Details

Time bar (total: 2.2m)

sample210.0ms

Algorithm
intervals
Results
101.0ms56×body1280valid
38.0ms40×body640valid
37.0ms158×body80valid
15.0ms19×body320valid
7.0ms12×body160valid

simplify107.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
107.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

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)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
232×add-sqr-sqrt
224×*-un-lft-identity
215×add-cube-cbrt
182×prod-diff
31×div-inv
14×tan-quot associate-/r/
13×fma-neg
9×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l* difference-of-squares
5×add-log-exp
4×pow1
3×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u distribute-lft-out--
2×cbrt-undiv clear-num frac-2neg
1×rec-exp sub-neg flip3-- diff-log 1-exp frac-sub pow-flip flip-- inv-pow
Counts
3 → 285
Calls
3 calls:
Slowest
28.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
10.0ms
(/ x (tan B))
6.0ms
(/ 1 (sin B))

series309.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
148.0ms
(/ x (tan B))
134.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
27.0ms
(/ 1 (sin B))

simplify1.1m

Counts
456 → 294
Calls
456 calls:
Slowest
655.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ (cbrt x) (tan B)) (/ (* (cbrt x) (cbrt x)) 1))))
576.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
568.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
567.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
544.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
107×add-sqr-sqrt
105×*-un-lft-identity
98×add-cube-cbrt
91×prod-diff
28×div-inv
15×add-exp-log
13×add-cbrt-cube fma-neg
7×pow1
6×associate-/r* add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u 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 → 208
Calls
4 calls:
Slowest
34.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
12.0ms
(/ (* x (cos B)) (sin B))
8.0ms
(/ 1 (sin B))
7.0ms
(* x (cos B))

series379.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(/ (* x (cos B)) (sin B))
137.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
60.0ms
(* x (cos B))
14.0ms
(/ 1 (sin B))

simplify40.3s

Counts
274 → 220
Calls
274 calls:
Slowest
585.0ms
(fma (- (/ (* x (cos B)) (sin B))) 1 (* (/ (* x (cos B)) (sin B)) 1))
540.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
404.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
399.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (cbrt (/ (* x (cos B)) (sin B))) (* (cbrt (/ (* x (cos B)) (sin B))) (cbrt (/ (* x (cos B)) (sin B)))))))
388.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (/ 1 (sin B)) (* x (cos B)))))

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 54
Calls
2 calls:
Slowest
16.0ms
(* x (cos B))
15.0ms
(/ (- 1 (* x (cos B))) (sin B))

series150.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
97.0ms
(/ (- 1 (* x (cos B))) (sin B))
53.0ms
(* x (cos B))

simplify2.2s

Counts
44 → 60
Calls
44 calls:
Slowest
329.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
318.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
262.0ms
(- (pow 1 3) (pow (* x (cos B)) 3))
113.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
105.0ms
(/ (- 1 (* x (cos B))) (sqrt (sin B)))

prune582.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

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))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
46×times-frac
42×*-un-lft-identity add-cube-cbrt
15×add-exp-log
13×add-cbrt-cube fma-neg associate-*r* prod-diff
7×pow1
6×associate-/r* associate-/l* add-log-exp
5×div-inv
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-*l* associate-*r/
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 → 142
Calls
4 calls:
Slowest
22.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
18.0ms
(/ (cos B) (sin B))
13.0ms
(* x (/ (cos B) (sin B)))
9.0ms
(/ 1 (sin B))

series327.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(* x (/ (cos B) (sin B)))
127.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
33.0ms
(/ (cos B) (sin B))
24.0ms
(/ 1 (sin B))

simplify5.4s

Counts
131 → 154
Calls
131 calls:
Slowest
438.0ms
(/ (* (* (cos B) (cos B)) (cos B)) (* (* (sin B) (sin B)) (sin B)))
418.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
277.0ms
(/ (exp (/ 1 (sin B))) (exp (* x (/ (cos B) (sin B)))))
263.0ms
(* (* (* x x) x) (* (* (/ (cos B) (sin B)) (/ (cos B) (sin B))) (/ (cos B) (sin B))))
194.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample7.7s

Algorithm
intervals
Results
2.8s1653×body1280valid
2.6s1459×body640valid
1.3s4895×body80valid
632.0ms727×body320valid
227.0ms363×body160valid