Details

Time bar (total: 25.2s)

sample327.0ms

Algorithm
intervals
Results
138.0ms56×body1280valid
72.0ms158×body80valid
42.0ms40×body640valid
13.0ms19×body320valid
6.0ms12×body160valid

simplify191.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
190.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

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)))

rewrite62.0ms

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
37.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
12.0ms
(/ x (tan B))
9.0ms
(/ 1 (sin B))

series376.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
210.0ms
(/ x (tan B))
149.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
17.0ms
(/ 1 (sin B))

simplify2.3s

Counts
81 → 93
Calls
81 calls:
Slowest
415.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
338.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
135.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
97.0ms
(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
81.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune890.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

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
26.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
20.0ms
(/ (* x (cos B)) (sin B))
7.0ms
(* x (cos B))
5.0ms
(/ 1 (sin B))

series297.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(/ (* x (cos B)) (sin B))
117.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
41.0ms
(* x (cos B))
14.0ms
(/ 1 (sin B))

simplify3.1s

Counts
81 → 108
Calls
81 calls:
Slowest
440.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
248.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
202.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
172.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
143.0ms
(/ (exp (/ 1 (sin B))) (exp (/ (* x (cos B)) (sin B))))

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.1b
(* x (cos B))
0.1b
(/ (- 1 (* x (cos B))) (sin 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
100.0ms
(/ (- 1 (* x (cos B))) (sin B))
64.0ms
(* x (cos B))

simplify2.5s

Counts
44 → 56
Calls
44 calls:
Slowest
424.0ms
(* x (cos B))
361.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
283.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
230.0ms
(- (pow 1 3) (pow (* x (cos B)) 3))
97.0ms
(/ (- 1 (* x (cos B))) (sqrt (sin B)))

prune514.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (/ (cos B) (sin B)))
0.2b
(/ (cos B) (sin B))
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
28×*-un-lft-identity times-frac add-cube-cbrt
15×add-exp-log
13×add-cbrt-cube associate-*r*
7×pow1
6×associate-/r* associate-/l* add-log-exp
4×div-exp insert-posit16
3×cbrt-undiv associate-*l* associate-*r/ div-inv
2×clear-num frac-2neg prod-exp cbrt-unprod unswap-sqr
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down *-commutative frac-sub pow-flip flip-- inv-pow sub-div
Counts
4 → 108
Calls
4 calls:
Slowest
17.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
11.0ms
(* x (/ (cos B) (sin B)))
8.0ms
(/ (cos B) (sin B))
8.0ms
(/ 1 (sin B))

series320.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
132.0ms
(* x (/ (cos B) (sin B)))
20.0ms
(/ (cos B) (sin B))
18.0ms
(/ 1 (sin B))

simplify3.5s

Counts
94 → 120
Calls
94 calls:
Slowest
389.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
387.0ms
(/ (* (* (cos B) (cos B)) (cos B)) (* (* (sin B) (sin B)) (sin B)))
299.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
262.0ms
(/ (exp (/ 1 (sin B))) (exp (* x (/ (cos B) (sin B)))))
252.0ms
(* (* (* x x) x) (* (* (/ (cos B) (sin B)) (/ (cos B) (sin B))) (/ (cos B) (sin B))))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes125.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
2.8s1653×body1280valid
2.0s1459×body640valid
1.7s4895×body80valid
1.0s727×body320valid
220.0ms363×body160valid