Details

Time bar (total: 7.7m)

sample389.0ms

Algorithm
intervals
Results
94.0ms155×body80valid
86.0ms53×body1280valid
41.0ms41×body640valid
20.0ms24×body320valid
7.0ms14×body160valid

simplify94.0ms

Calls
1 calls:
Slowest
93.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
279×times-frac
268×add-sqr-sqrt
260×*-un-lft-identity
251×add-cube-cbrt
182×prod-diff
81×frac-sub
60×associate-/r* associate-/l*
31×div-inv
20×clear-num frac-2neg
14×tan-quot associate-/r/
13×fma-neg
9×add-exp-log
7×add-cbrt-cube
6×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
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-flip flip-- inv-pow
Calls
3 calls:
Slowest
38.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
7.0ms
(/ x (tan B))
5.0ms
(/ 1 (sin B))

series272.0ms

Calls
3 calls:
Slowest
129.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
128.0ms
(/ x (tan B))
15.0ms
(/ 1 (sin B))

simplify1.5m

Calls
616 calls:
Slowest
935.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))
641.0ms
(fma (/ 1 (sqrt (sin B))) (/ 1 (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
623.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
619.0ms
(- (* (/ 1 (sqrt (sin B))) (/ (tan B) x)) (* (sqrt (sin B)) 1))
614.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune3.4s

Pruning

10 alts after pruning (10 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))
0.2b
(/ 1 (sin B))
0.1b
(/ x (sin B))
0.0b
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
455×add-sqr-sqrt
389×times-frac
372×*-un-lft-identity
355×add-cube-cbrt
299×prod-diff
187×associate-*l*
97×associate-*l/
81×frac-sub
71×associate-/r*
63×associate-/l*
42×associate-*r* div-inv
34×unswap-sqr
23×frac-2neg
21×clear-num
15×add-exp-log
14×*-commutative
13×add-cbrt-cube fma-neg
9×difference-of-squares
7×pow1 distribute-lft-out-- sub-div
6×add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×cbrt-undiv
2×prod-exp cbrt-unprod
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
74.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
17.0ms
(* (/ x (sin B)) (cos B))
6.0ms
(/ x (sin B))
5.0ms
(/ 1 (sin B))

series348.0ms

Calls
4 calls:
Slowest
130.0ms
(* (/ x (sin B)) (cos B))
110.0ms
(- (/ 1 (sin B)) (* (/ x (sin B)) (cos B)))
90.0ms
(/ x (sin B))
18.0ms
(/ 1 (sin B))

simplify2.9m

Calls
910 calls:
Slowest
756.0ms
(- (* 1 (/ (sin B) (cbrt x))) (* (/ (sin B) 1) (* (* (cbrt x) (cbrt x)) (cos B))))
736.0ms
(fma (/ (sqrt 1) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) (cbrt (sin B))) (- (* (cbrt (cos B)) (* (/ x (sin B)) (* (cbrt (cos B)) (cbrt (cos B)))))))
715.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (cbrt 1) (cbrt (sin B))) (- (* (* (/ x (cbrt (sin B))) (cos B)) (/ 1 (* (cbrt (sin B)) (cbrt (sin B)))))))
710.0ms
(fma 1 (/ 1 (sin B)) (- (* (* (/ (cbrt x) (sqrt (sin B))) (cos B)) (/ (* (cbrt x) (cbrt x)) (sqrt (sin B))))))
675.0ms
(- (* 1 (/ (sin B) (cbrt x))) (* (/ (sin B) 1) (* (* (cbrt x) (cbrt x)) (cos B))))

prune5.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
42×*-un-lft-identity
27×times-frac
18×add-cube-cbrt
16×difference-of-squares
9×associate-/l* unswap-sqr
8×distribute-lft-out--
7×associate-*l*
6×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* associate-*r*
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--
Calls
2 calls:
Slowest
70.0ms
(/ (- 1 (* x (cos B))) (sin B))
7.0ms
(* x (cos B))

series159.0ms

Calls
2 calls:
Slowest
102.0ms
(/ (- 1 (* x (cos B))) (sin B))
56.0ms
(* x (cos B))

simplify4.4s

Calls
84 calls:
Slowest
463.0ms
(/ (* (* (- 1 (* x (cos B))) (- 1 (* x (cos B)))) (- 1 (* x (cos B)))) (* (* (sin B) (sin B)) (sin B)))
325.0ms
(* (* (* x x) x) (* (* (cos B) (cos B)) (cos B)))
270.0ms
(- (pow 1 3) (pow (* x (cos B)) 3))
127.0ms
(/ (- 1 (* (sqrt x) (sqrt (cos B)))) (sin B))
120.0ms
(/ (- (sqrt 1) (* (sqrt x) (sqrt (cos B)))) (sin B))

prune823.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (/ (cos B) (sin B)))
0.2b
(/ (cos B) (sin B))
0.2b
(/ 1 (sin B))
0.0b
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
457×add-sqr-sqrt
384×times-frac
381×*-un-lft-identity
357×add-cube-cbrt
299×prod-diff
185×associate-*r*
99×frac-sub
97×associate-*r/
79×associate-/l*
77×associate-/r*
46×div-inv
44×associate-*l*
34×unswap-sqr
33×clear-num
25×frac-2neg
20×un-div-inv
15×add-exp-log
14×*-commutative
13×add-cbrt-cube fma-neg
9×difference-of-squares
7×pow1 sub-div
6×add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u distribute-lft-out--
3×cbrt-undiv distribute-rgt-out--
2×prod-exp cbrt-unprod
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-prod-down pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
50.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
30.0ms
(* x (/ (cos B) (sin B)))
17.0ms
(/ (cos B) (sin B))
5.0ms
(/ 1 (sin B))

series295.0ms

Calls
4 calls:
Slowest
137.0ms
(* x (/ (cos B) (sin B)))
114.0ms
(- (/ 1 (sin B)) (* x (/ (cos B) (sin B))))
25.0ms
(/ (cos B) (sin B))
20.0ms
(/ 1 (sin B))

simplify2.8m

Calls
949 calls:
Slowest
706.0ms
(- (* 1 (- (sin B))) (* (/ (sin B) 1) (* x (- (cos B)))))
687.0ms
(- (* 1 (/ (sin B) (cbrt (cos B)))) (* (/ (sin B) 1) (* x (* (cbrt (cos B)) (cbrt (cos B))))))
652.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sin B)) (- (* (* (sqrt x) (/ (sqrt (cos B)) (sqrt (sin B)))) (* (sqrt x) (/ (sqrt (cos B)) (sqrt (sin B)))))))
630.0ms
(- (* 1 (- (sin B))) (* (/ (sin B) 1) (* x (- (cos B)))))
579.0ms
(- (* (/ 1 1) (/ (sin B) (cbrt (cos B)))) (* (sin B) (* x (* (cbrt (cos B)) (cbrt (cos B))))))

prune5.8s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes149.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample9.2s

Algorithm
intervals
Results
3.7s1741×body1280valid
2.5s1494×body640valid
1.8s4838×body80valid
672.0ms706×body320valid
240.0ms373×body160valid