Details

Time bar (total: 16.8s)

sample152.0ms

Algorithm
intervals
Results
55.0ms46×body1280valid
39.0ms40×body640valid
26.0ms156×body80valid
16.0ms31×body320valid
6.0ms15×body160valid

simplify92.0ms

Calls
1 calls:
Slowest
91.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
7×add-sqr-sqrt
6×associate-/r*
5×add-cube-cbrt add-log-exp
4×pow1 add-exp-log
3×add-cbrt-cube insert-posit16 div-inv
2×clear-num frac-2neg distribute-lft-out--
1×rec-exp sub-neg flip3-- diff-log tan-quot associate-/r/ frac-sub pow-flip flip-- inv-pow difference-of-squares
Calls
3 calls:
Slowest
10.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
2.0ms
(/ 1 (sin B))
1.0ms
(/ x (tan B))

series260.0ms

Calls
3 calls:
Slowest
129.0ms
(/ x (tan B))
114.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
17.0ms
(/ 1 (sin B))

simplify592.0ms

Calls
24 calls:
Slowest
81.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
77.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
72.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
67.0ms
(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
45.0ms
(- (/ x B) (* 1/3 (* x B)))

prune526.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
10×add-sqr-sqrt
8×add-cube-cbrt
7×add-exp-log
6×associate-/r* add-cbrt-cube div-inv add-log-exp
5×pow1
4×insert-posit16
3×times-frac associate-*r*
2×clear-num frac-2neg distribute-rgt-out-- distribute-lft-out--
1×cbrt-undiv rec-exp sub-neg flip3-- diff-log div-exp *-commutative frac-sub pow-flip flip-- associate-/l* inv-pow sub-div difference-of-squares
Calls
4 calls:
Slowest
10.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
5.0ms
(/ (* x (cos B)) (sin B))
2.0ms
(* x (cos B))
1.0ms
(/ 1 (sin B))

series270.0ms

Calls
4 calls:
Slowest
113.0ms
(/ (* x (cos B)) (sin B))
105.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
32.0ms
(* x (cos B))
19.0ms
(/ 1 (sin B))

simplify1.5s

Calls
43 calls:
Slowest
283.0ms
(/ (cos B) (sqrt (sin B)))
151.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
136.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
100.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
79.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))

prune686.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (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)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
20×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×cbrt-div pow1/3 associate-*r* associate-*l*
6×add-exp-log
5×div-inv
4×add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
9.0ms
(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
1.0ms
(cbrt (/ 1 (sin B)))
1.0ms
(cbrt (/ 1 (sin B)))
1.0ms
(cbrt (/ 1 (sin B)))

series572.0ms

Calls
4 calls:
Slowest
169.0ms
(* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B))))
160.0ms
(cbrt (/ 1 (sin B)))
123.0ms
(cbrt (/ 1 (sin B)))
120.0ms
(cbrt (/ 1 (sin B)))

simplify695.0ms

Calls
53 calls:
Slowest
70.0ms
(+ (pow B -1/3) (+ (* 11/3240 (pow (pow B 11) 1/3)) (* 1/18 (pow (pow B 5) 1/3))))
54.0ms
(+ (pow B -1/3) (+ (* 11/3240 (pow (pow B 11) 1/3)) (* 1/18 (pow (pow B 5) 1/3))))
52.0ms
(+ (pow B -1/3) (+ (* 11/3240 (pow (pow B 11) 1/3)) (* 1/18 (pow (pow B 5) 1/3))))
44.0ms
(+ (* 1/9 (pow (pow B 4) 1/3)) (+ (pow B -2/3) (* 4/405 (pow (pow B 10) 1/3))))
29.0ms
(pow (/ 1 (pow (sin B) 2)) 1/3)

prune987.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×pow1/3
6×associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
6.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
5.0ms
(cbrt (sin B))
1.0ms
(cbrt (sin B))
1.0ms
(cbrt (sin B))

series602.0ms

Calls
4 calls:
Slowest
164.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
157.0ms
(cbrt (sin B))
146.0ms
(cbrt (sin B))
135.0ms
(cbrt (sin B))

simplify561.0ms

Calls
41 calls:
Slowest
128.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
118.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
96.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
89.0ms
(- (+ (pow B 2/3) (* 1/405 (pow (pow B 14) 1/3))) (* 1/9 (pow (pow B 8) 1/3)))
6.0ms
(cbrt (* (cbrt (sin B)) (cbrt (sin B))))

prune839.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes90.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.9s1680×body1280valid
1.8s1435×body640valid
1.4s5024×body80valid
768.0ms687×body320valid
180.0ms345×body160valid