Details

Time bar (total: 6.0m)

sample802.0ms

Algorithm
intervals
Results
174.0ms56×body640valid
119.0ms45×body1280valid
60.0ms158×body80valid
26.0ms23×body320valid
21.0ms60×body80nan
10.0ms11×body160valid

simplify446.0ms

Calls
1 calls:
Slowest
445.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.1b

localize71.0ms

Local error

Found 4 expressions with local error:

16.7b
(pow (fma 2 x (fma F F 2)) -1/2)
5.3b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.1b
(/ x (tan B))
0.1b
(/ (sin B) F)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
181×times-frac
106×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
45×unpow-prod-down
22×add-exp-log
19×associate-/r*
15×sqr-pow
13×add-cbrt-cube associate-/l*
11×div-exp div-inv
5×pow1 cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow clear-num frac-2neg pow-exp
2×associate-/r/
1×pow-pow tan-quot
Calls
4 calls:
Slowest
15.0ms
(/ (sin B) F)
10.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
7.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
5.0ms
(/ x (tan B))

series646.0ms

Calls
4 calls:
Slowest
266.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
215.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
125.0ms
(/ x (tan B))
40.0ms
(/ (sin B) F)

simplify55.1s

Calls
278 calls:
Slowest
802.0ms
(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
696.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
680.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
664.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
602.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) (sqrt F)))

prune3.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.8b

localize44.0ms

Local error

Found 4 expressions with local error:

16.7b
(pow (fma 2 x (fma F F 2)) -1/2)
0.3b
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
0.3b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
0.1b
(/ x (tan B))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
883×times-frac
408×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
141×unpow-prod-down
56×add-exp-log
47×sqr-pow
43×div-inv
40×div-exp
35×associate-/l*
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
6×pow-to-exp pow-exp
5×pow1
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow clear-num frac-2neg
2×associate-/r/
1×pow-pow tan-quot associate-/l/
Calls
4 calls:
Slowest
27.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
14.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
10.0ms
(/ x (tan B))
5.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series754.0ms

Calls
4 calls:
Slowest
241.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
200.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
190.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
123.0ms
(/ x (tan B))

simplify4.8m

Calls
808 calls:
Slowest
1.2s
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (cbrt (sin B))) (/ (cbrt 1) F))
1.2s
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ (cbrt 1) (cbrt F)))
1.0s
(/ (/ (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) 1))
1.0s
(/ (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B)) (/ (sqrt 1) F))
1.0s
(/ (/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (* (cbrt 1) (cbrt 1)) 1))

prune8.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.8b

localize81.0ms

Local error

Found 4 expressions with local error:

16.7b
(pow (fma 2 x (fma F F 2)) -1/2)
0.3b
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
0.3b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
0.2b
(/ (* x (cos B)) (sin B))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
877×times-frac
402×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
141×unpow-prod-down
59×add-exp-log
47×sqr-pow
43×div-inv
41×div-exp
33×associate-/l*
23×add-cbrt-cube
19×associate-/r*
11×cbrt-undiv
6×pow-to-exp pow-exp
5×pow1
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow clear-num frac-2neg
1×pow-pow prod-exp associate-/r/ cbrt-unprod associate-/l/
Calls
4 calls:
Slowest
28.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
23.0ms
(/ (* x (cos B)) (sin B))
14.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series859.0ms

Calls
4 calls:
Slowest
289.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
247.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
179.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
144.0ms
(/ (* x (cos B)) (sin B))