Details

Time bar (total: 2.2m)

sample309.0ms

Algorithm
intervals
Results
129.0ms56×body1280valid
44.0ms40×body640valid
36.0ms158×body80valid
16.0ms19×body320valid
6.0ms12×body160valid

simplify162.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
162.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

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)))

rewrite59.0ms

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
36.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
7.0ms
(/ x (tan B))
5.0ms
(/ 1 (sin B))

series366.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
176.0ms
(/ x (tan B))
163.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
27.0ms
(/ 1 (sin B))

simplify1.1m

Counts
456 → 294
Calls
456 calls:
Slowest
682.0ms
(fma (- (/ (cbrt x) (tan B))) (/ (* (cbrt x) (cbrt x)) 1) (* (/ (cbrt x) (tan B)) (/ (* (cbrt x) (cbrt x)) 1)))
592.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
570.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
560.0ms
(fma (- (/ (cbrt x) (sqrt (tan B)))) (/ (* (cbrt x) (cbrt x)) (sqrt (tan B))) (* (/ (cbrt x) (sqrt (tan B))) (/ (* (cbrt x) (cbrt x)) (sqrt (tan B)))))
554.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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)))

rewrite82.0ms

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
35.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
24.0ms
(/ (* x (cos B)) (sin B))
11.0ms
(* x (cos B))
6.0ms
(/ 1 (sin B))

series375.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(/ (* x (cos B)) (sin B))
129.0ms
(- (/ 1 (sin B)) (/ (* x (cos B)) (sin B)))
67.0ms
(* x (cos B))
22.0ms
(/ 1 (sin B))

simplify39.7s

Counts
274 → 220
Calls
274 calls:
Slowest
573.0ms
(fma (- (/ (* x (cos B)) (sin B))) 1 (* (/ (* x (cos B)) (sin B)) 1))
493.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
415.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
379.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))
363.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (/ 1 (sin B)) (* x (cos B)))))

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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
24.0ms
(/ (- 1 (* x (cos B))) (sin B))
8.0ms
(* x (cos B))

series137.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
89.0ms
(/ (- 1 (* x (cos B))) (sin B))
49.0ms
(* x (cos B))

simplify2.2s

Counts
44 → 60
Calls
44 calls:
Slowest
343.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
269.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
239.0ms
(- (pow 1 3) (pow (* x (cos B)) 3))
98.0ms
(/ (* (cbrt (- 1 (* x (cos B)))) (cbrt (- 1 (* x (cos B))))) (* (cbrt (sin B)) (cbrt (sin B))))
92.0ms
(/ (- 1 (* x (cos B))) (sqrt (sin B)))

prune588.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

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))))

rewrite94.0ms

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
40.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
23.0ms
(* x (/ (cos B) (sin B)))
18.0ms
(/ (cos B) (sin B))
10.0ms
(/ 1 (sin B))

series324.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
153.0ms
(* x (/ (cos B) (sin B)))
128.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
23.0ms
(/ (cos B) (sin B))
19.0ms
(/ 1 (sin B))

simplify5.1s

Counts
131 → 154
Calls
131 calls:
Slowest
408.0ms
(/ (* (* (cos B) (cos B)) (cos B)) (* (* (sin B) (sin B)) (sin B)))
398.0ms
(- (/ 1 B) (+ (* 1/3 B) (* 1/45 (pow B 3))))
264.0ms
(* (* (* x x) x) (* (* (/ (cos B) (sin B)) (/ (cos B) (sin B))) (/ (cos B) (sin B))))
241.0ms
(/ (exp (/ 1 (sin B))) (exp (* x (/ (cos B) (sin B)))))
190.0ms
(+ (* 1/6 B) (+ (/ 1 B) (* 7/360 (pow B 3))))

prune1.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes111.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.2s1653×body1280valid
1.9s1459×body640valid
1.8s4895×body80valid
631.0ms727×body320valid
288.0ms363×body160valid