Details

Time bar (total: 13.4s)

sample59.0ms

Algorithm
intervals
Results
17.0ms209×body80valid
10.0ms256×pre80true
9.0ms16×body1280valid
4.0ms13×body640valid
3.0ms13×body320valid
1.0ms5×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2.0 i))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.1b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite411.0ms

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:
12.0ms
(+ (+ alpha beta) (* 2.0 i))
87.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
284.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series190.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (+ alpha beta) (* 2.0 i))
72.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
93.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify97.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07011981
139801865
250021865

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.2b

localize15.0ms

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))
2.1b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.3b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite368.0ms

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)))
89.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
190.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
49.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series225.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
42.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
73.0ms
(* (+ 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)

simplify67.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010804781
150014605

prune2.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
2.1b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.3b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
4.1b
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
134×*-un-lft-identity
99×add-sqr-sqrt
90×associate-*r*
66×add-cube-cbrt
22×distribute-lft-out
14×add-exp-log
13×add-cbrt-cube
12×distribute-lft-out-- difference-of-squares
10×flip3-+ associate-/r/ flip-+
8×pow1
6×log-prod add-log-exp
5×div-inv
4×log-div exp-prod associate-*l*
3×cbrt-undiv div-exp exp-sum prod-exp cbrt-unprod unswap-sqr
2×frac-times exp-diff associate-*l/ log-pow
1×+-commutative associate-*r/ rem-log-exp pow-prod-down sum-log *-commutative rem-exp-log
Counts
4 → 159
Calls
4 calls:
51.0ms
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
193.0ms
(* (+ 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))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
49.0ms
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))

series367.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
72.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
92.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
111.0ms
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09282698
150022523

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

localize19.0ms

Local error

Found 4 expressions with local error:

2.1b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.3b
(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
4.1b
(log (+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0))
13.4b
(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
137×*-un-lft-identity
98×add-sqr-sqrt
90×associate-*r*
65×add-cube-cbrt
24×distribute-lft-out
14×add-exp-log
13×add-cbrt-cube
12×distribute-lft-out-- difference-of-squares
11×flip3-+ flip-+
10×associate-/r/
8×cbrt-prod
7×pow1
6×add-log-exp
5×cube-div cbrt-div div-inv
4×frac-times log-prod associate-*l* associate-*l/
3×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
2×log-div associate-*r/
1×+-commutative cube-mult unpow-prod-down pow1/3 unpow3 cube-prod rem-log-exp pow-prod-down sum-log log-pow *-commutative rem-cbrt-cube sqr-pow
Counts
4 → 166
Calls
4 calls:
191.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.0ms
(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
8.0ms
(log (+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0))
2.0ms
(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

series350.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
93.0ms
(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
110.0ms
(log (+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0))
74.0ms
(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

simplify49.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010052772
150022633

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

regimes611.0ms

Accuracy

10.5% (7.1b remaining)

Error of 11.2b against oracle of 4.1b and baseline of 12.0b

bsearch21.0ms

Steps
ItersRangePoint
4
8.790873633702001e+153
1.2605266572077815e+154
1.248606679275357e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05444
15444

end0.0ms

sample1.5s

Algorithm
intervals
Results
510.0ms6403×body80valid
333.0ms8000×pre80true
191.0ms471×body1280valid
186.0ms582×body640valid
84.0ms352×body320valid
31.0ms192×body160valid