Details

Time bar (total: 7.3m)

sample190.0ms

Algorithm
intervals
Results
97.0ms59×body1280valid
39.0ms44×body640valid
29.0ms157×body80valid
9.0ms16×body320valid
5.0ms12×body160valid

simplify83.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
83.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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)))

rewrite47.0ms

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
31.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms
(/ 1 (sin B))
5.0ms
(/ x (tan B))

series307.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
145.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
140.0ms
(/ x (tan B))
22.0ms
(/ 1 (sin B))

simplify1.2m

Counts
504 → 294
Calls
504 calls:
Slowest
918.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
838.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))
608.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
606.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))
580.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

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-*l* 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-*r* associate-*l/
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
52.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
29.0ms
(* (/ x (sin B)) (cos B))
10.0ms
(/ 1 (sin B))
9.0ms
(/ x (sin B))

series382.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
130.0ms
(* (/ x (sin B)) (cos B))
67.0ms
(/ x (sin B))
25.0ms
(/ 1 (sin B))

simplify9.1s

Counts
190 → 154
Calls
190 calls:
Slowest
480.0ms
(/ (* (* x x) x) (* (* (sin B) (sin B)) (sin B)))
313.0ms
(+ (* (/ 1 (sin B)) (/ 1 (sin B))) (+ (* (* (/ x (sin B)) (cos B)) (* (/ x (sin B)) (cos B))) (* (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))))
278.0ms
(exp (- (/ 1 (sin B)) (* (/ x (sin B)) (cos B))))
273.0ms
(- (* 1 (sin B)) (* (sin B) (* x (cos B))))
265.0ms
(* (* (* (/ x (sin B)) (cos B)) (* (/ x (sin B)) (cos B))) (* (/ x (sin B)) (cos B)))

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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
17.0ms
(/ (- 1 (* x (cos B))) (sin B))
7.0ms
(* x (cos B))

series160.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
107.0ms
(/ (- 1 (* x (cos B))) (sin B))
53.0ms
(* x (cos B))

simplify4.5s

Counts
71 → 60
Calls
71 calls:
Slowest
507.0ms
(* (* (/ (- 1 (* x (cos B))) (sin B)) (/ (- 1 (* x (cos B))) (sin B))) (/ (- 1 (* x (cos B))) (sin B)))
354.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
329.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
296.0ms
(* (sin B) (+ (* 1 1) (+ (* (* x (cos B)) (* x (cos B))) (* 1 (* x (cos B))))))
201.0ms
(* (* (* x (cos B)) (* x (cos B))) (* x (cos B)))

prune561.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (tan B) x))
0.2b
(/ (tan B) x)
0.1b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
1390×times-frac
881×add-sqr-sqrt
855×*-un-lft-identity
834×add-cube-cbrt
572×prod-diff
108×div-inv
21×add-exp-log
19×associate-/r*
15×difference-of-squares
14×associate-/r/
13×add-cbrt-cube fma-neg
10×div-exp
9×associate-/l*
7×distribute-lft-out--
6×pow1 add-log-exp
5×cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp clear-num frac-2neg 1-exp
2×pow-flip inv-pow
1×sub-neg flip3-- diff-log tan-quot frac-sub flip-- associate-/l/
Counts
4 → 767
Calls
4 calls:
Slowest
37.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
13.0ms
(/ 1 (/ (tan B) x))
11.0ms
(/ 1 (sin B))
11.0ms
(/ (tan B) x)

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(/ 1 (/ (tan B) x))
132.0ms
(- (/ 1 (sin B)) (/ 1 (/ (tan B) x)))
59.0ms
(/ (tan B) x)
15.0ms
(/ 1 (sin B))

simplify5.4m

Counts
1427 → 779
Calls
1427 calls:
Slowest
927.0ms
(fma (- (/ (sqrt 1) (/ (cbrt (tan B)) (sqrt x)))) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))) (* (/ (sqrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x)))))
878.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ 1 (/ (cbrt (tan B)) (cbrt x))) (/ 1 (/ (* (cbrt (tan B)) (cbrt (tan B))) (* (cbrt x) (cbrt x)))))))
875.0ms
(fma (- (/ (sqrt 1) (/ (cbrt (tan B)) (sqrt x)))) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))) (* (/ (sqrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (sqrt 1) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x)))))
827.0ms
(fma (- (/ (cbrt 1) (/ (cbrt (tan B)) (sqrt x)))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))) (* (/ (cbrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x)))))
700.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (/ (cbrt 1) (/ (cbrt (tan B)) (sqrt x))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (tan B)) (cbrt (tan B))) (sqrt x))))))

prune7.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes125.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
3.2s1782×body1280valid
1.9s1402×body640valid
1.5s4886×body80valid
1.2s701×body320valid
698.0ms363×body160valid