Details

Time bar (total: 13.1s)

sample37.0ms

Algorithm
intervals
Results
7.0ms187×body80valid
4.0ms28×body640valid
4.0ms22×body1280valid
4.0ms256×pre80true
1.0ms13×body320valid
0.0ms6×body160valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
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)
24.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite805.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity times-frac
32×add-sqr-sqrt
28×add-cube-cbrt
20×add-exp-log add-cbrt-cube
14×flip3-+ associate-/r/ flip-+
12×distribute-lft-out
10×associate-/l*
9×associate-/l/
8×frac-times
7×cbrt-undiv div-exp associate-/r* div-inv
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r*
4×associate-*r/ associate-*l* associate-*l/
3×prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in clear-num
1×+-commutative pow-prod-down sum-log *-commutative distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 144
Calls
4 calls:
33.0ms
(* (+ alpha beta) (- beta alpha))
173.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
541.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
51.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series678.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (+ alpha beta) (- beta alpha))
252.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
298.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
86.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify133.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07672103
143531976
250031976

prune434.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

localize12.0ms

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))
1.3b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.0b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite691.0ms

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:
42.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
174.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
359.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
97.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series799.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
176.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
247.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
293.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify68.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
010804781
150014605

prune912.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)
1.3b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.0b
(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
8.6b
(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

rewrite487.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
135×*-un-lft-identity
98×add-sqr-sqrt
90×associate-*r*
65×add-cube-cbrt
23×add-exp-log add-cbrt-cube distribute-lft-out
12×flip3-+ flip-+ distribute-lft-out-- difference-of-squares
10×cube-div associate-/r/
9×pow1
8×cbrt-prod
6×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod add-log-exp
5×cbrt-div div-inv
4×associate-*l* pow-exp rem-cube-cbrt
3×pow-unpow associate-*r/ unswap-sqr
2×cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down sqr-pow
1×+-commutative pow-to-exp pow1/3 sum-log *-commutative rem-cbrt-cube
Counts
4 → 182
Calls
4 calls:
96.0ms
(pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)
363.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.0ms
(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
3.0ms
(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

series3.9s

Counts
4 → 12
Calls
4 calls:
3.1s
(pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)
237.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
293.0ms
(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
255.0ms
(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

simplify54.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
09982759
150012613

prune594.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.3b
(log (+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0))
4.0b
(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
8.6b
(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

rewrite402.0ms

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:
360.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.0ms
(log (+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0))
15.0ms
(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
3.0ms
(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

series1.1s

Counts
4 → 12
Calls
4 calls:
246.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
299.0ms
(log (+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0))
291.0ms
(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
252.0ms
(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

simplify52.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010082774
150022635

prune616.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

regimes273.0ms

Accuracy

14.9% (7.1b remaining)

Error of 11.3b against oracle of 4.2b and baseline of 12.5b

bsearch55.0ms

Steps
ItersRangePoint
7
3.983641286803721e+113
1.3564002753670157e+115
1.3368421275617846e+115

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04834
14834

end0.0ms

sample876.0ms

Algorithm
intervals
Results
255.0ms6331×body80valid
113.0ms534×body1280valid
111.0ms8000×pre80true
98.0ms616×body640valid
39.0ms342×body320valid
14.0ms177×body160valid