Details

Time bar (total: 8.5s)

sample34.0ms

Algorithm
intervals
Results
8.0ms205×body80valid
4.0ms256×pre80true
4.0ms19×body1280valid
2.0ms15×body640valid
1.0ms10×body320valid
1.0ms7×body160valid

simplify51.0ms

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: 24.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2.0 i))
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite429.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
48×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×associate-/r/
12×flip3-+ flip-+
11×distribute-lft-out add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
4×pow1 frac-times sum-log
3×flip3-- flip--
2×+-commutative frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×associate-+l+
Counts
4 → 124
Calls
4 calls:
13.0ms
(+ (+ alpha beta) (* 2.0 i))
90.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
299.0ms
(+ (/ (/ (* (+ 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)))

series733.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ alpha beta) (* 2.0 i))
219.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
415.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
80.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify96.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07011981
139801865
250021865

prune385.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

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))))
1.7b
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite387.0ms

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:
23.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
76.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
50.0ms
(* (+ alpha beta) (/ (- 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)) 1.0)

series650.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
222.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
80.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
271.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify91.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06571569
135541429
250011429

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b
(exp (log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
1.7b
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
2.4b
(log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))

rewrite569.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
28×add-sqr-sqrt
21×associate-*r*
17×add-cube-cbrt
16×times-frac
10×add-exp-log
9×add-cbrt-cube
8×pow1 log-prod
6×flip3-+ flip-+ add-log-exp
4×log-div exp-prod associate-*l* exp-sum distribute-lft-out
3×distribute-lft-out-- difference-of-squares
2×frac-times exp-diff associate-*l/ prod-exp associate-/r/ log-pow cbrt-unprod unswap-sqr
1×cbrt-undiv +-commutative associate-*r/ div-exp rem-log-exp pow-prod-down sum-log *-commutative div-inv rem-exp-log
Counts
4 → 90
Calls
4 calls:
50.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
140.0ms
(exp (log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
231.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
142.0ms
(log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))

series889.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
271.0ms
(exp (log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
268.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
271.0ms
(log (+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))

simplify68.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05391525
124811384
250011348

prune326.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize16.0ms

Local error

Found 4 expressions with local error:

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))))
1.7b
(+ (log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
2.4b
(log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

rewrite936.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
31×add-sqr-sqrt
24×times-frac
21×associate-*r*
20×add-cube-cbrt
18×add-exp-log add-cbrt-cube
12×log-pow
10×exp-prod
8×pow1 flip3-+ flip-+
6×log-prod associate-/r/ distribute-lft-out
5×cbrt-undiv div-exp associate-/l/ add-log-exp
4×frac-times associate-*l* associate-*l/ prod-exp associate-/r* cbrt-unprod
3×associate-+l+ div-inv distribute-lft-out-- difference-of-squares
2×associate-*r/ unswap-sqr
1×+-commutative frac-2neg rem-log-exp pow-prod-down clear-num sum-log *-commutative associate-/l*
Counts
4 → 115
Calls
4 calls:
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))))
676.0ms
(+ (log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
129.0ms
(log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

series802.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
80.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
269.0ms
(+ (log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
226.0ms
(log (exp (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

simplify90.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06291596
132981439
250021439

prune377.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

regimes194.0ms

Accuracy

6.4% (7.7b remaining)

Error of 11.7b against oracle of 4.1b and baseline of 12.3b

bsearch75.0ms

Steps
ItersRangePoint
8
4.428991759387381e+90
6.067708768752393e+93
5.983234319528818e+93

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04828
14828

end0.0ms

sample830.0ms

Algorithm
intervals
Results
259.0ms6372×body80valid
133.0ms8000×pre80true
104.0ms495×body1280valid
92.0ms567×body640valid
43.0ms363×body320valid
16.0ms203×body160valid