Details

Time bar (total: 12.6s)

sample36.0ms

Algorithm
intervals
Results
8.0ms210×body80valid
5.0ms256×pre80true
3.0ms18×body640valid
2.0ms11×body1280valid
1.0ms11×body320valid
0.0ms6×body160valid

simplify53.0ms

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: 21.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (/ (* (+ 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)
20.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite72.0ms

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:
20.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
34.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
14.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series589.0ms

Counts
3 → 9
Calls
3 calls:
230.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
277.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
81.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify101.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250031789

prune356.0ms

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) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.1b
(* (+ 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)

rewrite125.0ms

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:
19.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
10.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
45.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
26.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series757.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
78.0ms
(/ (- 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)))
278.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify75.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010804781
150014605

prune810.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.4b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.1b
(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
5.9b
(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite598.0ms

Algorithm
rewrite-expression-head
Rules
3139×times-frac
2176×*-un-lft-identity
1574×add-sqr-sqrt
1297×sqrt-prod
1180×add-cube-cbrt
1077×associate-*r*
323×distribute-lft-out
175×distribute-lft-out-- difference-of-squares
134×associate-/r/
70×flip3-+ flip-+
67×div-inv
26×associate-/l*
25×add-exp-log add-cbrt-cube
18×sqrt-div
11×unswap-sqr
10×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l* prod-exp cbrt-unprod
3×div-sub associate-/l/
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 1358
Calls
4 calls:
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
21.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
277.0ms
(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
103.0ms
(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series798.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
223.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
224.0ms
(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
275.0ms
(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify292.0ms

Algorithm
egg-herbie
Counts
1370 → 1370
Iterations

Useful iterations: 1 (59.0ms)

IterNodesCost
0377827536
1500126027

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.4b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.1b
(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
5.9b
(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite597.0ms

Algorithm
rewrite-expression-head
Rules
3139×times-frac
2176×*-un-lft-identity
1574×add-sqr-sqrt
1297×sqrt-prod
1180×add-cube-cbrt
1077×associate-*r*
323×distribute-lft-out
175×distribute-lft-out-- difference-of-squares
134×associate-/r/
70×flip3-+ flip-+
67×div-inv
26×associate-/l*
25×add-exp-log add-cbrt-cube
18×sqrt-div
11×unswap-sqr
10×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l* prod-exp cbrt-unprod
3×div-sub associate-/l/
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 1358
Calls
4 calls:
10.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
28.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
272.0ms
(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
102.0ms
(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series817.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
226.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
227.0ms
(* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
286.0ms
(+ (* (+ alpha beta) (/ (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify293.0ms

Algorithm
egg-herbie
Counts
1370 → 1370
Iterations

Useful iterations: 1 (60.0ms)

IterNodesCost
0378827536
1500126027

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

regimes198.0ms

Accuracy

0% (6.4b remaining)

Error of 12.0b against oracle of 5.7b and baseline of 12.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02817
12817

end0.0ms

sample818.0ms

Algorithm
intervals
Results
253.0ms6404×body80valid
135.0ms8000×pre80true
101.0ms492×body1280valid
91.0ms551×body640valid
43.0ms362×body320valid
15.0ms191×body160valid