Details

Time bar (total: 10.4s)

sample47.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
6.0ms256×pre80true

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05826
128326
2162026
3500326

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.8b
(/ (/ (* (* 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))
44.6b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite565.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×distribute-lft-out
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 189
Calls
4 calls:
87.0ms
(* i (+ (+ alpha beta) i))
99.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
226.0ms
(/ (/ (* (* 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))
139.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series969.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* i (+ (+ alpha beta) i))
92.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
701.0ms
(/ (/ (* (* 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))
156.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify101.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
012085419
150014944

prune584.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* 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))))
35.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
264×times-frac
191×add-sqr-sqrt
178×*-un-lft-identity
110×add-cube-cbrt
96×associate-*r*
74×add-exp-log add-cbrt-cube
42×associate-*l*
40×associate-/r/
35×cbrt-undiv div-exp
30×difference-of-squares
21×flip3-+ flip-+
20×div-inv
19×distribute-lft-out
17×prod-exp cbrt-unprod
15×sqrt-prod distribute-lft-out--
13×associate-/l*
10×associate-/r*
6×pow1 unswap-sqr
5×associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 304
Calls
4 calls:
195.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
771.0ms
(* (/ (/ (* 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))))
63.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
132.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.5s

Counts
4 → 12
Calls
4 calls:
231.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.1s
(* (/ (/ (* 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))))
79.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
107.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify103.0ms

Algorithm
egg-herbie
Counts
316 → 316
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
015818513
150017655

prune953.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.5b

localize21.0ms

Local error

Found 4 expressions with local error:

32.8b
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
35.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite311.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log add-cbrt-cube
14×*-un-lft-identity
12×add-sqr-sqrt
10×add-cube-cbrt
8×cbrt-undiv sqrt-div div-exp
7×flip3-+ times-frac associate-/r* flip-+ associate-/l/
6×pow1 sqrt-prod
5×prod-exp cbrt-unprod
4×associate-*r/ associate-/r/ add-log-exp
2×frac-times rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num div-inv distribute-lft-out associate-/l*
1×associate-*l/
Counts
4 → 89
Calls
4 calls:
226.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
68.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series835.0ms

Counts
4 → 12
Calls
4 calls:
656.0ms
(/ (* (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
78.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
47.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
52.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify87.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06381492
135541275
250031273

prune518.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 34.5b

localize25.0ms

Local error

Found 4 expressions with local error:

35.2b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×add-exp-log add-cube-cbrt *-un-lft-identity sqrt-prod add-cbrt-cube
7×pow1
6×sqrt-div
5×flip3-+ flip-+
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 associate-/r*
2×cbrt-undiv associate-*r/ div-exp associate-/r/ associate-/l/
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
66.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
8.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series224.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
48.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
50.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
50.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0334753
11681682
25002679

prune331.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 34.5b

regimes124.0ms

Accuracy

21.8% (3.0b remaining)

Error of 36.9b against oracle of 33.9b and baseline of 37.8b

bsearch49.0ms

Steps
ItersRangePoint
8
5.762254725775896e+165
1.8772993717287972e+170
6.301800243409153e+165

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03637
13637

end0.0ms

sample683.0ms

Algorithm
intervals
Results
342.0ms8000×body80valid
107.0ms8000×pre80true