.0ms26×body1280valid
4.0ms256×pre80true
2.0ms13×body320valid
1.0ms9×body640valid
0.0ms4×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

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))
1.3b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite425.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
94.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
303.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
23.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series577.0ms

Counts
3 → 9
Calls
3 calls:
226.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
271.0ms
(+ (/ (/ (* (+ 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)))

simplify97.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250031789

prune344.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite736.0ms

Algorithm
rewrite-expression-head
Rules
1250×times-frac
1055×*-un-lft-identity
619×add-sqr-sqrt
461×add-cube-cbrt
218×distribute-lft-out
96×associate-/l*
79×distribute-lft-out-- difference-of-squares
60×associate-/r/
33×div-inv
30×associate-/r*
26×flip3-- flip--
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×add-log-exp
5×associate-/l/
4×pow1 flip3-+ flip-+
3×frac-2neg clear-num
1×+-commutative sum-log
Counts
4 → 645
Calls
4 calls:
38.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
120.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
32.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
490.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series691.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
221.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
78.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
274.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify162.0ms

Algorithm
egg-herbie
Counts
657 → 657
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0178313720
1500113481

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.9b
(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.3b
(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
324×times-frac
298×*-un-lft-identity
212×add-sqr-sqrt
138×add-cube-cbrt
49×distribute-lft-out
42×associate-/r*
34×difference-of-squares
31×distribute-lft-out--
22×associate-/r/
14×add-exp-log add-cbrt-cube
12×div-inv
11×flip3-- flip--
8×associate-/l* add-log-exp
6×cbrt-undiv div-exp
4×pow1 unpow-prod-down cube-prod associate-/l/
3×flip3-+ flip-+
2×frac-2neg clear-num
1×+-commutative sub-neg diff-log sum-log sum-cubes
Counts
4 → 286
Calls
4 calls:
32.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
29.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
243.0ms
(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.4s
(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))

series4.5s

Counts
4 → 12
Calls
4 calls:
215.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
79.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
174.0ms
(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.1s
(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))

simplify111.0ms

Algorithm
egg-herbie
Counts
298 → 298
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07304525
134084336
250014332

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.1b
(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 6)
0.9b
(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.3b
(+ (pow (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

rewrite4.6s

Algorithm
rewrite-expression-head
Rules
1097×times-frac
954×*-un-lft-identity
534×add-sqr-sqrt
398×unpow-prod-down
394×add-cube-cbrt
216×distribute-lft-out
67×difference-of-squares
64×distribute-lft-out--
49×associate-/r/
36×cube-prod
27×div-inv
22×flip3-- flip--
21×associate-/r*
19×add-exp-log
9×div-exp add-cbrt-cube
8×add-log-exp
5×pow1
4×pow-exp associate-/l*
3×cbrt-undiv pow-unpow flip3-+ flip-+
2×associate-/l/
1×+-commutative pow-to-exp sub-neg pow-pow frac-2neg diff-log clear-num sum-log sum-cubes sqr-pow
Counts
4 → 555
Calls
4 calls:
29.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
148.0ms
(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 6)
238.0ms
(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.2s
(+ (pow (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

series8.2m

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
2.1m
(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 6)
158.0ms
(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.1m
(+ (pow (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

simplify164.0ms

Algorithm
egg-herbie
Counts
567 → 567
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0281314068
1500213926

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

regimes239.0ms

Accuracy

20.7% (5.3b remaining)

Error of 11.4b against oracle of 6.1b and baseline of 12.8b

bsearch25.0ms

Steps
ItersRangePoint
3
1.6625064603448269e+159
2.093216826817002e+159
1.994668306731855e+159

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04726
14726

end0.0ms

sample790.0ms

Algorithm
intervals
Results
246.0ms6302×body80valid
120.0ms8000×pre80true
101.0ms540×body1280valid
86.0ms577×body640valid
46.0ms395×body320valid
14.0ms186×body160valid