Details

Time bar (total: 33.5s)

sample830.0ms

Algorithm
intervals
Results
573.0ms48×body1280valid
58.0ms41×body640valid
54.0ms171×body80valid
29.0ms28×body320valid
18.0ms60×body80nan
4.0ms5×body160valid

simplify233.0ms

Calls
1 calls:
Slowest
232.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize61.0ms

Local error

Found 4 expressions with local error:

18.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
9.0b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.1b
(/ 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
15.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
6.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ x (tan B))
1.0ms
(/ F (sin B))

series446.0ms

Calls
4 calls:
Slowest
153.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
115.0ms
(/ x (tan B))
111.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
67.0ms
(/ F (sin B))

simplify1.9s

Calls
38 calls:
Slowest
295.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
257.0ms
(* (* (* (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))))
136.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log (/ F (sin B))))
134.0ms
(- (/ (* 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 (+ (+ 2 (* F F)) (* 2 x))) -1/2) (log (/ F (sin B))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

18.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.1b
(/ x (tan B))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×add-exp-log
6×associate-/r* unpow-prod-down add-cbrt-cube associate-*l*
5×pow1
4×insert-posit16 add-log-exp
3×times-frac
2×clear-num frac-2neg div-inv
1×pow-to-exp cbrt-undiv pow-pow div-exp pow-exp tan-quot associate-/r/ *-commutative associate-/l*
Calls
4 calls:
Slowest
11.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
11.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
5.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ x (tan B))

series362.0ms

Calls
4 calls:
Slowest
145.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
114.0ms
(/ x (tan B))
53.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
51.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify2.3s

Calls
38 calls:
Slowest
399.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
277.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
184.0ms
(/ (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (* (* (sin B) (sin B)) (sin B)))
142.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
136.0ms
(- (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (sin B)))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

18.3b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(* x (/ 1 (tan B)))
0.2b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×add-exp-log
6×unpow-prod-down add-cbrt-cube associate-*l*
5×pow1 associate-*r*
4×insert-posit16 add-log-exp
3×associate-/r* times-frac
2×*-commutative div-inv
1×pow-to-exp cbrt-undiv clear-num pow-pow frac-2neg div-exp pow-exp tan-quot associate-*r/ associate-/r/ un-div-inv associate-/l*
Calls
4 calls:
Slowest
26.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
22.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
10.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
2.0ms
(* x (/ 1 (tan B)))

series410.0ms

Calls
4 calls:
Slowest
138.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
129.0ms
(* x (/ 1 (tan B)))
81.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
63.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify2.3s

Calls
41 calls:
Slowest
398.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
288.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
261.0ms
(/ (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (* (* (sin B) (sin B)) (sin B)))
127.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
104.0ms
(- (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (sin B)))

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

18.3b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
18.3b
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
0.6b
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
0.3b
(* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F)

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log
14×add-sqr-sqrt
12×unpow-prod-down *-un-lft-identity add-cube-cbrt sqrt-prod
10×associate-*l*
9×associate-*r* prod-exp
6×pow-to-exp add-cbrt-cube pow-exp
4×pow1 sqrt-div insert-posit16 add-log-exp
2×rem-sqrt-square flip3-+ pow1/2 *-commutative flip-+
1×pow2 pow-prod-down pow-prod-up cbrt-unprod
Calls
4 calls:
Slowest
58.0ms
(* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F)
22.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
7.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
7.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

series133.0ms

Calls
4 calls:
Slowest
47.0ms
(* (* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2)) F)
31.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))
30.0ms
(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2))
25.0ms
(sqrt (+ (+ 2 (* F F)) (* 2 x)))

simplify4.2s

Calls
55 calls:
Slowest
323.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
307.0ms
(- (sqrt 1/2) (+ (* 1/4 (/ x (sqrt 1/2))) (* 1/2 (* (pow F 2) (sqrt 1/8)))))
217.0ms
(sqrt (- (* (+ 2 (* F F)) (+ 2 (* F F))) (* (* 2 x) (* 2 x))))
213.0ms
(sqrt (- (* (+ 2 (* F F)) (+ 2 (* F F))) (* (* 2 x) (* 2 x))))
208.0ms
(sqrt (+ (pow (+ 2 (* F F)) 3) (pow (* 2 x) 3)))

prune1.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes345.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 11.1b

bsearch532.0ms

end0.0ms

sample14.1s

Algorithm
intervals
Results
5.7s1633×body1280valid
3.4s1421×body640valid
2.8s4788×body80valid
1.0s694×body320valid
661.0ms1621×body80nan
331.0ms325×body160valid