Details

Time bar (total: 39.1s)

sample1.1s

Algorithm
intervals
Results
127.0ms56×body640valid
126.0ms45×body1280valid
78.0ms158×body80valid
25.0ms23×body320valid
19.0ms60×body80nan
7.0ms11×body160valid

simplify194.0ms

Calls
1 calls:
Slowest
193.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize44.0ms

Local error

Found 4 expressions with local error:

16.7b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.5b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.2b
(/ F (sin B))
0.1b
(/ x (tan B))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-exp-log add-cube-cbrt
6×associate-/r* unpow-prod-down add-cbrt-cube associate-*l*
5×pow1
4×associate-*r* insert-posit16 add-log-exp
3×prod-exp div-inv
2×pow-to-exp clear-num frac-2neg pow-exp
1×pow-pow tan-quot associate-*r/ associate-/r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
12.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
7.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.0ms
(/ F (sin B))
0.0ms
(/ x (tan B))

series527.0ms

Calls
4 calls:
Slowest
216.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
131.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
127.0ms
(/ x (tan B))
53.0ms
(/ F (sin B))

simplify1.9s

Calls
38 calls:
Slowest
291.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
236.0ms
(* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (* (* (/ F (sin B)) (/ F (sin B))) (/ F (sin B))))
160.0ms
(+ (* (log (+ (+ 2 (* F F)) (* 2 x))) -1/2) (log (/ F (sin B))))
143.0ms
(+ (* (log (+ (+ 2 (* F F)) (* 2 x))) -1/2) (log (/ F (sin B))))
142.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log (/ F (sin B))))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

16.7b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.5b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.2b
(/ (* x (cos B)) (sin B))
0.2b
(/ F (sin B))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
12×add-exp-log
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube
6×associate-/r* unpow-prod-down associate-*l*
5×pow1
4×associate-*r* insert-posit16 add-log-exp
3×times-frac prod-exp div-inv
2×pow-to-exp clear-num frac-2neg pow-exp
1×cbrt-undiv pow-pow div-exp associate-*r/ *-commutative cbrt-unprod associate-/l*
Calls
4 calls:
Slowest
23.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
9.0ms
(/ (* x (cos B)) (sin B))
5.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ F (sin B))

series565.0ms

Calls
4 calls:
Slowest
247.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
144.0ms
(/ (* x (cos B)) (sin B))
107.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
66.0ms
(/ F (sin B))

simplify2.1s

Calls
45 calls:
Slowest
312.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
265.0ms
(* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (* (* (/ F (sin B)) (/ F (sin B))) (/ F (sin B))))
135.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
121.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log (/ F (sin B))))
120.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

16.7b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.5b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.2b
(* (/ x (sin B)) (cos B))
0.2b
(/ F (sin B))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
12×add-exp-log
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×associate-*l*
8×add-cbrt-cube
7×pow1 associate-*r*
6×unpow-prod-down
4×prod-exp insert-posit16 add-log-exp
3×associate-/r* div-inv
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×clear-num pow-pow frac-2neg pow-prod-down associate-*l/ associate-*r/
Calls
4 calls:
Slowest
30.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
9.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
9.0ms
(* (/ x (sin B)) (cos B))
1.0ms
(/ F (sin B))

series513.0ms

Calls
4 calls:
Slowest
203.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
133.0ms
(* (/ x (sin B)) (cos B))
99.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
77.0ms
(/ F (sin B))

simplify2.3s

Calls
43 calls:
Slowest
307.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
255.0ms
(* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (* (* (/ F (sin B)) (/ F (sin B))) (/ F (sin B))))
177.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
175.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log (/ F (sin B))))
161.0ms
(+ (* (log (+ (+ 2 (* F F)) (* 2 x))) -1/2) (log (/ F (sin B))))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

16.7b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
16.7b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
5.5b
(* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (/ F (sin B)))
0.7b
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
15×add-sqr-sqrt
13×*-un-lft-identity associate-*r* add-cube-cbrt
12×pow-to-exp unpow-prod-down pow-exp sqrt-prod
11×add-cbrt-cube
10×associate-*l*
6×pow1
4×sqrt-div cbrt-unprod insert-posit16 add-log-exp
2×rem-sqrt-square flip3-+ pow1/2 pow-prod-down *-commutative flip-+
1×pow2 associate-*r/ pow-prod-up div-inv
Calls
4 calls:
Slowest
39.0ms
(* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (/ F (sin B)))
29.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
4.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
3.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

series417.0ms

Calls
4 calls:
Slowest
188.0ms
(* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (/ F (sin B)))
101.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
66.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
62.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

simplify8.3s

Calls
73 calls:
Slowest
903.0ms
(* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (* (/ F (sin B)) (/ F (sin B))) (/ F (sin B))))
772.0ms
(* (* (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (* (* (/ F (sin B)) (/ F (sin B))) (/ F (sin B))))
309.0ms
(- (sqrt 1/2) (+ (* 1/4 (/ x (sqrt 1/2))) (* 1/2 (* (pow F 2) (sqrt 1/8)))))
269.0ms
(+ (+ (* (log (sqrt (+ (+ 2 (* F F)) (* 2 x)))) -1/2) (* (log (sqrt (+ (+ 2 (* F F)) (* 2 x)))) -1/2)) (log (/ F (sin B))))
263.0ms
(+ (+ (* (log (sqrt (+ (+ 2 (* F F)) (* 2 x)))) -1/2) (log (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))) (log (/ F (sin B))))

prune1.8s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes387.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 13.4b

bsearch613.0ms

end0.0ms

sample14.4s

Algorithm
intervals
Results
6.4s1675×body1280valid
3.5s1421×body640valid
2.1s4754×body80valid
960.0ms684×body320valid
770.0ms1679×body80nan
362.0ms352×body160valid