Details

Time bar (total: 8.1s)

sample32.0ms

Algorithm
intervals
Results
8.0ms211×body80valid
4.0ms256×pre80true
3.0ms18×body1280valid
2.0ms14×body640valid
1.0ms10×body320valid
0.0ms3×body160valid

simplify54.0ms

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: 21.0b

localize12.0ms

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)
18.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite423.0ms

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))
304.0ms
(+ (/ (/ (* (+ 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)))

series571.0ms

Counts
3 → 9
Calls
3 calls:
221.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
270.0ms
(+ (/ (/ (* (+ 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)))

simplify95.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250031789

prune339.0ms

Filtered
120 candidates to 89 candidates (74.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.8b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.5b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite393.0ms

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:
22.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
96.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
202.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
54.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series723.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
157.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
221.0ms
(* (+ 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)

simplify74.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010804781
150014605

prune764.0ms

Filtered
307 candidates to 199 candidates (64.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
1.8b
(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.5b
(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite377.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
32×add-cbrt-cube
28×add-sqr-sqrt *-un-lft-identity
25×associate-*r*
19×times-frac
18×prod-exp
17×add-cube-cbrt
16×div-exp
10×cbrt-unprod
9×cbrt-undiv associate-*l*
8×pow1
6×frac-times flip3-+ associate-*l/ associate-/r/ flip-+ associate-/l/ add-log-exp
4×flip3-- associate-/r* flip-- distribute-lft-out unswap-sqr
3×rec-exp 1-exp associate-*r/ div-inv
2×pow-prod-down un-div-inv *-commutative
1×+-commutative frac-2neg clear-num sum-log associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 129
Calls
4 calls:
76.0ms
(/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
48.0ms
(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
174.0ms
(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
74.0ms
(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series731.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
72.0ms
(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
226.0ms
(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
270.0ms
(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify117.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
07691773
143371515
250031493

prune514.0ms

Filtered
141 candidates to 98 candidates (69.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
1.8b
(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.5b
(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
4.4b
(log (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log
18×add-cbrt-cube
14×*-un-lft-identity
12×add-sqr-sqrt
10×add-cube-cbrt associate-*r* prod-exp
8×pow1
7×div-exp
6×log-prod flip3-+ cbrt-unprod flip-+ add-log-exp
4×cbrt-undiv log-div exp-prod times-frac associate-*l*
3×exp-sum
2×frac-times exp-diff associate-*l/ associate-/r/ log-pow distribute-lft-out
1×+-commutative rec-exp 1-exp associate-*r/ rem-log-exp pow-prod-down sum-log *-commutative div-inv rem-exp-log unswap-sqr
Counts
4 → 81
Calls
4 calls:
73.0ms
(exp (log (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
176.0ms
(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
75.0ms
(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
75.0ms
(log (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
271.0ms
(exp (log (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
224.0ms
(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
270.0ms
(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
264.0ms
(log (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))

simplify83.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06171764
129661548
250011508

prune270.0ms

Filtered
93 candidates to 65 candidates (69.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

regimes240.0ms

Accuracy

60.5% (3.2b remaining)

Error of 7.6b against oracle of 4.4b and baseline of 12.5b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05238
15238

end0.0ms

sample802.0ms

Algorithm
intervals
Results
243.0ms6342×body80valid
122.0ms8000×pre80true
103.0ms535×body1280valid
85.0ms557×body640valid
49.0ms386×body320valid
13.0ms180×body160valid