Details

Time bar (total: 17.0s)

sample52.0ms

Algorithm
intervals
Results
17.0ms210×body80valid
8.0ms19×body1280valid
6.0ms256×pre80true
4.0ms15×body320valid
3.0ms9×body640valid
0.0ms3×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize18.0ms

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)
21.3b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite436.0ms

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:
95.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
312.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
24.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series596.0ms

Counts
3 → 9
Calls
3 calls:
229.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
282.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
85.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify91.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06811905
136221789
250031789

prune334.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- 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)))
2.9b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite404.0ms

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:
24.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
99.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
210.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
53.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series761.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
169.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
233.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
282.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify77.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010804781
150014605

prune794.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (* (+ 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))))
1.2b
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite408.0ms

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:
22.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
80.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
55.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
246.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series703.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
238.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
87.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
297.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify95.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06571569
135541429
250011429

prune409.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.1b
(pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
1.2b
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
1.4b
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
94×add-exp-log add-cbrt-cube
47×*-un-lft-identity
36×cbrt-undiv div-exp
34×prod-exp cbrt-unprod
28×times-frac
21×add-sqr-sqrt
17×add-cube-cbrt
14×unpow-prod-down cube-prod
13×distribute-lft-out
12×pow1 swap-sqr associate-/r/
10×associate-*r* associate-*l*
8×add-log-exp
7×flip3-+ flip-+
6×div-inv
4×pow-exp rem-cube-cbrt
3×pow-unpow
1×+-commutative cube-div pow2 cube-mult frac-times pow-to-exp sub-neg flip3-- pow-pow pow-plus diff-log unpow3 associate-*r/ pow-prod-down associate-*l/ sum-log pow-sqr sum-cubes *-commutative pow-prod-up flip-- distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 156
Calls
4 calls:
363.0ms
(* (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
82.0ms
(pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
485.0ms
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
105.0ms
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series8.4s

Counts
4 → 12
Calls
4 calls:
1.4s
(* (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.8s
(pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
4.1s
(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
184.0ms
(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify55.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09093458
150012785

prune464.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

regimes198.0ms

Accuracy

0% (6.4b remaining)

Error of 12.4b against oracle of 6.0b and baseline of 12.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03359
13359

end0.0ms

sample1.5s

Algorithm
intervals
Results
537.0ms6349×body80valid
207.0ms513×body1280valid
194.0ms8000×pre80true
181.0ms551×body640valid
95.0ms383×body320valid
34.0ms204×body160valid