Details

Time bar (total: 3.5m)

sample66.0ms

Algorithm
intervals
Results
36.0ms256×body80valid
11.0ms256×pre80true

simplify527.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
527.0ms
(/ (/ (* (* 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))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize54.0ms

Local error

Found 4 expressions with local error:

46.1b
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
37.8b
(/ (/ (* (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)))

rewrite251.0ms

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
91.0ms
(/ (/ (* (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))
85.0ms
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
66.0ms
(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
7.0ms
(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))

series1.0s

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))
347.0ms
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
243.0ms
(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
65.0ms
(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))

simplify34.0s

Counts
128 → 154
Calls
128 calls:
Slowest
2.4s
(/ (* (* (* (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)))))
1.8s
(/ (* (* (* (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)))))
1.8s
(/ (* (* (* (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)) (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

9 alts after pruning (9 fresh and 0 done)

Merged error: 36.0b

localize42.0ms

Local error

Found 4 expressions with local error:

38.3b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
37.4b
(/ (* (+ (+ 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)))

rewrite159.0ms

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
69.0ms
(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
58.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
22.0ms
(/ (/ (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)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
414.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
385.0ms
(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
146.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
99.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify53.1s

Counts
285 → 234
Calls
285 calls:
Slowest
966.0ms
(/ (/ (* (* (* (+ (+ 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))))
892.0ms
(/ (/ (* (* (* (+ (+ 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))))
612.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (cbrt (fma 2 i (+ alpha beta)))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
448.0ms
(/ (* (* (/ (* (+ (+ 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))))
416.0ms
(/ (* (* (* (+ (+ 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))))

prune3.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 36.0b

localize75.0ms

Local error

Found 4 expressions with local error:

38.3b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
37.4b
(/ (* (+ (+ 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
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))

rewrite121.0ms

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
50.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
45.0ms
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))
12.0ms
(/ (/ (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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
458.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
336.0ms
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))
177.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
123.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify53.6s

Counts
285 → 235
Calls
285 calls:
Slowest
1.1s
(/ (* (* (- (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)))))
966.0ms
(/ (* (* (- (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) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i)) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta)))))
495.0ms
(/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta)))))
474.0ms
(- (log (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (+ (log (+ (+ alpha beta) i)) (log i)) (log (fma 2 i (+ alpha beta)))))
460.0ms
(/ (* (* (- (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)))))

prune3.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 36.0b

localize62.0ms

Local error

Found 4 expressions with local error:

38.3b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
37.4b
(/ (* (+ (+ 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)))
0.2b
(* (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
110×*-un-lft-identity
94×add-sqr-sqrt
75×add-cube-cbrt
55×add-exp-log
37×add-cbrt-cube
24×associate-*r*
20×div-exp
17×prod-exp associate-/l*
14×distribute-lft-out
13×cbrt-undiv
10×associate-/r* div-inv
9×cbrt-unprod
7×associate-*l*
6×pow1 difference-of-squares
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg 1-exp associate-*l/ sqrt-prod distribute-lft-out-- unswap-sqr associate-/l/
2×flip3-+ flip-+
1×frac-times flip3-- pow-prod-down associate-*r/ un-div-inv *-commutative flip--
Counts
4 → 213
Calls
4 calls:
Slowest
121.0ms
(* (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
62.0ms
(/ (* (+ (+ 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)))
8.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
467.0ms
(* (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
431.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
165.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
146.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify46.4s

Counts
240 → 225
Calls
240 calls:
Slowest
1.1s
(* (/ (* (* (* (+ (+ 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 1) 1) (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
1.0s
(* (/ (* (* (* (+ (+ 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 (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))) (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
1.0s
(* (/ (* (* (* (+ (+ 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 1) 1) (* (* (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))))
814.0ms
(/ (* (* (* (+ (+ 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))))
782.0ms
(* (/ (* (* (* (+ (+ 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)))) (* (* (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0))) (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))) (/ 1 (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))))

prune3.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 36.0b

regimes288.0ms

Accuracy

20.4% (2.3b remaining)

Error of 36.4b against oracle of 34.1b and baseline of 37.0b

bsearch85.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.6s8000×body80valid
705.0ms8000×pre80true