Details

Time bar (total: 3.2m)

sample92.0ms

Algorithm
intervals
Results
53.0ms256×body80valid
15.0ms256×pre80true

simplify518.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
518.0ms
(/ (/ (* (* 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))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize55.0ms

Local error

Found 4 expressions with local error:

47.8b
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
35.8b
(/ (/ (* (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)))

rewrite323.0ms

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
122.0ms
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
114.0ms
(/ (/ (* (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))
72.0ms
(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
11.0ms
(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
386.0ms
(/ (/ (* (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))
360.0ms
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
228.0ms
(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
97.0ms
(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))

simplify32.9s

Counts
128 → 154
Calls
128 calls:
Slowest
2.2s
(/ (* (* (* (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)))))
1.6s
(/ (* (* (* (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)))))
1.4s
(/ (* (* (* (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 (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))) (/ (* (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) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)))

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 32.6b

localize58.0ms

Local error

Found 4 expressions with local error:

34.5b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
34.0b
(/ (* (+ (+ 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)))

rewrite131.0ms

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
54.0ms
(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
46.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
20.0ms
(/ (/ (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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
417.0ms
(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
380.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
140.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
127.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify53.3s

Counts
285 → 234
Calls
285 calls:
Slowest
923.0ms
(/ (/ (* (* (* (+ (+ 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))))
904.0ms
(/ (/ (* (* (* (+ (+ 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))))
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))))
498.0ms
(/ (* (cbrt (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))) (cbrt (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))) 1)
468.0ms
(/ (* (* (* (+ (+ 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

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.6b

localize65.0ms

Local error

Found 4 expressions with local error:

34.5b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
34.0b
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
0.3b
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (* (+ (+ 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)))

rewrite90.0ms

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
23×associate-/l*
17×associate-/r*
16×div-inv difference-of-squares
14×distribute-lft-out
11×cbrt-undiv div-exp
8×sqrt-prod distribute-lft-out--
5×associate-/l/
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r/
2×flip3-+ associate-*l/ prod-exp cbrt-unprod flip-+
1×flip3-- div-sub flip--
Counts
4 → 223
Calls
4 calls:
Slowest
33.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
25.0ms
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))
21.0ms
(/ (/ (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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
426.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
331.0ms
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))
173.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
131.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify53.7s

Counts
285 → 235
Calls
285 calls:
Slowest
1.0s
(/ (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (* (* (+ (+ 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)))))
1.0s
(/ (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (* (* (+ (+ 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)))))
632.0ms
(/ (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) 1)
605.0ms
(/ (cbrt (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (cbrt (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))))
478.0ms
(/ (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (* (* (/ (* (+ (+ 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)))))

prune3.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 32.6b

localize79.0ms

Local error

Found 4 expressions with local error:

34.5b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
34.5b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
34.0b
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
0.3b
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
76×add-sqr-sqrt
60×*-un-lft-identity
44×add-cube-cbrt
22×add-cbrt-cube add-exp-log
16×associate-/r* difference-of-squares
13×associate-/l*
11×div-inv
9×cbrt-undiv div-exp
8×sqrt-prod distribute-lft-out--
4×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×associate-*l/ prod-exp cbrt-unprod
1×flip3-+ flip3-- div-sub associate-/r/ flip-+ flip--
Counts
4 → 164
Calls
4 calls:
Slowest
54.0ms
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))
32.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
4.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
4.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series732.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
291.0ms
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))
163.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
152.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
125.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify31.3s

Counts
183 → 176
Calls
183 calls:
Slowest
1.0s
(/ (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (* (* (+ (+ 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)))))
1.0s
(/ (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ (* (* (* (+ (+ 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)))))
664.0ms
(/ (cbrt (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ i (fma 2 i (+ alpha beta))))
475.0ms
(/ (* (* (* (+ (+ 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))))
473.0ms
(/ (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (* (* (/ (* (+ (+ 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)))))

prune3.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 32.6b

regimes241.0ms

Accuracy

48.2% (1.4b remaining)

Error of 35.3b against oracle of 33.8b and baseline of 36.6b

bsearch97.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.9s8000×body80valid
376.0ms8000×pre80true