Details

Time bar (total: 33.9s)

sample207.0ms

Algorithm
intervals
Results
75.0ms57×body1280valid
72.0ms48×body640valid
33.0ms162×body80valid
14.0ms22×body320valid
3.0ms7×body160valid

simplify92.0ms

Calls
1 calls:
Slowest
92.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

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)))

rewrite11.0ms

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
8.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
1.0ms
(/ 1 (sin B))
1.0ms
(/ x (tan B))

series247.0ms

Calls
3 calls:
Slowest
133.0ms
(/ x (tan B))
101.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
13.0ms
(/ 1 (sin B))

simplify531.0ms

Calls
24 calls:
Slowest
73.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
67.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
65.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
58.0ms
(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
50.0ms
(/ (exp (/ 1 (sin B))) (exp (/ x (tan B))))

prune431.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)))

rewrite16.0ms

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
7.0ms
(/ (* x (cos B)) (sin B))
6.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
1.0ms
(* x (cos B))
1.0ms
(/ 1 (sin B))

series246.0ms

Calls
4 calls:
Slowest
106.0ms
(/ (* x (cos B)) (sin B))
85.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
42.0ms
(* x (cos B))
13.0ms
(/ 1 (sin B))

simplify1.1s

Calls
43 calls:
Slowest
134.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
130.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
101.0ms
(/ (exp (/ 1 (sin B))) (exp (/ (* x (cos B)) (sin B))))
72.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
63.0ms
(+ (sqrt (/ 1 (sin B))) (sqrt (/ (* x (cos B)) (sin B))))

prune727.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

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)))

rewrite8.0ms

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))

series634.0ms

Calls
4 calls:
Slowest
177.0ms
(cbrt (tan B))
175.0ms
(cbrt (tan B))
150.0ms
(* (cbrt (tan B)) (cbrt (tan B)))
132.0ms
(cbrt (tan B))

simplify447.0ms

Calls
48 calls:
Slowest
63.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
45.0ms
(pow (/ (pow (sin B) 2) (pow (cos B) 2)) 1/3)
43.0ms
(+ (pow B 2/3) (+ (* 31/405 (pow (pow B 14) 1/3)) (* 2/9 (pow (pow B 8) 1/3))))
43.0ms
(+ (pow B 1/3) (+ (* 1/9 (pow (pow B 7) 1/3)) (* 13/405 (pow (pow B 13) 1/3))))
38.0ms
(pow (/ (pow (sin B) 2) (pow (cos B) 2)) 1/3)

prune988.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

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))))

rewrite47.0ms

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
34.0ms
(* (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))) (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))))
4.0ms
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))

series506.0ms

Calls
4 calls:
Slowest
152.0ms
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))
145.0ms
(* (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))) (cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))))
106.0ms
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))
103.0ms
(cbrt (- (/ 1 (sin B)) (/ (* x (cos B)) (sin B))))

simplify17.0s

Calls
118 calls:
Slowest
753.0ms
(- (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))))))
473.0ms
(* (cbrt (- (pow (/ 1 (sin B)) 3) (pow (/ (* x (cos B)) (sin B)) 3))) (cbrt (- 1 (* x (cos B)))))
468.0ms
(* (cbrt (* (sin B) (sin B))) (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)))))))
452.0ms
(cbrt (- (pow (/ 1 (sin B)) 3) (pow (/ (* x (cos B)) (sin B)) 3)))
438.0ms
(- (exp (* 1/3 (- (log (/ (cos B) (sin B))) (log (/ -1 x))))) (+ (* 1/3 (/ (exp (* 1/3 (- (log (/ (cos B) (sin B))) (log (/ -1 x))))) (* x (cos B)))) (* 1/9 (/ (exp (* 1/3 (- (log (/ (cos B) (sin B))) (log (/ -1 x))))) (* (pow x 2) (pow (cos B) 2))))))

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes113.0ms

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
3.8s1733×body1280valid
2.2s1470×body640valid
1.5s4895×body80valid
674.0ms680×body320valid
222.0ms373×body160valid