Details

Time bar (total: 31.6s)

sample1.0s

Algorithm
intervals
Results
322.0ms57×body1280valid
148.0ms44×body640valid
147.0ms147×body80valid
128.0ms24×body320valid
20.0ms34×body80nan
13.0ms11×body160valid

simplify588.0ms

Calls
1 calls:
Slowest
587.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.0b

localize40.0ms

Local error

Found 4 expressions with local error:

17.9b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
6.9b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.1b
(/ x (tan B))
0.1b
(/ F (sin B))

rewrite24.0ms

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)))
7.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ x (tan B))
0.0ms
(/ F (sin B))

series417.0ms

Calls
4 calls:
Slowest
144.0ms
(/ x (tan B))
130.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
82.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
60.0ms
(/ F (sin B))

simplify1.8s

Calls
38 calls:
Slowest
293.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
207.0ms
(* (* (* (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))))
124.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log (/ F (sin B))))
119.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
108.0ms
(+ (* (log (+ (+ 2 (* F F)) (* 2 x))) -1/2) (log (/ F (sin B))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

17.9b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.2b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b
(/ x (tan B))

rewrite43.0ms

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
22.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
12.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
9.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ x (tan B))

series360.0ms

Calls
4 calls:
Slowest
127.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
127.0ms
(/ x (tan B))
59.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
46.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify2.3s

Calls
38 calls:
Slowest
379.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
335.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
197.0ms
(/ (* (* (* (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)))
125.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
107.0ms
(- (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (sin B)))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

17.9b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b
(/ 1 (/ (tan B) x))
0.2b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-exp-log
7×associate-/r*
6×pow1 unpow-prod-down add-cbrt-cube associate-*l*
4×insert-posit16 add-log-exp
3×times-frac div-inv
2×clear-num frac-2neg
1×pow-to-exp cbrt-undiv rec-exp pow-pow div-exp pow-exp associate-/r/ *-commutative pow-flip associate-/l* inv-pow
Calls
4 calls:
Slowest
22.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
15.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
7.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ 1 (/ (tan B) x))

series361.0ms

Calls
4 calls:
Slowest
152.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
103.0ms
(/ 1 (/ (tan B) x))
58.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
48.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify2.3s

Calls
39 calls:
Slowest
369.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
318.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
254.0ms
(/ (* (* (* (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)))
137.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
106.0ms
(- (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (sin B)))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

17.9b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b
(* (/ 1 (tan B)) x)
0.2b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
11×associate-*l*
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×add-exp-log
6×unpow-prod-down add-cbrt-cube
5×pow1
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 associate-*l/ pow-exp tan-quot associate-/r/ associate-/l*
Calls
4 calls:
Slowest
12.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
11.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
9.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.0ms
(* (/ 1 (tan B)) x)

series356.0ms

Calls
4 calls:
Slowest
174.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
71.0ms
(* (/ 1 (tan B)) x)
57.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
53.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify2.4s

Calls
38 calls:
Slowest
393.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
286.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
229.0ms
(/ (* (* (* (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)))
158.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
128.0ms
(- (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (sin B)))

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes279.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 11.3b

bsearch573.0ms

end0.0ms

sample14.2s

Algorithm
intervals
Results
5.1s1678×body1280valid
3.4s1433×body640valid
2.5s4749×body80valid
1.5s656×body320valid
731.0ms359×body160valid
676.0ms1631×body80nan