Details

Time bar (total: 3.4m)

sample87.0ms

Algorithm
intervals
Results
52.0ms256×body80valid
12.0ms256×pre80true

simplify548.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
548.0ms
(/ (/ (* (* 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))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.2b

localize71.0ms

Local error

Found 4 expressions with local error:

48.4b
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
38.7b
(/ (/ (* (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)))

rewrite293.0ms

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
127.0ms
(/ (/ (* (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))
97.0ms
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
59.0ms
(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
7.0ms
(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
861.0ms
(/ (/ (* (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))
333.0ms
(/ (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))
215.0ms
(* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))
99.0ms
(* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))

simplify33.1s

Counts
128 → 154
Calls
128 calls:
Slowest
2.0s
(/ (* (* (* (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)) (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)))))
1.7s
(/ (* (* (* (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)))))
1.4s
(/ (* (* (* (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)))

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 36.0b

localize47.0ms

Local error

Found 4 expressions with local error:

37.3b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
37.1b
(/ (* (+ (+ 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)))

rewrite94.0ms

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
44.0ms
(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
29.0ms
(/ (* (+ (+ 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)))
5.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
461.0ms
(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))
436.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
185.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
106.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify52.8s

Counts
285 → 234
Calls
285 calls:
Slowest
928.0ms
(/ (/ (* (* (* (+ (+ 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))))
868.0ms
(/ (/ (* (* (* (+ (+ 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))))
698.0ms
(/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (cbrt (- (fma 2 i (+ alpha beta)) (sqrt 1.0))))
626.0ms
(/ (/ (* (cbrt (fma (+ (+ alpha beta) i) i (* beta alpha))) (cbrt (fma (+ (+ alpha beta) i) i (* beta alpha)))) (sqrt (fma 2 i (+ alpha beta)))) 1)
476.0ms
(/ (* (* (* (+ (+ 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))))

prune3.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 36.0b

localize49.0ms

Local error

Found 4 expressions with local error:

37.3b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
37.1b
(/ (* (+ (+ 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))))

rewrite107.0ms

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
49.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))
29.0ms
(/ (- (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)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
396.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
313.0ms
(/ (- (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)))
126.0ms
(/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta)))

simplify54.0s

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) 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)))))
827.0ms
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))))
621.0ms
(/ (/ (sqrt (fma (+ (+ alpha beta) i) i (* beta alpha))) 1) (sqrt (+ (fma 2 i (+ alpha beta)) (sqrt 1.0))))
510.0ms
(/ (* (* (* (+ (+ 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))))

prune3.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 36.0b

localize64.0ms

Local error

Found 4 expressions with local error:

37.3b
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (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) 1) (/ i (fma 2 i (+ alpha beta)))))
0.3b
(/ i (fma 2 i (+ alpha beta)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
121×times-frac
103×*-un-lft-identity
79×add-sqr-sqrt
71×add-cube-cbrt
38×add-exp-log
31×add-cbrt-cube
25×associate-/l*
19×div-exp
14×cbrt-undiv distribute-lft-out
11×associate-/r*
9×div-inv
6×prod-exp
5×associate-/r/
4×expm1-log1p-u pow1 clear-num frac-2neg cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp difference-of-squares
3×associate-/l/
2×1-exp sqrt-prod distribute-lft-out--
1×frac-times flip3-+ flip3-- div-sub associate-*l/ associate-*r/ flip-+ flip--
Counts
4 → 193
Calls
4 calls:
Slowest
39.0ms
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (* (/ (+ (+ alpha beta) i) 1) (/ 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)))
8.0ms
(/ i (fma 2 i (+ alpha beta)))
4.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
412.0ms
(/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))
307.0ms
(/ (- (fma 2 i (+ alpha beta)) (sqrt 1.0)) (* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta)))))
180.0ms
(/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta)))
153.0ms
(/ i (fma 2 i (+ alpha beta)))

simplify41.0s

Counts
223 → 205
Calls
223 calls:
Slowest
988.0ms
(/ (* (* (- (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) (+ (+ alpha beta) i)) (+ (+ alpha beta) i)) (* (* 1 1) 1)) (/ (* (* i i) i) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))))
964.0ms
(/ (* (* (- (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) 1) (/ (+ (+ alpha beta) i) 1)) (/ (+ (+ alpha beta) i) 1)) (/ (* (* i i) i) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))))
803.0ms
(/ (* (* (- (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) 1) (/ i (fma 2 i (+ alpha beta)))) (* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta))))) (* (/ (+ (+ alpha beta) i) 1) (/ i (fma 2 i (+ alpha beta))))))
655.0ms
(/ (* (* (- (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) 1) (/ (+ (+ alpha beta) i) 1)) (/ (+ (+ alpha beta) i) 1)) (* (* (/ i (fma 2 i (+ alpha beta))) (/ i (fma 2 i (+ alpha beta)))) (/ i (fma 2 i (+ alpha beta))))))
602.0ms
(/ (* (* (- (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) (+ (+ alpha beta) i)) (+ (+ alpha beta) i)) (* (* 1 1) 1)) (* (* (/ i (fma 2 i (+ alpha beta))) (/ i (fma 2 i (+ alpha beta)))) (/ i (fma 2 i (+ alpha beta))))))

prune3.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.9b

regimes347.0ms

Accuracy

39.4% (9.6b remaining)

Error of 11.7b against oracle of 2.1b and baseline of 18.0b

bsearch207.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.9s8000×body80valid
470.0ms8000×pre80true