Details

Time bar (total: 14.5s)

sample29.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms256×pre80true

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
39.8b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
45.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 200
Calls
4 calls:
73.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
53.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
118.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
70.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.3s

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
106.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
948.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
173.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify74.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012495670
150015161

prune619.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
37.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite716.0ms

Algorithm
rewrite-expression-head
Rules
366×times-frac
300×add-sqr-sqrt
235×*-un-lft-identity
155×add-cube-cbrt
96×associate-*r*
70×add-exp-log add-cbrt-cube
62×difference-of-squares
44×associate-/r/
42×associate-*l*
33×cbrt-undiv div-exp
31×sqrt-prod distribute-lft-out--
22×flip3-+ flip-+ div-inv
19×associate-/l*
16×prod-exp cbrt-unprod
12×associate-/r*
9×distribute-lft-out
6×pow1 unswap-sqr
5×associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 364
Calls
4 calls:
138.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
459.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
33.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
65.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.8s

Counts
4 → 12
Calls
4 calls:
337.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
87.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
120.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify125.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0168310749
150019903

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 37.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
37.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite567.0ms

Algorithm
rewrite-expression-head
Rules
166×times-frac
145×add-sqr-sqrt
110×*-un-lft-identity
96×associate-*r*
94×add-exp-log add-cbrt-cube
76×add-cube-cbrt
43×cbrt-undiv div-exp
30×difference-of-squares
25×prod-exp cbrt-unprod
22×associate-/r/
15×sqrt-prod distribute-lft-out--
12×flip3-+ flip-+
11×div-inv
10×associate-/r*
9×associate-*l*
7×associate-/l/
6×pow1
5×associate-/l*
4×associate-*r/ add-log-exp
3×frac-2neg clear-num unswap-sqr
2×frac-times associate-*l/ distribute-lft-out
1×flip3-- pow-prod-down *-commutative flip--
Counts
4 → 238
Calls
4 calls:
170.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
283.0ms
(* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
33.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
66.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.2s

Counts
4 → 12
Calls
4 calls:
2.3s
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
672.0ms
(* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
87.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
118.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify79.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013656476
150015398

prune725.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 37.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
0.5b
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
0.5b
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
38.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite276.0ms

Algorithm
rewrite-expression-head
Rules
141×*-un-lft-identity
117×times-frac
106×add-sqr-sqrt
76×add-cube-cbrt
60×sqrt-prod
39×distribute-lft-out
36×associate-*r*
24×associate-*l*
22×add-exp-log add-cbrt-cube
15×associate-/r*
11×associate-/l*
10×associate-/r/
9×unswap-sqr
8×sqrt-div
7×cbrt-undiv flip3-+ div-exp flip-+
6×pow1
5×div-inv
4×prod-exp cbrt-unprod associate-/l/ add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 218
Calls
4 calls:
129.0ms
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
19.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
49.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
67.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series517.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (/ i (sqrt (+ (+ alpha beta) (* 2.0 i)))) (/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i)))))
129.0ms
(/ i (sqrt (+ (+ alpha beta) (* 2.0 i))))
160.0ms
(/ (+ (+ alpha beta) i) (sqrt (+ (+ alpha beta) (* 2.0 i))))
117.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify119.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
09273170
145472902
250012812

prune743.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.2b

regimes180.0ms

Accuracy

32.8% (10.7b remaining)

Error of 12.9b against oracle of 2.2b and baseline of 18.1b

bsearch164.0ms

Steps
ItersRangePoint
0
5.742669426456722e+178
5.893031870312281e+178
5.8178506483845014e+178
4
1.6635807527914217e+168
2.9455749349115376e+168
2.8985313523571793e+168
6
5.540346198531466e+155
7.941915973428938e+156
5.669919209743873e+155
7
7.132585125088937e+135
1.5715840627491381e+137
1.5553661537212927e+137

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068143
171143
274143
374143

end0.0ms

sample731.0ms

Algorithm
intervals
Results
405.0ms8000×body80valid
135.0ms8000×pre80true