Details

Time bar (total: 24.5s)

sample223.0ms

Algorithm
intervals
Results
82.0ms53×body1280valid
70.0ms177×body80valid
40.0ms38×body640valid
13.0ms19×body320valid
4.0ms10×body160valid

simplify59.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
59.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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)))

rewrite41.0ms

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
30.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms
(/ 1 (sin B))
5.0ms
(/ x (tan B))

series305.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
147.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
144.0ms
(/ x (tan B))
14.0ms
(/ 1 (sin B))

simplify2.1s

Counts
81 → 93
Calls
81 calls:
Slowest
387.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
368.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
127.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
86.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
84.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune719.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 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)))

rewrite44.0ms

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
20.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
11.0ms
(/ (* x (cos B)) (sin B))
7.0ms
(* x (cos B))
5.0ms
(/ 1 (sin B))

series272.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
103.0ms
(/ (* x (cos B)) (sin B))
38.0ms
(* x (cos B))
14.0ms
(/ 1 (sin B))

simplify2.9s

Counts
81 → 108
Calls
81 calls:
Slowest
396.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
279.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
249.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
173.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
153.0ms
(/ (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))) (* (* (sin B) (sin B)) (sin B)))

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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)))

rewrite49.0ms

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
34.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
8.0ms
(/ x (tan B))
5.0ms
(/ 1 (sin B))

series321.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
164.0ms
(/ x (tan B))
133.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
24.0ms
(/ 1 (sin B))

simplify2.3s

Counts
81 → 93
Calls
81 calls:
Slowest
378.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
353.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
162.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
82.0ms
(- (+ (* 1/6 B) (/ 1 B)) (/ x B))
72.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))

prune892.0ms

Pruning

5 alts after pruning (4 fresh and 1 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))))

rewrite61.0ms

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
22.0ms
(* x (/ (cos B) (sin B)))
17.0ms
(/ (cos B) (sin B))
16.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
5.0ms
(/ 1 (sin B))

series348.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(* x (/ (cos B) (sin B)))
135.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
40.0ms
(/ (cos B) (sin B))
25.0ms
(/ 1 (sin B))

simplify3.4s

Counts
94 → 120
Calls
94 calls:
Slowest
468.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
428.0ms
(/ (* (* (cos B) (cos B)) (cos B)) (* (* (sin B) (sin B)) (sin B)))
297.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
285.0ms
(* (* (* x x) x) (* (* (/ (cos B) (sin B)) (/ (cos B) (sin B))) (/ (cos B) (sin B))))
245.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes92.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch1.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
2.9s1655×body1280valid
2.1s1395×body640valid
1.8s5018×body80valid
699.0ms679×body320valid
268.0ms404×body160valid