Details

Time bar (total: 2.4m)

sample76.0ms

Algorithm
intervals
Results
47.0ms256×body80valid
12.0ms256×pre80true

simplify480.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
479.0ms
(/ (/ (* (* 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))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.2b

localize54.0ms

Local error

Found 4 expressions with local error:

45.6b
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
38.2b
(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))
0.1b
(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
0.0b
(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
28×add-sqr-sqrt
26×times-frac
22×prod-exp cbrt-unprod
20×*-un-lft-identity add-cube-cbrt
19×cbrt-undiv div-exp
16×pow1
7×div-inv
6×associate-*l* associate-/l* difference-of-squares
5×associate-/r*
4×expm1-log1p-u associate-*r* pow-prod-down associate-*l/ associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-/l/
2×clear-num frac-2neg flip3-+ associate-/r/ *-commutative flip-+ fma-udef
1×pow2 distribute-rgt-in distribute-lft-in pow-plus flip3-- pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 142
Calls
4 calls:
Slowest
94.0ms
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
88.0ms
(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))
67.0ms
(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
6.0ms
(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
426.0ms
(/ (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))
370.0ms
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
166.0ms
(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
96.0ms
(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))

simplify32.9s

Counts
128 → 154
Calls
128 calls:
Slowest
2.1s
(/ (* (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))))
1.7s
(/ (* (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta)))))
1.5s
(/ (* (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma (+ (+ alpha beta) i) i (* beta alpha))) (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i))) (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta)))))
1.5s
(/ (* (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma (+ (+ alpha beta) i) i (* beta alpha))) (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i))) (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))))
1.3s
(* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.8b

localize64.0ms

Local error

Found 4 expressions with local error:

35.8b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
35.6b
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
0.3b
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
0.3b
(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
172×times-frac
129×*-un-lft-identity
117×add-sqr-sqrt
85×add-cube-cbrt
25×add-cbrt-cube add-exp-log
24×associate-/l*
16×associate-/r* div-inv difference-of-squares
14×distribute-lft-out
11×cbrt-undiv div-exp
8×sqrt-prod distribute-lft-out--
4×expm1-log1p-u pow1 clear-num frac-2neg associate-/r/ insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×flip3-+ associate-*l/ prod-exp cbrt-unprod flip-+
1×flip3-- flip--
Counts
4 → 222
Calls
4 calls:
Slowest
67.0ms
(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
40.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
25.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
4.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
462.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
407.0ms
(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
183.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
126.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify52.4s

Counts
285 → 234
Calls
285 calls:
Slowest
929.0ms
(/ (/ (* (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i)) (* (* i i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta)))) (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
887.0ms
(/ (/ (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta)))) (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
823.0ms
(/ (* (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i)) (* (* i i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))
808.0ms
(/ (* (* (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))) (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
425.0ms
(/ (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))

prune3.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 35.8b

localize94.0ms

Local error

Found 4 expressions with local error:

35.8b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
35.6b
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
35.6b
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
0.3b
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
112×times-frac
93×*-un-lft-identity
65×add-sqr-sqrt add-cube-cbrt
21×add-cbrt-cube add-exp-log
18×associate-/l*
14×distribute-lft-out
13×associate-/r*
9×div-inv
8×cbrt-undiv div-exp
5×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×prod-exp associate-/r/ cbrt-unprod
Counts
4 → 171
Calls
4 calls:
Slowest
53.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
40.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
13.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
9.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series825.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
411.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
151.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
151.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
112.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify33.3s

Counts
196 → 183
Calls
196 calls:
Slowest
692.0ms
(/ (* (* (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))) (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))) (* (* (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))))
484.0ms
(/ (* (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i)) (* (* i i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))
445.0ms
(/ (* (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i)) (* (* i i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))
430.0ms
(/ (/ (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma (+ (+ alpha beta) i) i (* beta alpha))) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta)))) (* (* (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))))
422.0ms
(/ (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))

prune3.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 35.8b

localize110.0ms

Local error

Found 4 expressions with local error:

35.7b
(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
35.7b
(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
35.6b
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
35.6b
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
6×pow1 associate-/r* times-frac sqrt-prod
4×expm1-log1p-u cbrt-undiv div-exp associate-*l/ insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 prod-exp cbrt-unprod flip-+ div-inv associate-/l*
Counts
4 → 84
Calls
4 calls:
Slowest
53.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
37.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
2.0ms
(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
1.0ms
(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
127.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
85.0ms
(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))
81.0ms
(sqrt (fma (+ (+ alpha beta) i) i (* beta alpha)))

simplify5.4s

Counts
54 → 96
Calls
54 calls:
Slowest
552.0ms
(* (+ (pow (+ alpha beta) 3) (pow i 3)) i)
451.0ms
(/ (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))
434.0ms
(/ (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))
419.0ms
(/ (* (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i)) (* (* i i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))
405.0ms
(/ (* (* (* (+ (+ alpha beta) i) (+ (+ alpha beta) i)) (+ (+ alpha beta) i)) (* (* i i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.8b

regimes226.0ms

Accuracy

0% (2.7b remaining)

Error of 36.0b against oracle of 33.4b and baseline of 36.0b

bsearch6.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.4s8000×body80valid
392.0ms8000×pre80true