Details

Time bar (total: 32.2s)

sample923.0ms

Algorithm
intervals
Results
234.0ms61×body1280valid
76.0ms41×body640valid
63.0ms152×body80valid
25.0ms20×body320valid
18.0ms46×body80nan
9.0ms10×body160valid

simplify214.0ms

Calls
1 calls:
Slowest
213.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize61.0ms

Local error

Found 4 expressions with local error:

16.7b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
6.5b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.2b
(/ x (tan B))
0.1b
(/ F (sin B))

rewrite26.0ms

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
14.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
6.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ F (sin B))
1.0ms
(/ x (tan B))

series639.0ms

Calls
4 calls:
Slowest
245.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
166.0ms
(/ x (tan B))
133.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
94.0ms
(/ F (sin B))

simplify2.0s

Calls
38 calls:
Slowest
279.0ms
(* (* (* (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))))
275.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
140.0ms
(+ (* (log (+ (+ 2 (* F F)) (* 2 x))) -1/2) (log (/ F (sin B))))
139.0ms
(+ (* (log (+ (+ 2 (* F F)) (* 2 x))) -1/2) (log (/ F (sin B))))
131.0ms
(+ (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

localize18.0ms

Local error

Found 4 expressions with local error:

16.7b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
6.5b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.2b
(* (/ x (sin B)) (cos B))
0.1b
(/ F (sin B))

rewrite47.0ms

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
26.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
10.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
9.0ms
(* (/ x (sin B)) (cos B))
1.0ms
(/ F (sin B))

series538.0ms

Calls
4 calls:
Slowest
221.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
154.0ms
(* (/ x (sin B)) (cos B))
103.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
60.0ms
(/ F (sin B))

simplify2.3s

Calls
43 calls:
Slowest
330.0ms
(* (* (* (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))))
289.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
198.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
144.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log (/ F (sin B))))
136.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

16.7b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
6.5b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.2b
(/ (* x (cos B)) (sin B))
0.1b
(/ F (sin B))

rewrite50.0ms

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
26.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
11.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms
(/ (* x (cos B)) (sin B))
1.0ms
(/ F (sin B))

series557.0ms

Calls
4 calls:
Slowest
222.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
173.0ms
(/ (* x (cos B)) (sin B))
104.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
57.0ms
(/ F (sin B))

simplify2.3s

Calls
45 calls:
Slowest
352.0ms
(* (* (* (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))))
270.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
200.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
156.0ms
(+ (* (log (+ (+ 2 (* F F)) (* 2 x))) -1/2) (log (/ F (sin B))))
137.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log (/ F (sin B))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

16.7b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
6.5b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.3b
(/ 1 (/ (tan B) x))
0.1b
(/ F (sin B))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
11×add-exp-log
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-/r*
6×pow1 unpow-prod-down add-cbrt-cube associate-*l*
4×associate-*r* insert-posit16 div-inv add-log-exp
3×prod-exp
2×pow-to-exp clear-num frac-2neg pow-exp
1×rec-exp pow-pow associate-*r/ associate-/r/ *-commutative cbrt-unprod pow-flip inv-pow
Calls
4 calls:
Slowest
13.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
5.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ 1 (/ (tan B) x))
1.0ms
(/ F (sin B))

series514.0ms

Calls
4 calls:
Slowest
201.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
148.0ms
(/ 1 (/ (tan B) x))
93.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
72.0ms
(/ F (sin B))

simplify2.1s

Calls
39 calls:
Slowest
305.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
263.0ms
(* (* (* (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))))
146.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log (/ F (sin B))))
138.0ms
(+ (* (log (+ (+ 2 (* F F)) (* 2 x))) -1/2) (log (/ F (sin B))))
137.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes269.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.7b

bsearch646.0ms

end0.0ms

sample14.2s

Algorithm
intervals
Results
4.8s1665×body1280valid
3.4s4759×body80valid
3.1s1415×body640valid
1.5s696×body320valid
737.0ms1631×body80nan
370.0ms345×body160valid