Details

Time bar (total: 1.4m)

sample241.0ms

Algorithm
intervals
Results
92.0ms53×body1280valid
47.0ms41×body640valid
40.0ms155×body80valid
36.0ms24×body320valid
9.0ms14×body160valid

simplify139.0ms

Calls
1 calls:
Slowest
138.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
72×add-sqr-sqrt
64×*-un-lft-identity
60×associate-/r* associate-/l*
55×add-cube-cbrt
27×times-frac
20×clear-num frac-2neg
9×add-exp-log
7×add-cbrt-cube
6×difference-of-squares
5×add-log-exp
4×pow1
3×div-exp insert-posit16 div-inv distribute-lft-out--
2×cbrt-undiv
1×rec-exp sub-neg flip3-- diff-log 1-exp tan-quot associate-/r/ pow-flip flip-- inv-pow
Calls
3 calls:
Slowest
41.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
18.0ms
(/ 1 (sin B))
10.0ms
(/ x (tan B))

series325.0ms

Calls
3 calls:
Slowest
150.0ms
(/ x (tan B))
149.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
26.0ms
(/ 1 (sin B))

simplify17.2s

Calls
241 calls:
Slowest
481.0ms
(- (* (/ 1 (* (cbrt (sin B)) (cbrt (sin B)))) (/ (tan B) x)) (* (cbrt (sin B)) 1))
465.0ms
(- (* (/ 1 (* (cbrt (sin B)) (cbrt (sin B)))) (/ (tan B) x)) (* (cbrt (sin B)) 1))
441.0ms
(- (* (/ 1 (* (cbrt (sin B)) (cbrt (sin B)))) (/ (tan B) (cbrt x))) (* (cbrt (sin B)) (* (cbrt x) (cbrt x))))
422.0ms
(- (* (- 1) (cbrt (tan B))) (* (- (sin B)) (/ x (* (cbrt (tan B)) (cbrt (tan B))))))
399.0ms
(- (* (/ 1 (sqrt (sin B))) (cbrt (tan B))) (* (sqrt (sin B)) (/ x (* (cbrt (tan B)) (cbrt (tan B))))))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
105×add-sqr-sqrt
97×associate-*l/
87×*-un-lft-identity
81×frac-sub
71×associate-/r*
70×add-cube-cbrt
63×associate-/l*
43×times-frac
23×frac-2neg
21×clear-num
18×associate-*l*
15×add-exp-log
13×add-cbrt-cube
9×difference-of-squares
8×unswap-sqr
7×pow1 distribute-lft-out-- sub-div
6×add-log-exp
5×div-inv
4×div-exp insert-posit16
3×cbrt-undiv associate-*r*
2×prod-exp cbrt-unprod
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
56.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
17.0ms
(* (/ x (sin B)) (cos B))
5.0ms
(/ 1 (sin B))
5.0ms
(/ x (sin B))

series319.0ms

Calls
4 calls:
Slowest
127.0ms
(* (/ x (sin B)) (cos B))
118.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
59.0ms
(/ x (sin B))
14.0ms
(/ 1 (sin B))

simplify33.3s

Calls
301 calls:
Slowest
927.0ms
(- (* 1 (- (sin B))) (* (sin B) (* (- x) (cos B))))
791.0ms
(- (* 1 (sin B)) (* (/ (sin B) 1) (* x (cos B))))
695.0ms
(- (* 1 (sin B)) (* (/ (sin B) 1) (* x (cos B))))
641.0ms
(- (* 1 (- (sin B))) (* (/ (sin B) 1) (* (- x) (cos B))))
610.0ms
(- (* (- 1) (/ (sin B) (sqrt x))) (* (- (sin B)) (* (sqrt x) (cos B))))

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
42×*-un-lft-identity
27×times-frac
18×add-cube-cbrt
16×difference-of-squares
9×associate-/l* unswap-sqr
8×distribute-lft-out--
7×associate-*l*
6×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* associate-*r*
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--
Calls
2 calls:
Slowest
75.0ms
(/ (- 1 (* x (cos B))) (sin B))
19.0ms
(* x (cos B))

series166.0ms

Calls
2 calls:
Slowest
117.0ms
(/ (- 1 (* x (cos B))) (sin B))
49.0ms
(* x (cos B))

simplify4.0s

Calls
84 calls:
Slowest
408.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
312.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
296.0ms
(- (pow 1 3) (pow (* x (cos B)) 3))
115.0ms
(/ (- (sqrt 1) (* (sqrt x) (sqrt (cos B)))) (sin B))
108.0ms
(/ (- (sqrt 1) (* (sqrt x) (sqrt (cos B)))) (sqrt (sin B)))

prune819.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
0.5b
(cbrt (/ 1 (sin B)))
0.5b
(cbrt (/ 1 (sin B)))
0.5b
(cbrt (/ 1 (sin B)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
207×cbrt-div
143×add-sqr-sqrt
119×cbrt-prod
113×*-un-lft-identity
103×add-cube-cbrt
81×frac-times
79×times-frac
69×associate-/r* associate-/l*
23×clear-num frac-2neg
18×swap-sqr
16×associate-*r* associate-*l* unswap-sqr
11×pow1
9×pow1/3 associate-*l/ associate-*r/ div-inv
8×add-cbrt-cube
6×add-exp-log
4×cbrt-unprod insert-posit16 add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative
Calls
4 calls:
Slowest
38.0ms
(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
3.0ms
(cbrt (/ 1 (sin B)))
3.0ms
(cbrt (/ 1 (sin B)))
3.0ms
(cbrt (/ 1 (sin B)))

series653.0ms

Calls
4 calls:
Slowest
188.0ms
(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
179.0ms
(cbrt (/ 1 (sin B)))
143.0ms
(cbrt (/ 1 (sin B)))
143.0ms
(cbrt (/ 1 (sin B)))

simplify8.8s

Calls
373 calls:
Slowest
414.0ms
(* (/ 1 (sin B)) (/ 1 (sin B)))
270.0ms
(* (/ 1 (sin B)) (* (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B)))))
269.0ms
(+ (pow B -1/3) (+ (* 11/3240 (pow (pow B 11) 1/3)) (* 1/18 (pow (pow B 5) 1/3))))
267.0ms
(+ (pow B -1/3) (+ (* 11/3240 (pow (pow B 11) 1/3)) (* 1/18 (pow (pow B 5) 1/3))))
235.0ms
(* (* (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B)))) (/ 1 (sin B)))

prune3.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes121.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample8.7s

Algorithm
intervals
Results
3.9s1741×body1280valid
1.9s1494×body640valid
1.7s4838×body80valid
720.0ms706×body320valid
236.0ms373×body160valid