Details

Time bar (total: 26.5s)

sample530.0ms

Algorithm
intervals
Results
182.0ms55×body640valid
93.0ms44×body1280valid
56.0ms158×body80valid
51.0ms19×body320valid
14.0ms14×body160valid

simplify89.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
88.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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)))

rewrite40.0ms

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
19.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
6.0ms
(/ x (tan B))
5.0ms
(/ 1 (sin B))

series294.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
158.0ms
(/ x (tan B))
122.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
15.0ms
(/ 1 (sin B))

simplify2.2s

Counts
81 → 93
Calls
81 calls:
Slowest
446.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
292.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
113.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
84.0ms
(- (/ x B) (* 1/3 (* x B)))
79.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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)))

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
22.0ms
(/ (* x (cos B)) (sin B))
17.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
12.0ms
(/ 1 (sin B))
7.0ms
(* x (cos B))

series340.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(/ (* x (cos B)) (sin B))
120.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
66.0ms
(* x (cos B))
14.0ms
(/ 1 (sin B))

simplify2.9s

Counts
81 → 108
Calls
81 calls:
Slowest
341.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
318.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
209.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
169.0ms
(/ (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))) (* (* (sin B) (sin B)) (sin B)))
142.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))

prune958.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos B))
0.3b
(cbrt (cos B))
0.3b
(cbrt (cos B))
0.2b
(* (cbrt (cos B)) (cbrt (cos B)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 77
Calls
4 calls:
Slowest
9.0ms
(* (cbrt (cos B)) (cbrt (cos B)))
2.0ms
(cbrt (cos B))
2.0ms
(cbrt (cos B))
2.0ms
(cbrt (cos B))

series642.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
243.0ms
(* (cbrt (cos B)) (cbrt (cos B)))
145.0ms
(cbrt (cos B))
131.0ms
(cbrt (cos B))
123.0ms
(cbrt (cos B))

simplify1.3s

Counts
65 → 89
Calls
65 calls:
Slowest
388.0ms
(- 1 (+ (* 1/405 (pow B 6)) (* 1/3 (pow B 2))))
179.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
159.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
144.0ms
(- 1 (+ (* 1/72 (pow B 4)) (* 1/6 (pow B 2))))
65.0ms
(* (* (cbrt (cbrt (cos B))) (cbrt (cbrt (cos B)))) (* (cbrt (cbrt (cos B))) (cbrt (cbrt (cos B)))))

prune995.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

10.8b
(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
0.3b
(* (sin B) (sin B))
0.2b
(* (sin B) (* x (cos B)))
0.1b
(* x (cos B))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-cbrt-cube add-exp-log
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
9×associate-*l*
7×associate-*r*
6×prod-exp cbrt-unprod
5×pow-prod-down
4×insert-posit16 add-log-exp
3×times-frac swap-sqr *-commutative associate-/l*
2×cbrt-undiv div-exp sin-mult unswap-sqr associate-/l/
1×pow2 clear-num associate-/r* frac-2neg pow-plus flip3-- div-sub associate-/r/ pow-sqr pow-prod-up sqr-sin div-inv flip--
Counts
4 → 92
Calls
4 calls:
Slowest
38.0ms
(* (sin B) (* x (cos B)))
23.0ms
(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
21.0ms
(* (sin B) (sin B))
14.0ms
(* x (cos B))

series786.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
588.0ms
(/ (- (sin B) (* (sin B) (* x (cos B)))) (* (sin B) (sin B)))
112.0ms
(* (sin B) (* x (cos B)))
54.0ms
(* x (cos B))
32.0ms
(* (sin B) (sin B))

simplify4.3s

Counts
70 → 104
Calls
70 calls:
Slowest
484.0ms
(* (* (* (sin B) (sin B)) (sin B)) (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))))
460.0ms
(* (* (* (sin B) (sin B)) (sin B)) (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))))
350.0ms
(- (* (sin B) (sin B)) (* (* (sin B) (* x (cos B))) (* (sin B) (* x (cos B)))))
292.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
231.0ms
(- (+ (* 2/45 (pow B 6)) (pow B 2)) (* 1/3 (pow B 4)))

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes87.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
3.4s1653×body1280valid
2.1s4982×body80valid
1.9s1413×body640valid
769.0ms762×body320valid
218.0ms342×body160valid