Details

Time bar (total: 34.8s)

sample264.0ms

Algorithm
intervals
Results
96.0ms57×body1280valid
67.0ms48×body640valid
27.0ms162×body80valid
14.0ms22×body320valid
3.0ms7×body160valid

simplify95.0ms

Calls
1 calls:
Slowest
94.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

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)))

rewrite21.0ms

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
13.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
4.0ms
(/ x (tan B))
2.0ms
(/ 1 (sin B))

series276.0ms

Calls
3 calls:
Slowest
172.0ms
(/ x (tan B))
86.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
18.0ms
(/ 1 (sin B))

simplify617.0ms

Calls
24 calls:
Slowest
66.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
65.0ms
(/ (exp (/ 1 (sin B))) (exp (/ x (tan B))))
62.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
59.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
57.0ms
(- (+ (* 1/6 B) (/ 1 B)) (/ x B))

prune717.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)))

rewrite29.0ms

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
14.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
10.0ms
(/ (* x (cos B)) (sin B))
3.0ms
(* x (cos B))
2.0ms
(/ 1 (sin B))

series307.0ms

Calls
4 calls:
Slowest
126.0ms
(/ (* x (cos B)) (sin B))
110.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
49.0ms
(* x (cos B))
22.0ms
(/ 1 (sin B))

simplify1.3s

Calls
43 calls:
Slowest
173.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
123.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
97.0ms
(/ (exp (/ 1 (sin B))) (exp (/ (* x (cos B)) (sin B))))
83.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
81.0ms
(- (sqrt (/ 1 (sin B))) (sqrt (/ (* x (cos B)) (sin B))))

prune812.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×cbrt-div pow1/3 tan-quot
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 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
6.0ms
(* (cbrt (tan B)) (cbrt (tan B)))
1.0ms
(cbrt (tan B))
1.0ms
(cbrt (tan B))
1.0ms
(cbrt (tan B))

series744.0ms

Calls
4 calls:
Slowest
209.0ms
(cbrt (tan B))
182.0ms
(cbrt (tan B))
180.0ms
(* (cbrt (tan B)) (cbrt (tan B)))
173.0ms
(cbrt (tan B))

simplify439.0ms

Calls
48 calls:
Slowest
66.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
51.0ms
(+ (pow B 2/3) (+ (* 31/405 (pow (pow B 14) 1/3)) (* 2/9 (pow (pow B 8) 1/3))))
47.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
34.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
33.0ms
(pow (/ (pow (sin B) 2) (pow (cos B) 2)) 1/3)

prune925.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))) (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))))
0.5b
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))
0.5b
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))
0.5b
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
52×cbrt-div
40×cbrt-prod
31×*-un-lft-identity
21×add-sqr-sqrt
20×div-inv
16×frac-times
13×flip3-- frac-sub flip-- sub-div
11×associate-*r* associate-*l* add-cube-cbrt
10×distribute-rgt-out-- distribute-lft-out--
9×pow1
7×pow1/3
6×add-exp-log
5×difference-of-squares
4×add-cbrt-cube associate-*l/ associate-*r/ 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
23.0ms
(* (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))) (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))))
6.0ms
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))
4.0ms
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))
4.0ms
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))

series475.0ms

Calls
4 calls:
Slowest
138.0ms
(* (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))) (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))))
126.0ms
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))
106.0ms
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))
105.0ms
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))

simplify17.3s

Calls
118 calls:
Slowest
481.0ms
(cbrt (- (pow (/ 1 (sin B)) 3) (pow (/ (* x (cos B)) (sin B)) 3)))
453.0ms
(cbrt (* (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))) (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))))
447.0ms
(* (cbrt (+ (* (/ 1 (sin B)) (/ 1 (sin B))) (+ (* (/ (* x (cos B)) (sin B)) (/ (* x (cos B)) (sin B))) (* (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))))) (cbrt (sin B)))
444.0ms
(* (cbrt (- (pow (/ 1 (sin B)) 3) (pow (/ (* x (cos B)) (sin B)) 3))) (cbrt (- (pow (/ 1 (sin B)) 3) (pow (/ (* x (cos B)) (sin B)) 3))))
439.0ms
(- (exp (* 1/3 (- (log (- (/ (cos B) (sin B)))) (log (/ 1 x))))) (+ (* 1/9 (/ (exp (* 1/3 (- (log (- (/ (cos B) (sin B)))) (log (/ 1 x))))) (* (pow x 2) (pow (cos B) 2)))) (* 1/3 (/ (exp (* 1/3 (- (log (- (/ (cos B) (sin B)))) (log (/ 1 x))))) (* x (cos B))))))

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes128.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
3.8s1733×body1280valid
2.2s1470×body640valid
1.5s4895×body80valid
647.0ms680×body320valid
294.0ms373×body160valid