Details

Time bar (total: 1.1m)

sample64.0ms

Algorithm
intervals
Results
38.0ms256×body80valid
11.0ms256×pre80true

simplify4.0s

Counts
1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize47.0ms

Local error

Found 4 expressions with local error:

46.0b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
36.8b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
0.0b
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

rewrite682.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×*-un-lft-identity add-cube-cbrt
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 insert-posit16 add-log-exp
3×swap-sqr
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in *-commutative
1×pow2 pow-plus flip3-- pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 204
Calls
4 calls:
Slowest
285.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
157.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
133.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
102.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
991.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
235.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))
152.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
79.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

simplify3.3s

Counts
216 → 216

prune3.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.6b

localize58.0ms

Local error

Found 4 expressions with local error:

37.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
36.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
0.0b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

rewrite1.3s

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-cbrt-cube add-exp-log
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×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r/
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 368
Calls
4 calls:
Slowest
765.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
275.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
162.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
68.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

series3.8s

Counts
4 → 12
Calls
4 calls:
Slowest
3.1s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
447.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
174.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
122.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))

simplify1.3s

Counts
380 → 380

prune6.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.6b

localize82.0ms

Local error

Found 4 expressions with local error:

37.4b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.4b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))

rewrite990.0ms

Algorithm
rewrite-expression-head
Rules
2499×times-frac
1610×add-sqr-sqrt
1254×*-un-lft-identity
938×add-cube-cbrt
921×sqrt-prod
900×associate-*r*
298×difference-of-squares
149×distribute-lft-out--
92×associate-/r/
89×add-cbrt-cube add-exp-log
76×sqrt-div
49×div-inv
46×cbrt-undiv div-exp
45×flip3-+ flip-+
42×associate-*l*
21×prod-exp cbrt-unprod
16×unswap-sqr
9×distribute-lft-out
8×pow1
4×insert-posit16 add-log-exp
3×associate-/r* associate-*r/
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
1×frac-times clear-num frac-2neg flip3-- pow-prod-down associate-*l/ *-commutative flip-- associate-/l*
Counts
4 → 1061
Calls
4 calls:
Slowest
783.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
88.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
13.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
12.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series3.5s

Counts
4 → 12
Calls
4 calls:
Slowest
3.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
119.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
96.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
72.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify6.1s

Counts
1073 → 1073

prune21.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.6b

localize47.0ms

Local error

Found 3 expressions with local error:

36.1b
(/ (* (* i i) 1/4) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
0.2b
(* (* i i) 1/4)
0.0b
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
19×add-cbrt-cube add-exp-log
15×add-sqr-sqrt pow1
10×*-un-lft-identity add-cube-cbrt
7×prod-exp cbrt-unprod
6×flip3-+ associate-*r* flip-+
4×frac-times associate-/r* times-frac associate-*l* pow-prod-down
3×cbrt-undiv swap-sqr div-exp insert-posit16 add-log-exp
2×associate-*l/ associate-*r/ associate-/r/ *-commutative difference-of-squares unswap-sqr
1×pow2 distribute-rgt-in clear-num frac-2neg distribute-lft-in pow-plus flip3-- pow-sqr pow-prod-up div-inv flip-- associate-/l*
Counts
3 → 84
Calls
3 calls:
Slowest
164.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
97.0ms
(/ (* (* i i) 1/4) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
26.0ms
(* (* i i) 1/4)

series346.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
226.0ms
(/ (* (* i i) 1/4) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
87.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
33.0ms
(* (* i i) 1/4)

simplify907.0ms

Counts
93 → 93

prune970.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 35.3b

regimes272.0ms

Accuracy

43.1% (3.4b remaining)

Error of 37.1b against oracle of 33.7b and baseline of 39.7b

bsearch103.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.4s8000×body80valid
758.0ms8000×pre80true