Details

Time bar (total: 8.6m)

sample258.0ms

Algorithm
intervals
Results
125.0ms58×body1280valid
58.0ms48×body640valid
40.0ms145×body80valid
15.0ms19×body320valid
7.0ms11×body160valid

simplify126.0ms

Calls
1 calls:
Slowest
126.0ms
(+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B)))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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
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
34.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
5.0ms
(/ 1 (sin B))
5.0ms
(/ x (tan B))

series334.0ms

Calls
3 calls:
Slowest
160.0ms
(- (/ 1 (sin B)) (/ x (tan B)))
148.0ms
(/ x (tan B))
26.0ms
(/ 1 (sin B))

simplify1.4m

Calls
616 calls:
Slowest
857.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))
834.0ms
(fma (- (/ x (cbrt (tan B)))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))) (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B))))))
615.0ms
(fma (* (cbrt (/ 1 (sin B))) (cbrt (/ 1 (sin B)))) (cbrt (/ 1 (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
601.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))
579.0ms
(fma (/ (sqrt 1) (sqrt (sin B))) (/ (sqrt 1) (sqrt (sin B))) (- (* (/ x (cbrt (tan B))) (/ 1 (* (cbrt (tan B)) (cbrt (tan B)))))))

prune3.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
1526×times-frac
1056×add-sqr-sqrt
1036×*-un-lft-identity
1026×add-cube-cbrt
676×prod-diff
235×associate-/r*
171×frac-sub
135×associate-/l*
126×associate-/r/
122×div-inv
45×clear-num frac-2neg
15×add-exp-log
13×add-cbrt-cube fma-neg
9×difference-of-squares
6×div-exp add-log-exp
5×pow1 cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-out--
1×rec-exp sub-neg flip3-- diff-log 1-exp pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
58.0ms
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))
20.0ms
(/ (sin B) x)
11.0ms
(/ (cos B) (/ (sin B) x))
9.0ms
(/ 1 (sin B))

series329.0ms

Calls
4 calls:
Slowest
153.0ms
(- (/ 1 (sin B)) (/ (cos B) (/ (sin B) x)))
126.0ms
(/ (cos B) (/ (sin B) x))
32.0ms
(/ (sin B) x)
17.0ms
(/ 1 (sin B))

simplify6.9m

Calls
1895 calls:
Slowest
1.0s
(fma (/ 1 1) (/ 1 (sin B)) (- (* (/ (cos B) (/ (cbrt (sin B)) (sqrt x))) (/ 1 (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt x))))))
839.0ms
(fma (- (/ (cos B) (/ (sqrt (sin B)) x))) (/ 1 (/ (sqrt (sin B)) 1)) (* (/ (cos B) (/ (sqrt (sin B)) x)) (/ 1 (/ (sqrt (sin B)) 1))))
825.0ms
(fma (sqrt (/ 1 (sin B))) (sqrt (/ 1 (sin B))) (- (* (/ (sqrt (cos B)) (/ (cbrt (sin B)) (sqrt x))) (/ (sqrt (cos B)) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt x))))))
825.0ms
(fma 1 (/ 1 (sin B)) (- (* (/ (cos B) (/ (sqrt (sin B)) (cbrt x))) (/ 1 (/ (sqrt (sin B)) (* (cbrt x) (cbrt x)))))))
801.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sin B))) (/ (cbrt 1) (sqrt (sin B))) (- (* (/ (sqrt (cos B)) (/ (sqrt (sin B)) (cbrt x))) (/ (sqrt (cos B)) (/ (sqrt (sin B)) (* (cbrt x) (cbrt x)))))))

prune12.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite159.0ms

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
77.0ms
(- (/ 1 (sin B)) (* (/ (cos B) (sin B)) x))
39.0ms
(* (/ (cos B) (sin B)) x)
17.0ms
(/ (cos B) (sin B))
10.0ms
(/ 1 (sin B))

series310.0ms

Calls
4 calls:
Slowest
153.0ms
(- (/ 1 (sin B)) (* (/ (cos B) (sin B)) x))
116.0ms
(* (/ (cos B) (sin B)) x)
27.0ms
(/ (cos B) (sin B))
14.0ms
(/ 1 (sin B))