Details

Time bar (total: 36.1s)

sample1.3s

Algorithm
intervals
Results
574.0ms140×body80valid
357.0ms63×body1280valid
93.0ms43×body640valid
33.0ms21×body320valid
21.0ms44×body80nan
12.0ms11×body160valid

simplify162.0ms

Calls
1 calls:
Slowest
161.0ms
(+ (- (* 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: 12.8b

localize47.0ms

Local error

Found 4 expressions with local error:

15.9b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
6.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.2b
(/ x (tan B))
0.2b
(/ 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
13.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
8.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ x (tan B))
1.0ms
(/ F (sin B))

series414.0ms

Calls
4 calls:
Slowest
145.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
121.0ms
(/ x (tan B))
88.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
60.0ms
(/ F (sin B))

simplify2.1s

Calls
38 calls:
Slowest
304.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
240.0ms
(* (* (* (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))))
167.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))
135.0ms
(+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log (/ F (sin B))))
129.0ms
(+ (* (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

localize13.0ms

Local error

Found 4 expressions with local error:

15.9b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
0.2b
(/ x (tan B))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-exp-log add-cube-cbrt
7×pow1 associate-*l*
6×unpow-prod-down add-cbrt-cube
4×associate-*r* insert-posit16 add-log-exp
3×associate-/r*
2×prod-exp *-commutative div-inv
1×pow-to-exp rec-exp clear-num pow-pow frac-2neg pow-prod-down pow-exp tan-quot associate-*r/ associate-/r/ un-div-inv cbrt-unprod
Calls
4 calls:
Slowest
28.0ms
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
13.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
5.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ x (tan B))

series359.0ms

Calls
4 calls:
Slowest
135.0ms
(/ x (tan B))
125.0ms
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
58.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
41.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify3.1s

Calls
37 calls:
Slowest
686.0ms
(* (* (* (* (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)) (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))))
441.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
351.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
216.0ms
(+ (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (/ 1 (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))))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

15.9b
(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)
0.2b
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
10×add-exp-log
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1
7×associate-*l*
6×unpow-prod-down add-cbrt-cube
4×associate-/r* associate-*r* insert-posit16 add-log-exp
3×div-inv
2×rec-exp prod-exp *-commutative
1×pow-to-exp clear-num pow-pow frac-2neg pow-prod-down pow-exp associate-*r/ associate-/r/ un-div-inv cbrt-unprod pow-flip inv-pow
Calls
4 calls:
Slowest
31.0ms
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
11.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
7.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
1.0ms
(/ 1 (/ (tan B) x))

series342.0ms

Calls
4 calls:
Slowest
127.0ms
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
95.0ms
(/ 1 (/ (tan B) x))
83.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
37.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify3.1s

Calls
38 calls:
Slowest
770.0ms
(* (* (* (* (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)) (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))))
475.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
312.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
178.0ms
(+ (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (/ 1 (sin B))))
154.0ms
(- (/ (* F (sqrt 1/2)) B) (+ (* 1/2 (/ (* (pow F 3) (sqrt 1/8)) B)) (* 1/4 (/ (* x F) (* B (sqrt 1/2))))))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

15.9b
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b
(/ (/ 1 (tan B)) (/ 1 x))
0.2b
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
20×times-frac
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×add-exp-log div-inv
8×add-cbrt-cube
7×pow1 associate-*l*
6×unpow-prod-down associate-/r/
5×tan-quot associate-/l*
4×associate-/r* associate-*r* insert-posit16 add-log-exp
2×rec-exp div-exp prod-exp *-commutative
1×pow-to-exp cbrt-undiv clear-num pow-pow frac-2neg pow-prod-down pow-exp associate-*r/ un-div-inv cbrt-unprod associate-/l/
Calls
4 calls:
Slowest
38.0ms
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
23.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
10.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
9.0ms
(/ (/ 1 (tan B)) (/ 1 x))

series323.0ms

Calls
4 calls:
Slowest
136.0ms
(* (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (/ 1 (sin B)))
81.0ms
(/ (/ 1 (tan B)) (/ 1 x))
55.0ms
(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
50.0ms
(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify5.0s

Calls
83 calls:
Slowest
1.0s
(/ (* (* (/ 1 (tan B)) (/ 1 (tan B))) (/ 1 (tan B))) (* (* (/ 1 x) (/ 1 x)) (/ 1 x)))
644.0ms
(* (* (* (* (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)) (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))))
328.0ms
(- (* F (sqrt 1/2)) (+ (* 1/4 (/ (* x F) (sqrt 1/2))) (* 1/2 (* (pow F 3) (sqrt 1/8)))))
304.0ms
(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
127.0ms
(+ (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)) (log (/ 1 (sin B))))

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes323.0ms

Accuracy

96.4% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 10.7b

bsearch325.0ms

end0.0ms

sample13.8s

Algorithm
intervals
Results
5.4s1682×body1280valid
2.7s1316×body640valid
2.6s4835×body80valid
1.5s726×body320valid
803.0ms1703×body80nan
367.0ms363×body160valid