Details

Time bar (total: 8.5s)

sample36.0ms

Algorithm
intervals
Results
9.0ms213×body80valid
7.0ms256×pre80true
3.0ms17×body1280valid
2.0ms13×body640valid
1.0ms11×body320valid
0.0ms2×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize13.0ms

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)))

rewrite408.0ms

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:
89.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
292.0ms
(+ (/ (/ (* (+ 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)))

series585.0ms

Counts
3 → 9
Calls
3 calls:
227.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
276.0ms
(+ (/ (/ (* (+ 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)))

simplify97.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06811905
136221789
250031789

prune355.0ms

Filtered
120 candidates to 89 candidates (74.2%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite386.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
45×add-sqr-sqrt
35×times-frac
26×add-cube-cbrt
21×associate-*r*
20×add-exp-log add-cbrt-cube
8×flip3-+ flip-+
7×associate-/r* associate-/l/ distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv div-exp associate-/r/ associate-/l* add-log-exp
4×frac-times associate-*l* associate-*l/ prod-exp cbrt-unprod distribute-lft-out
3×div-inv
2×frac-2neg associate-*r/ clear-num unswap-sqr
1×+-commutative flip3-- div-sub pow-prod-down sum-log *-commutative flip--
Counts
4 → 129
Calls
4 calls:
21.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
75.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
52.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
233.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series680.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
234.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
82.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
286.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify94.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06571569
135541429
250011429

prune547.0ms

Filtered
141 candidates to 102 candidates (72.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.1b
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite323.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
51×add-sqr-sqrt
50×add-exp-log
43×times-frac
39×associate-*r*
32×add-cube-cbrt add-cbrt-cube
22×prod-exp
12×div-exp cbrt-unprod
11×pow1 frac-times associate-*l/
10×flip3-+ flip-+
7×cbrt-undiv distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
5×associate-*l* associate-/l*
4×associate-*r/ pow-prod-down distribute-lft-out
3×rec-exp 1-exp associate-/r* div-inv
2×*-commutative associate-/l/ unswap-sqr
1×+-commutative flip3-- frac-2neg div-sub clear-num sum-log un-div-inv flip--
Counts
4 → 155
Calls
4 calls:
23.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
50.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
153.0ms
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
89.0ms
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series663.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
83.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
229.0ms
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
272.0ms
(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify125.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
08552016
148211785
250021784

prune448.0ms

Filtered
167 candidates to 112 candidates (67.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b
(* (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
4.3b
(+ (* (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
54×sqrt-prod
49×*-un-lft-identity
42×associate-*r*
38×frac-times times-frac associate-*l/
34×add-sqr-sqrt
31×sqrt-div
30×add-cube-cbrt
27×add-exp-log add-cbrt-cube
20×pow1
16×flip3-+ flip-+
14×prod-exp cbrt-unprod
10×associate-*r/
9×pow-prod-down distribute-lft-out
6×associate-/r/ add-log-exp
3×rem-sqrt-square sqrt-pow1 div-inv
2×cbrt-undiv div-exp associate-*l* *-commutative
1×+-commutative pow-flip pow1/2 sum-log inv-pow
Counts
4 → 157
Calls
4 calls:
64.0ms
(sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
445.0ms
(* (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
155.0ms
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
382.0ms
(+ (* (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series953.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
240.0ms
(* (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
301.0ms
(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
284.0ms
(+ (* (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify119.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
08592978
141342554
250022399

prune510.0ms

Filtered
169 candidates to 111 candidates (65.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.2b

regimes122.0ms

Accuracy

8.4% (5.6b remaining)

Error of 11.5b against oracle of 6.0b and baseline of 12.0b

bsearch84.0ms

Steps
ItersRangePoint
9
3.088617839269422e+142
1.495088011218417e+148
6.131593311031189e+144

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05242
15242

end0.0ms

sample839.0ms

Algorithm
intervals
Results
266.0ms6396×body80valid
128.0ms8000×pre80true
100.0ms499×body1280valid
93.0ms574×body640valid
43.0ms341×body320valid
15.0ms190×body160valid