Details

Time bar (total: 1.8m)

sample100.0ms

Algorithm
intervals
Results
24.0ms187×body80valid
23.0ms256×pre80true
14.0ms26×body640valid
13.0ms19×body1280valid
6.0ms16×body320valid
2.0ms8×body160valid

simplify111.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
111.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.3b

localize40.0ms

Local error

Found 4 expressions with local error:

20.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.7b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

rewrite879.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
87×*-un-lft-identity
45×add-sqr-sqrt fma-def add-cube-cbrt
24×associate-/r/
21×distribute-lft-out
18×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
15×add-log-exp
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* sum-log div-exp
4×expm1-log1p-u frac-times pow1 insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Counts
4 → 183
Calls
4 calls:
Slowest
537.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
170.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
111.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)
56.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series843.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
378.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
316.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
109.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
40.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

simplify34.2s

Counts
179 → 195
Calls
179 calls:
Slowest
783.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
726.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
703.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
684.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
660.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i)))) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.2b

localize62.0ms

Local error

Found 4 expressions with local error:

2.7b
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.0b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
0.0b
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
0.0b
(+ 2.0 (fma 2 i (+ beta alpha)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
33×add-sqr-sqrt
31×times-frac
25×add-cube-cbrt
11×distribute-lft-out
9×associate-/l*
8×add-cbrt-cube add-exp-log
7×associate-/r*
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out-- difference-of-squares associate-/l/
3×fma-def flip3-+ flip-+
2×cbrt-undiv clear-num frac-2neg div-exp associate-/r/ fma-udef div-inv
1×+-commutative associate-+r+ sum-log flip3-- div-sub flip--
Counts
4 → 114
Calls
4 calls:
Slowest
25.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
17.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
8.0ms
(+ 2.0 (fma 2 i (+ beta alpha)))
1.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series461.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
114.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
92.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
41.0ms
(+ 2.0 (fma 2 i (+ beta alpha)))

simplify7.2s

Counts
102 → 126
Calls
102 calls:
Slowest
458.0ms
(+ (* 2.0 2.0) (- (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (* 2.0 (fma 2 i (+ beta alpha)))))
398.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha))))
377.0ms
(- (log (- beta alpha)) (log (fma 2 i (+ beta alpha))))
291.0ms
(/ (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (* (* (+ 2.0 (fma 2 i (+ beta alpha))) (+ 2.0 (fma 2 i (+ beta alpha)))) (+ 2.0 (fma 2 i (+ beta alpha)))))
285.0ms
(* (exp 2.0) (exp (fma 2 i (+ beta alpha))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.2b

localize53.0ms

Local error

Found 4 expressions with local error:

2.7b
(fma (/ (+ beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.0b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
0.0b
(/ (+ beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
0.0b
(fma 2 i (+ beta alpha))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
32×add-sqr-sqrt
31×times-frac
24×add-cube-cbrt
10×distribute-lft-out
9×associate-/l*
8×add-cbrt-cube add-exp-log
7×associate-/r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares associate-/l/
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+ fma-udef div-inv
1×flip3-- div-sub flip--
Counts
4 → 106
Calls
4 calls:
Slowest
26.0ms
(/ (+ beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
12.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
1.0ms
(fma 2 i (+ beta alpha))
0.0ms
(fma (/ (+ beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series387.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(fma (/ (+ beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0)) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
101.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
87.0ms
(/ (+ beta alpha) (+ (fma 2 i (+ beta alpha)) 2.0))
33.0ms
(fma 2 i (+ beta alpha))

simplify6.2s

Counts
97 → 118
Calls
97 calls:
Slowest
521.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (fma 2 i (+ beta alpha))))
293.0ms
(+ (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))) (- (* 2.0 2.0) (* (fma 2 i (+ beta alpha)) 2.0)))
278.0ms
(/ (* (* (+ beta alpha) (+ beta alpha)) (+ beta alpha)) (* (* (+ (fma 2 i (+ beta alpha)) 2.0) (+ (fma 2 i (+ beta alpha)) 2.0)) (+ (fma 2 i (+ beta alpha)) 2.0)))
275.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
256.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.2b

localize48.0ms

Local error

Found 4 expressions with local error:

15.9b
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

rewrite370.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
166×*-un-lft-identity
120×add-sqr-sqrt
82×add-cube-cbrt
26×associate-/l*
23×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
13×add-log-exp
11×add-cbrt-cube add-exp-log
8×flip3-+ flip-+
7×associate-/r* div-inv
6×sum-log
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×fma-def div-sub associate-/l/
2×clear-num frac-2neg
1×+-commutative associate-+l+ flip3-- fma-udef flip--
Counts
4 → 205
Calls
4 calls:
Slowest
184.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
131.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)
47.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
1.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series649.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
266.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
244.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
102.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
37.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

simplify42.7s

Counts
262 → 217
Calls
262 calls:
Slowest
896.0ms
(/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
820.0ms
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
796.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
787.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
755.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune3.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.2b

regimes586.0ms

Accuracy

10.1% (5.6b remaining)

Error of 11.6b against oracle of 6.0b and baseline of 12.2b

bsearch169.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.4s6373×body80valid
457.0ms600×body640valid
409.0ms8000×pre80true
390.0ms485×body1280valid
153.0ms357×body320valid
76.0ms185×body160valid