Details

Time bar (total: 33.8s)

sample627.0ms

Algorithm
intervals
Results
261.0ms43×body1280valid
135.0ms53×body640valid
117.0ms160×body80valid
24.0ms24×body320valid
7.0ms11×body160valid

simplify179.0ms

Calls
1 calls:
Slowest
178.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune69.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize74.0ms

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)))

rewrite76.0ms

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
Calls
3 calls:
Slowest
44.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
9.0ms
(/ 1 (sin B))
8.0ms
(/ x (tan B))

series480.0ms

Calls
3 calls:
Slowest
227.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
193.0ms
(/ x (tan B))
60.0ms
(/ 1 (sin B))

simplify2.5s

Calls
81 calls:
Slowest
486.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
422.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
126.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
102.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
82.0ms
(- (/ x B) (* 1/3 (* x B)))

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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)))

rewrite59.0ms

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
Calls
4 calls:
Slowest
25.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
20.0ms
(/ (* x (cos B)) (sin B))
8.0ms
(* x (cos B))
5.0ms
(/ 1 (sin B))

series375.0ms

Calls
4 calls:
Slowest
145.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
140.0ms
(/ (* x (cos B)) (sin B))
67.0ms
(* x (cos B))
22.0ms
(/ 1 (sin B))

simplify3.1s

Calls
81 calls:
Slowest
392.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
294.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
228.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
210.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
176.0ms
(/ (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))) (* (* (sin B) (sin B)) (sin B)))

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (tan B) x))
0.1b
(/ 1 (sin B))
0.1b
(/ (tan B) x)
0.0b
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
127×times-frac
111×add-sqr-sqrt
85×*-un-lft-identity
64×add-cube-cbrt
21×add-exp-log
19×associate-/r*
15×difference-of-squares
13×add-cbrt-cube
11×div-inv
10×div-exp
9×associate-/l*
7×distribute-lft-out--
6×pow1 add-log-exp
5×cbrt-undiv
4×insert-posit16
3×rec-exp clear-num frac-2neg 1-exp
2×pow-flip inv-pow
1×sub-neg flip3-- diff-log tan-quot associate-/r/ frac-sub flip-- associate-/l/
Calls
4 calls:
Slowest
27.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
13.0ms
(/ 1 (/ (tan B) x))
11.0ms
(/ (tan B) x)
10.0ms
(/ 1 (sin B))

series378.0ms

Calls
4 calls:
Slowest
159.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
131.0ms
(/ 1 (/ (tan B) x))
69.0ms
(/ (tan B) x)
19.0ms
(/ 1 (sin B))

simplify9.8s

Calls
207 calls:
Slowest
545.0ms
(/ (exp (/ 1 (sin B))) (exp (/ 1 (/ (tan B) x))))
443.0ms
(/ (* (* 1 1) 1) (* (* (/ (tan B) x) (/ (tan B) x)) (/ (tan B) x)))
438.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
421.0ms
(/ (* (* (tan B) (tan B)) (tan B)) (* (* x x) x))
346.0ms
(+ (/ B x) (+ (* 1/3 (/ (pow B 3) x)) (* 2/15 (/ (pow B 5) x))))

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

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
Calls
4 calls:
Slowest
15.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
1.0ms
(cbrt (sin B))
1.0ms
(cbrt (sin B))
1.0ms
(cbrt (sin B))

series548.0ms

Calls
4 calls:
Slowest
159.0ms
(* (cbrt (sin B)) (cbrt (sin B)))
148.0ms
(cbrt (sin B))
129.0ms
(cbrt (sin B))
112.0ms
(cbrt (sin B))

simplify1.6s

Calls
65 calls:
Slowest
319.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
310.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
247.0ms
(- (+ (pow B 2/3) (* 1/405 (pow (pow B 14) 1/3))) (* 1/9 (pow (pow B 8) 1/3)))
223.0ms
(- (pow B 1/3) (+ (* 1/18 (pow (pow B 7) 1/3)) (* 1/3240 (pow (pow B 13) 1/3))))
90.0ms
(* (* (cbrt (cbrt (sin B))) (cbrt (cbrt (sin B)))) (* (cbrt (cbrt (sin B))) (cbrt (cbrt (sin B)))))

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes123.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample8.3s

Algorithm
intervals
Results
3.0s1712×body1280valid
2.1s4850×body80valid
2.0s1461×body640valid
720.0ms742×body320valid
221.0ms336×body160valid