Details

Time bar (total: 33.1s)

sample597.0ms

Algorithm
intervals
Results
147.0ms53×body1280valid
111.0ms164×body80valid
103.0ms46×body640valid
63.0ms24×body320valid
10.0ms12×body160valid

simplify166.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
165.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize66.0ms

Local error

Found 3 expressions with local error:

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

rewrite100.0ms

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
73.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
14.0ms
(/ 1 (sin B))
7.0ms
(/ x (tan B))

series465.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
192.0ms
(/ x (tan B))
174.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
98.0ms
(/ 1 (sin B))

simplify2.4s

Counts
81 → 93
Calls
81 calls:
Slowest
429.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
387.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
225.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
93.0ms
(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
93.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune990.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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
33.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
15.0ms
(/ 1 (sin B))
11.0ms
(/ (tan B) x)
8.0ms
(/ 1 (/ (tan B) x))

series334.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
115.0ms
(/ 1 (/ (tan B) x))
55.0ms
(/ (tan B) x)
22.0ms
(/ 1 (sin B))

simplify9.2s

Counts
207 → 186
Calls
207 calls:
Slowest
475.0ms
(/ (* (* 1 1) 1) (* (* (/ (tan B) x) (/ (tan B) x)) (/ (tan B) x)))
411.0ms
(/ (* (* (tan B) (tan B)) (tan B)) (* (* x x) x))
385.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
343.0ms
(+ (/ B x) (+ (* 1/3 (/ (pow B 3) x)) (* 2/15 (/ (pow B 5) x))))
313.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x))))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
23×*-un-lft-identity
16×add-cube-cbrt
15×times-frac add-exp-log
13×add-cbrt-cube
7×pow1 div-inv
6×associate-/r* add-log-exp
4×div-exp insert-posit16 associate-/l*
3×cbrt-undiv distribute-rgt-out-- associate-*r* associate-*l* difference-of-squares
2×clear-num frac-2neg prod-exp cbrt-unprod distribute-lft-out--
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div unswap-sqr
Counts
4 → 96
Calls
4 calls:
Slowest
35.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
22.0ms
(/ (* x (cos B)) (sin B))
20.0ms
(* x (cos B))
10.0ms
(/ 1 (sin B))

series368.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ (* x (cos B)) (sin B))
136.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
69.0ms
(* x (cos B))
14.0ms
(/ 1 (sin B))

simplify3.3s

Counts
81 → 108
Calls
81 calls:
Slowest
414.0ms
(+ (/ 1 (sqrt (sin B))) (sqrt (/ (* x (cos B)) (sin B))))
362.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
268.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
169.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
157.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

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
12.0ms
(/ (- 1 (* x (cos B))) (sin B))
7.0ms
(* x (cos B))

series164.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
118.0ms
(/ (- 1 (* x (cos B))) (sin B))
46.0ms
(* x (cos B))

simplify2.1s

Counts
44 → 56
Calls
44 calls:
Slowest
352.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
260.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
212.0ms
(- (pow 1 3) (pow (* x (cos B)) 3))
111.0ms
(/ (- 1 (* x (cos B))) (sin B))
106.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune499.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes129.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample8.9s

Algorithm
intervals
Results
3.3s1786×body1280valid
2.4s1423×body640valid
2.1s4895×body80valid
625.0ms686×body320valid
271.0ms360×body160valid