Details

Time bar (total: 13.7s)

sample33.0ms

Algorithm
intervals
Results
8.0ms207×body80valid
4.0ms256×pre80true
3.0ms17×body1280valid
3.0ms18×body640valid
1.0ms7×body320valid
1.0ms7×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize16.0ms

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))
1.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite753.0ms

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:
171.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
528.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
50.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series553.0ms

Counts
3 → 9
Calls
3 calls:
216.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
263.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
74.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify95.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250031789

prune334.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.0b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.8b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite675.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 295
Calls
4 calls:
173.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
42.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
349.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
95.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series700.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
71.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
217.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
262.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify73.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010804781
150014605

prune746.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.3b
(/ beta (+ (+ alpha beta) (* 2.0 i)))
2.0b
(* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
3.8b
(+ (* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite3.8s

Algorithm
rewrite-expression-head
Rules
252×times-frac
245×*-un-lft-identity
129×add-sqr-sqrt
91×add-cube-cbrt
58×associate-*r*
45×distribute-lft-out
42×associate-/r/
27×flip3-+ flip-+
25×distribute-lft-out--
21×distribute-rgt-out-- div-inv
18×associate-/l*
13×add-exp-log add-cbrt-cube
9×difference-of-squares
8×frac-times
7×associate-/r*
6×pow1 add-log-exp
4×cbrt-undiv distribute-rgt-in sub-neg associate-+l+ distribute-lft-in associate-*r/ div-exp associate-*l*
3×flip3-- frac-sub flip-- sub-div
2×frac-2neg associate-*l/ clear-num
1×+-commutative pow-prod-down prod-exp sum-log *-commutative cbrt-unprod associate-/l/ unswap-sqr
Counts
4 → 232
Calls
4 calls:
164.0ms
(/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
32.0ms
(/ beta (+ (+ alpha beta) (* 2.0 i)))
2.8s
(* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
823.0ms
(+ (* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series891.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
70.0ms
(/ beta (+ (+ alpha beta) (* 2.0 i)))
333.0ms
(* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
319.0ms
(+ (* (+ alpha beta) (- (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify64.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010524197
150014028

prune671.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ beta (+ (+ alpha beta) (* 2.0 i)))
3.8b
(+ (* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta)) 1.0)
5.8b
(* (+ alpha beta) (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.0b
(* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
300×times-frac
241×*-un-lft-identity
158×add-sqr-sqrt
147×add-cube-cbrt
140×associate-*l*
70×associate-*r*
66×distribute-lft-neg-in distribute-rgt-neg-in
47×distribute-lft-out
32×associate-/r/
21×flip3-+ flip-+
17×add-exp-log add-cbrt-cube
16×div-inv
8×pow1
6×add-log-exp
4×cbrt-undiv frac-times div-exp prod-exp cbrt-unprod unswap-sqr
3×associate-*r/ associate-*l/ associate-/r* distribute-neg-frac associate-/l*
2×distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down *-commutative
1×+-commutative distribute-lft-neg-out neg-mul-1 frac-2neg clear-num sum-log
Counts
4 → 295
Calls
4 calls:
32.0ms
(/ beta (+ (+ alpha beta) (* 2.0 i)))
170.0ms
(+ (* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta)) 1.0)
331.0ms
(* (+ alpha beta) (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
659.0ms
(* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta))

series682.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ beta (+ (+ alpha beta) (* 2.0 i)))
258.0ms
(+ (* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta)) 1.0)
178.0ms
(* (+ alpha beta) (/ (/ beta (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
175.0ms
(* (- (/ (/ alpha (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (+ alpha beta))

simplify70.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
020053930
150033828

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

regimes195.0ms

Accuracy

0% (6.6b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03539
14139
24539
34539

end0.0ms

sample890.0ms

Algorithm
intervals
Results
258.0ms6337×body80valid
121.0ms8000×pre80true
109.0ms511×body1280valid
93.0ms595×body640valid
42.0ms365×body320valid
15.0ms192×body160valid