Details

Time bar (total: 25.1s)

sample213.0ms

Algorithm
intervals
Results
107.0ms56×body1280valid
40.0ms40×body640valid
37.0ms158×body80valid
14.0ms19×body320valid
5.0ms12×body160valid

simplify97.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
96.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

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
40.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
10.0ms
(/ x (tan B))
10.0ms
(/ 1 (sin B))

series318.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
148.0ms
(/ x (tan B))
147.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
23.0ms
(/ 1 (sin B))

simplify2.2s

Counts
81 → 93
Calls
81 calls:
Slowest
471.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
387.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
102.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
88.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
68.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune857.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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)))

rewrite62.0ms

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
35.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms
(/ (* x (cos B)) (sin B))
9.0ms
(* x (cos B))
5.0ms
(/ 1 (sin B))

series328.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(/ (* x (cos B)) (sin B))
122.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
48.0ms
(* x (cos B))
22.0ms
(/ 1 (sin B))

simplify3.0s

Counts
81 → 108
Calls
81 calls:
Slowest
383.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
291.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
246.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
202.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
145.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

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))

series140.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
100.0ms
(/ (- 1 (* x (cos B))) (sin B))
39.0ms
(* x (cos B))

simplify2.0s

Counts
44 → 56
Calls
44 calls:
Slowest
320.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
295.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
197.0ms
(- (pow 1 3) (pow (* x (cos B)) 3))
110.0ms
(/ (- 1 (* x (cos B))) (sqrt (sin B)))
94.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune528.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))))

rewrite62.0ms

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
30.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
13.0ms
(/ (cos B) (sin B))
12.0ms
(* x (/ (cos B) (sin B)))
5.0ms
(/ 1 (sin B))

series385.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
171.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
154.0ms
(* x (/ (cos B) (sin B)))
34.0ms
(/ (cos B) (sin B))
25.0ms
(/ 1 (sin B))

simplify3.4s

Counts
94 → 120
Calls
94 calls:
Slowest
434.0ms
(/ (* (* (cos B) (cos B)) (cos B)) (* (* (sin B) (sin B)) (sin B)))
387.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
307.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
266.0ms
(* (* (* x x) x) (* (* (/ (cos B) (sin B)) (/ (cos B) (sin B))) (/ (cos B) (sin B))))
259.0ms
(/ (exp (/ 1 (sin B))) (exp (* x (/ (cos B) (sin B)))))

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes96.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end1.0ms

sample8.6s

Algorithm
intervals
Results
3.7s1653×body1280valid
2.3s1459×body640valid
1.6s4895×body80valid
714.0ms727×body320valid
185.0ms363×body160valid