Details

Time bar (total: 40.7s)

sample201.0ms

Algorithm
intervals
Results
73.0ms61×body1280valid
48.0ms45×body640valid
29.0ms156×body80valid
11.0ms21×body320valid
3.0ms7×body160valid

simplify64.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
64.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ x (tan B))
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ x (tan B)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
28×*-un-lft-identity
27×times-frac
19×add-cube-cbrt
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l* difference-of-squares
5×add-log-exp
4×pow1
3×div-exp insert-posit16 div-inv distribute-lft-out--
2×cbrt-undiv clear-num frac-2neg
1×rec-exp sub-neg flip3-- diff-log 1-exp tan-quot associate-/r/ frac-sub pow-flip flip-- inv-pow
Counts
3 → 84
Calls
3 calls:
Slowest
20.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms
(/ 1 (sin B))
5.0ms
(/ x (tan B))

series272.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
152.0ms
(/ x (tan B))
106.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
14.0ms
(/ 1 (sin B))

simplify2.0s

Counts
81 → 93
Calls
81 calls:
Slowest
332.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
296.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
104.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
90.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
74.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune694.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (tan B) x))
0.1b
(/ (tan B) x)
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
111×add-sqr-sqrt
85×*-un-lft-identity
64×add-cube-cbrt
21×add-exp-log
19×associate-/r*
15×difference-of-squares
13×add-cbrt-cube
11×div-inv
10×div-exp
9×associate-/l*
7×distribute-lft-out--
6×pow1 add-log-exp
5×cbrt-undiv
4×insert-posit16
3×rec-exp clear-num frac-2neg 1-exp
2×pow-flip inv-pow
1×sub-neg flip3-- diff-log tan-quot associate-/r/ frac-sub flip-- associate-/l/
Counts
4 → 174
Calls
4 calls:
Slowest
24.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
6.0ms
(/ 1 (/ (tan B) x))
6.0ms
(/ (tan B) x)
5.0ms
(/ 1 (sin B))

series362.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
104.0ms
(/ 1 (/ (tan B) x))
73.0ms
(/ (tan B) x)
22.0ms
(/ 1 (sin B))

simplify7.9s

Counts
207 → 186
Calls
207 calls:
Slowest
424.0ms
(+ (/ B x) (+ (* 1/3 (/ (pow B 3) x)) (* 2/15 (/ (pow B 5) x))))
405.0ms
(/ (* (* (tan B) (tan B)) (tan B)) (* (* x x) x))
362.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
333.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x))))
320.0ms
(/ (* (* 1 1) 1) (* (* (/ (tan B) x) (/ (tan B) x)) (/ (tan B) x)))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (sin B) (* x (cos B))))
0.2b
(/ (sin B) (* x (cos B)))
0.2b
(* x (cos B))
0.1b
(/ 1 (sin B))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
36×add-exp-log
34×add-sqr-sqrt
32×*-un-lft-identity add-cube-cbrt
22×add-cbrt-cube
16×div-exp
11×associate-/r*
9×associate-/l*
8×pow1 cbrt-undiv
7×div-inv
5×prod-exp
4×rec-exp 1-exp insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* associate-*l* cbrt-unprod
2×pow-flip inv-pow
1×pow-prod-down associate-/r/ *-commutative unswap-sqr
Counts
4 → 130
Calls
4 calls:
Slowest
21.0ms
(/ (sin B) (* x (cos B)))
18.0ms
(/ 1 (/ (sin B) (* x (cos B))))
15.0ms
(* x (cos B))
10.0ms
(/ 1 (sin B))

series310.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(/ 1 (/ (sin B) (* x (cos B))))
111.0ms
(/ (sin B) (* x (cos B)))
62.0ms
(* x (cos B))
24.0ms
(/ 1 (sin B))

simplify5.8s

Counts
124 → 142
Calls
124 calls:
Slowest
421.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
402.0ms
(+ (/ B x) (+ (* 1/3 (/ (pow B 3) x)) (* 2/15 (/ (pow B 5) x))))
259.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
242.0ms
(/ (* (* 1 1) 1) (/ (* (* (sin B) (sin B)) (sin B)) (* (* (* x (cos B)) (* x (cos B))) (* x (cos B)))))
212.0ms
(/ (* (* 1 1) 1) (/ (* (* (sin B) (sin B)) (sin B)) (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin B) (/ 1 (* x (cos B))))
0.3b
(/ 1 (* (sin B) (/ 1 (* x (cos B)))))
0.2b
(/ 1 (* x (cos B)))
0.2b
(* x (cos B))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
104×add-exp-log
44×prod-exp
36×div-exp
34×add-cbrt-cube
18×rec-exp 1-exp
17×add-sqr-sqrt
14×pow1
13×*-un-lft-identity add-cube-cbrt
10×cbrt-undiv associate-*r* cbrt-unprod
9×times-frac
6×associate-*l* associate-/l*
4×pow-prod-down insert-posit16 pow-flip add-log-exp
3×div-inv
2×clear-num associate-/r* frac-2neg associate-*r/ associate-/r/ un-div-inv *-commutative inv-pow unswap-sqr
Counts
4 → 132
Calls
4 calls:
Slowest
46.0ms
(* (sin B) (/ 1 (* x (cos B))))
45.0ms
(/ 1 (* (sin B) (/ 1 (* x (cos B)))))
10.0ms
(/ 1 (* x (cos B)))
7.0ms
(* x (cos B))

series356.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(/ 1 (* (sin B) (/ 1 (* x (cos B)))))
105.0ms
(* (sin B) (/ 1 (* x (cos B))))
78.0ms
(/ 1 (* x (cos B)))
58.0ms
(* x (cos B))

simplify9.3s

Counts
96 → 144
Calls
96 calls:
Slowest
413.0ms
(- 0 (log (* (sin B) (/ 1 (* x (cos B))))))
387.0ms
(+ (/ B x) (+ (* 1/3 (/ (pow B 3) x)) (* 2/15 (/ (pow B 5) x))))
380.0ms
(- 0 (+ (log (sin B)) (- 0 (log (* x (cos B))))))
371.0ms
(/ (* (* 1 1) 1) (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))))
346.0ms
(- 0 (+ (log (sin B)) (- (log 1) (+ (log x) (log (cos B))))))

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes128.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch3.0ms

end0.0ms

sample7.9s

Algorithm
intervals
Results
3.0s1705×body1280valid
2.2s1370×body640valid
1.7s5084×body80valid
707.0ms717×body320valid
187.0ms362×body160valid