Details

Time bar (total: 27.8s)

sample266.0ms

Algorithm
intervals
Results
103.0ms58×body1280valid
77.0ms176×body80valid
48.0ms41×body640valid
22.0ms26×body320valid
2.0ms5×body160valid

simplify94.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
94.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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)))

rewrite52.0ms

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

series314.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
146.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
143.0ms
(/ x (tan B))
25.0ms
(/ 1 (sin B))

simplify2.4s

Counts
81 → 93
Calls
81 calls:
Slowest
455.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
431.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
119.0ms
(/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))
103.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
66.0ms
(- (+ (* 1/6 B) (/ 1 B)) (/ x B))

prune951.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)))

rewrite49.0ms

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
(- (/ 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))

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(/ (* x (cos B)) (sin B))
126.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
40.0ms
(* x (cos B))
14.0ms
(/ 1 (sin B))

simplify3.1s

Counts
81 → 108
Calls
81 calls:
Slowest
379.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
322.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
196.0ms
(/ (* (* (* x (cos B)) (* x (cos B))) (* x (cos B))) (* (* (sin B) (sin B)) (sin B)))
178.0ms
(/ (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))) (* (* (sin B) (sin B)) (sin B)))
162.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))))

rewrite54.0ms

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))))
16.0ms
(* x (/ (cos B) (sin B)))
15.0ms
(/ (cos B) (sin B))
5.0ms
(/ 1 (sin B))

series292.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(* x (/ (cos B) (sin B)))
111.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
43.0ms
(/ (cos B) (sin B))
16.0ms
(/ 1 (sin B))

simplify3.5s

Counts
94 → 120
Calls
94 calls:
Slowest
457.0ms
(/ (* (* (cos B) (cos B)) (cos B)) (* (* (sin B) (sin B)) (sin B)))
425.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
370.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
284.0ms
(* (* (* x x) x) (* (* (/ (cos B) (sin B)) (/ (cos B) (sin B))) (/ (cos B) (sin B))))
249.0ms
(/ (exp (/ 1 (sin B))) (exp (* x (/ (cos B) (sin B)))))

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

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-*l*
7×pow1
6×associate-/r* associate-/l* add-log-exp
4×div-exp insert-posit16
3×cbrt-undiv associate-*r* associate-*l/ 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
37.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
28.0ms
(* (/ x (sin B)) (cos B))
10.0ms
(/ 1 (sin B))
9.0ms
(/ x (sin B))

series360.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
134.0ms
(* (/ x (sin B)) (cos B))
55.0ms
(/ x (sin B))
27.0ms
(/ 1 (sin B))

simplify3.2s

Counts
93 → 120
Calls
93 calls:
Slowest
404.0ms
(/ (* (* x x) x) (* (* (sin B) (sin B)) (sin B)))
388.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))
297.0ms
(/ (exp (/ 1 (sin B))) (exp (* (/ x (sin B)) (cos B))))
215.0ms
(* (* (* (/ x (sin B)) (/ x (sin B))) (/ x (sin B))) (* (* (cos B) (cos B)) (cos B)))
190.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes82.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample9.1s

Algorithm
intervals
Results
3.4s1741×body1280valid
2.7s1450×body640valid
1.6s4939×body80valid
1.0s687×body320valid
207.0ms365×body160valid