Details

Time bar (total: 10.7s)

sample30.0ms

Algorithm
intervals
Results
9.0ms220×body80valid
4.0ms256×pre80true
3.0ms14×body1280valid
2.0ms10×body640valid
1.0ms8×body320valid
0.0ms4×body160valid

simplify50.0ms

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: 18.2b

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))
1.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite418.0ms

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:
92.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
296.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
26.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series559.0ms

Counts
3 → 9
Calls
3 calls:
221.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
260.0ms
(+ (/ (/ (* (+ 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)))

simplify92.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250031789

prune338.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
5.5b
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite687.0ms

Algorithm
rewrite-expression-head
Rules
603×times-frac
484×*-un-lft-identity
408×add-sqr-sqrt
260×add-cube-cbrt
219×sqrt-prod
153×associate-*r*
67×distribute-lft-out
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
34×associate-*l*
32×add-exp-log add-cbrt-cube
25×associate-/l*
21×flip3-+ flip-+
19×div-inv
15×unswap-sqr
14×associate-/r*
13×cbrt-undiv div-exp
8×sqrt-div
6×pow1 prod-exp cbrt-unprod add-log-exp
3×associate-/l/
2×frac-2neg div-sub clear-num
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 485
Calls
4 calls:
396.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
98.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
69.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
91.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series853.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
218.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
138.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
274.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify129.0ms

Algorithm
egg-herbie
Counts
497 → 497
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0172710548
1500110067

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.3b
(log (exp (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))))
4.1b
(+ (log (exp (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))) 1.0)

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
295×times-frac
261×*-un-lft-identity
188×add-sqr-sqrt
140×add-cube-cbrt
108×sqrt-prod
37×distribute-lft-out
25×associate-/l*
24×distribute-lft-out-- difference-of-squares
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×div-inv
6×pow1 log-prod add-log-exp
4×cbrt-undiv sqrt-div div-exp log-pow
3×associate-+l+ associate-/l/
2×frac-2neg div-sub clear-num
1×+-commutative exp-prod exp-to-pow rem-log-exp sum-log
Counts
4 → 278
Calls
4 calls:
98.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
71.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.0ms
(log (exp (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))))
6.0ms
(+ (log (exp (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))) 1.0)

series1.0s

Counts
4 → 12
Calls
4 calls:
211.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
335.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
225.0ms
(log (exp (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))))
274.0ms
(+ (log (exp (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))) 1.0)

simplify134.0ms

Algorithm
egg-herbie
Counts
290 → 290
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010565954
144165639
250015639

prune850.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
5.5b
(+ 1.0 (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))

rewrite600.0ms

Algorithm
rewrite-expression-head
Rules
603×times-frac
484×*-un-lft-identity
408×add-sqr-sqrt
260×add-cube-cbrt
219×sqrt-prod
153×associate-*r*
67×distribute-lft-out
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
34×associate-*l*
32×add-exp-log add-cbrt-cube
25×associate-/l*
21×flip3-+ flip-+
19×div-inv
15×unswap-sqr
14×associate-/r*
13×cbrt-undiv div-exp
8×sqrt-div
6×pow1 prod-exp cbrt-unprod add-log-exp
3×associate-/l/
2×frac-2neg div-sub clear-num
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 485
Calls
4 calls:
395.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
97.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
71.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.0ms
(+ 1.0 (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))

series862.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
221.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
134.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
279.0ms
(+ 1.0 (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))

simplify130.0ms

Algorithm
egg-herbie
Counts
497 → 497
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0172710529
1500210054

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.5b

regimes174.0ms

Accuracy

13.6% (5.8b remaining)

Error of 11.4b against oracle of 5.6b and baseline of 12.3b

bsearch65.0ms

Steps
ItersRangePoint
8
4.691534427487681e+136
1.114487485779193e+140
3.9671665599107027e+139

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05034
15034

end0.0ms

sample825.0ms

Algorithm
intervals
Results
259.0ms6356×body80valid
134.0ms8000×pre80true
106.0ms534×body1280valid
87.0ms544×body640valid
40.0ms345×body320valid
17.0ms221×body160valid