Details

Time bar (total: 10.9s)

sample55.0ms

Algorithm
intervals
Results
19.0ms202×body80valid
6.0ms21×body640valid
6.0ms256×pre80true
6.0ms16×body1280valid
3.0ms13×body320valid
1.0ms4×body160valid

simplify54.0ms

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: 21.2b

localize13.0ms

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)
19.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite416.0ms

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:
90.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
297.0ms
(+ (/ (/ (* (+ 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)))

series576.0ms

Counts
3 → 9
Calls
3 calls:
225.0ms
(/ (/ (* (+ 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)
73.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify91.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250031789

prune354.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize12.0ms

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)))
1.9b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.2b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite395.0ms

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:
97.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
24.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
201.0ms
(* (+ 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)

series725.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
74.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
222.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
267.0ms
(+ (* (+ 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 (26.0ms)

IterNodesCost
010804781
150014605

prune797.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
1.9b
(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
7.0b
(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
344×times-frac
273×add-sqr-sqrt
251×*-un-lft-identity
154×associate-*r*
141×add-cube-cbrt
132×sqrt-prod
100×add-exp-log
56×add-cbrt-cube
38×div-exp
37×prod-exp
31×associate-*l*
29×distribute-lft-out
25×unswap-sqr
21×distribute-lft-out-- difference-of-squares
20×associate-/r/
19×cbrt-undiv cbrt-unprod
15×flip3-+ flip-+
13×pow1
10×frac-times div-inv
7×rec-exp 1-exp associate-*r/ associate-/r*
6×sqrt-div associate-*l/ add-log-exp
4×pow-prod-down
3×pow-flip associate-/l*
2×*-commutative
1×+-commutative frac-2neg sqrt-pow1 pow1/2 clear-num sum-log inv-pow
Counts
4 → 343
Calls
4 calls:
64.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
381.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
273.0ms
(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
264.0ms
(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series785.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
161.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
228.0ms
(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
272.0ms
(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify98.0ms

Algorithm
egg-herbie
Counts
355 → 355
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
016437323
150026721

prune805.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
1.9b
(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
7.0b
(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
344×times-frac
273×add-sqr-sqrt
251×*-un-lft-identity
154×associate-*r*
141×add-cube-cbrt
132×sqrt-prod
100×add-exp-log
56×add-cbrt-cube
38×div-exp
37×prod-exp
31×associate-*l*
29×distribute-lft-out
25×unswap-sqr
21×distribute-lft-out-- difference-of-squares
20×associate-/r/
19×cbrt-undiv cbrt-unprod
15×flip3-+ flip-+
13×pow1
10×frac-times div-inv
7×rec-exp 1-exp associate-*r/ associate-/r*
6×sqrt-div associate-*l/ add-log-exp
4×pow-prod-down
3×pow-flip associate-/l*
2×*-commutative
1×+-commutative frac-2neg sqrt-pow1 pow1/2 clear-num sum-log inv-pow
Counts
4 → 343
Calls
4 calls:
64.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
381.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
271.0ms
(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
266.0ms
(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series787.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
161.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
231.0ms
(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
274.0ms
(+ (* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify99.0ms

Algorithm
egg-herbie
Counts
355 → 355
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
016487324
150026722

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.2b

regimes189.0ms

Accuracy

18.2% (5.2b remaining)

Error of 11.2b against oracle of 6.0b and baseline of 12.3b

bsearch53.0ms

Steps
ItersRangePoint
5
3.749479162223782e+181
1.156670155801419e+182
7.718884881344612e+181

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05235
15235

end0.0ms

sample1.4s

Algorithm
intervals
Results
505.0ms6369×body80valid
194.0ms523×body1280valid
182.0ms8000×pre80true
169.0ms554×body640valid
81.0ms366×body320valid
30.0ms188×body160valid