Details

Time bar (total: 45.2s)

sample340.0ms

Algorithm
intervals
Results
141.0ms59×body1280valid
53.0ms44×body640valid
38.0ms157×body80valid
13.0ms16×body320valid
7.0ms12×body160valid

simplify288.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
287.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ x (tan B))
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ x (tan B)))

rewrite68.0ms

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
41.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
12.0ms
(/ x (tan B))
10.0ms
(/ 1 (sin B))

series978.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
473.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
462.0ms
(/ x (tan B))
42.0ms
(/ 1 (sin B))

simplify4.1s

Counts
121 → 93
Calls
121 calls:
Slowest
515.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
320.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
299.0ms
(+ (* (/ 1 (sin B)) (/ 1 (sin B))) (+ (* (/ x (tan B)) (/ x (tan B))) (* (/ 1 (sin B)) (/ x (tan B)))))
274.0ms
(- (pow (/ 1 (sin B)) 3) (pow (/ x (tan B)) 3))
249.0ms
(- (* (/ 1 (sin B)) (/ 1 (sin B))) (* (/ x (tan B)) (/ x (tan B))))

prune917.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ x (sin B)) (cos B))
0.2b
(/ x (sin B))
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity times-frac add-cube-cbrt
15×add-exp-log
13×add-cbrt-cube associate-*l*
7×pow1
6×associate-/r* associate-/l* add-log-exp
4×div-exp insert-posit16
3×cbrt-undiv associate-*r* associate-*l/ div-inv
2×clear-num frac-2neg prod-exp cbrt-unprod unswap-sqr
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div
Counts
4 → 108
Calls
4 calls:
Slowest
40.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
15.0ms
(* (/ x (sin B)) (cos B))
9.0ms
(/ 1 (sin B))
5.0ms
(/ x (sin B))

series380.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(* (/ x (sin B)) (cos B))
134.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
71.0ms
(/ x (sin B))
25.0ms
(/ 1 (sin B))

simplify6.3s

Counts
143 → 120
Calls
143 calls:
Slowest
471.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
361.0ms
(/ (* (* x x) x) (* (* (sin B) (sin B)) (sin B)))
324.0ms
(exp (- (/ 1 (sin B)) (* (/ x (sin B)) (cos B))))
313.0ms
(* (* (* (/ x (sin B)) (cos B)) (* (/ x (sin B)) (cos B))) (* (/ x (sin B)) (cos B)))
269.0ms
(+ (* (/ 1 (sin B)) (/ 1 (sin B))) (+ (* (* (/ x (sin B)) (cos B)) (* (/ x (sin B)) (cos B))) (* (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* associate-*r* associate-*l* associate-/l*
2×insert-posit16 add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv flip-- unswap-sqr
Counts
2 → 50
Calls
2 calls:
Slowest
24.0ms
(/ (- 1 (* x (cos B))) (sin B))
15.0ms
(* x (cos B))

series145.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
97.0ms
(/ (- 1 (* x (cos B))) (sin B))
47.0ms
(* x (cos B))

simplify4.7s

Counts
67 → 56
Calls
67 calls:
Slowest
736.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
528.0ms
(* (* (/ (- 1 (* x (cos B))) (sin B)) (/ (- 1 (* x (cos B))) (sin B))) (/ (- 1 (* x (cos B))) (sin B)))
362.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
339.0ms
(* (sin B) (+ (* 1 1) (+ (* (* x (cos B)) (* x (cos B))) (* 1 (* x (cos B))))))
295.0ms
(* (* (* x (cos B)) (* x (cos B))) (* x (cos B)))

prune579.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (tan B) x))
0.2b
(/ (tan B) x)
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))

rewrite59.0ms

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
20.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
16.0ms
(/ (tan B) x)
13.0ms
(/ 1 (/ (tan B) x))
6.0ms
(/ 1 (sin B))

series368.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
120.0ms
(/ 1 (/ (tan B) x))
82.0ms
(/ (tan B) x)
33.0ms
(/ 1 (sin B))

simplify13.3s

Counts
262 → 186
Calls
262 calls:
Slowest
475.0ms
(/ (* (* 1 1) 1) (* (* (/ (tan B) x) (/ (tan B) x)) (/ (tan B) x)))
465.0ms
(* (* (/ 1 (/ (tan B) x)) (/ 1 (/ (tan B) x))) (/ 1 (/ (tan B) x)))
457.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
433.0ms
(- (* (/ 1 (sin B)) (/ 1 (sin B))) (* (/ 1 (/ (tan B) x)) (/ 1 (/ (tan B) x))))
367.0ms
(/ (* (* (tan B) (tan B)) (tan B)) (* (* x x) x))

prune1.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes152.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample9.3s

Algorithm
intervals
Results
3.7s1782×body1280valid
2.4s1402×body640valid
1.5s4886×body80valid
1.2s701×body320valid
236.0ms363×body160valid