Details

Time bar (total: 29.7s)Debug log

sample563.0ms

Algorithm
intervals
Results
194.0ms53×body1280valid
122.0ms150×body80valid
95.0ms49×body640valid
30.0ms22×body320valid
19.0ms47×body80nan
9.0ms9×body160valid

simplify523.0ms

Calls
1 calls:
Slowest
523.0ms
(+ (- (* 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: 10.6b

localize48.0ms

Local error

Found 4 expressions with local error:

14.1b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.9b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.2b
(/ x (tan B))
0.2b
(/ F (sin B))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
10×add-cube-cbrt
10×add-exp-log
10×*-un-lft-identity
10×add-sqr-sqrt
6×associate-*l*
6×add-cbrt-cube
6×unpow-prod-down
6×associate-/r*
5×pow1
4×add-log-exp
4×associate-*r*
3×div-inv
3×prod-exp
2×pow-exp
2×frac-2neg
2×clear-num
2×pow-to-exp
1×cbrt-unprod
1×*-commutative
1×associate-/r/
1×associate-*r/
1×tan-quot
1×pow-pow
Calls
4 calls:
Slowest
25.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
6.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.0ms
(/ x (tan B))
0.0ms
(/ F (sin B))

series382.0ms

Calls
4 calls:
Slowest
133.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
124.0ms
(/ x (tan B))
76.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
48.0ms
(/ F (sin B))

simplify1.1s

Calls
38 calls:
Slowest
195.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
162.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
157.0ms
(* (* (* (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))))
81.0ms
(+ (* (log (+ (+ 2 (* F F)) (* 2 x))) -1/2) (log (/ F (sin B))))
79.0ms
(+ (* (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

localize17.0ms

Local error

Found 4 expressions with local error:

14.1b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(/ x (tan B))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
10×add-cube-cbrt
10×*-un-lft-identity
10×add-sqr-sqrt
7×add-exp-log
6×associate-*l*
6×add-cbrt-cube
6×unpow-prod-down
6×associate-/r*
5×pow1
4×add-log-exp
3×times-frac
2×div-inv
2×frac-2neg
2×clear-num
1×associate-/l*
1×*-commutative
1×associate-/r/
1×tan-quot
1×pow-exp
1×div-exp
1×pow-pow
1×cbrt-undiv
1×pow-to-exp
Calls
4 calls:
Slowest
12.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
10.0ms
(/ (* (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))

series403.0ms

Calls
4 calls:
Slowest
141.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
137.0ms
(/ x (tan B))
65.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
59.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify1.8s

Calls
38 calls:
Slowest
509.0ms
(/ (* (* (* (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)))
250.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
229.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
203.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
52.0ms
(- (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (sin B)))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

14.1b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(* (/ x (sin B)) (cos B))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
11×add-cube-cbrt
11×*-un-lft-identity
11×add-sqr-sqrt
10×associate-*l*
9×add-exp-log
8×add-cbrt-cube
7×pow1
6×unpow-prod-down
4×add-log-exp
3×associate-*r*
3×times-frac
3×associate-/r*
2×div-inv
2×*-commutative
1×associate-/l*
1×cbrt-unprod
1×prod-exp
1×pow-exp
1×associate-*l/
1×pow-prod-down
1×div-exp
1×frac-2neg
1×pow-pow
1×clear-num
1×cbrt-undiv
1×pow-to-exp
Calls
4 calls:
Slowest
11.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
10.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
8.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
4.0ms
(* (/ x (sin B)) (cos B))

series370.0ms

Calls
4 calls:
Slowest
136.0ms
(* (/ x (sin B)) (cos B))
129.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
61.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
44.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify1.9s

Calls
43 calls:
Slowest
554.0ms
(/ (* (* (* (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)))
230.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
201.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
169.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
151.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

14.1b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.3b
(* x (* (/ 1 (sin B)) (cos B)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cube-cbrt
9×*-un-lft-identity
9×add-sqr-sqrt
7×add-exp-log
6×associate-*l*
6×add-cbrt-cube
6×unpow-prod-down
5×pow1
4×add-log-exp
3×times-frac
3×associate-/r*
2×*-commutative
1×associate-/l*
1×div-inv
1×associate-*r/
1×pow-exp
1×associate-*l/
1×associate-*r*
1×div-exp
1×frac-2neg
1×pow-pow
1×clear-num
1×cbrt-undiv
1×pow-to-exp
Calls
4 calls:
Slowest
20.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
18.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
8.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
8.0ms
(* x (* (/ 1 (sin B)) (cos B)))

series404.0ms

Calls
4 calls:
Slowest
167.0ms
(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
133.0ms
(* x (* (/ 1 (sin B)) (cos B)))
70.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
35.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify1.5s

Calls
36 calls:
Slowest
436.0ms
(/ (* (* (* (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)))
214.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
213.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
174.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
46.0ms
(- (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (sin B)))

prune973.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes382.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.2b

bsearch768.0ms

end0.0ms

sample14.8s

Algorithm
intervals
Results
6.0s1672×body1280valid
3.7s1413×body640valid
2.8s4755×body80valid
958.0ms668×body320valid
685.0ms1534×body80nan
415.0ms372×body160valid