Details

Time bar (total: 6.1m)

sample391.0ms

Algorithm
intervals
Results
108.0ms53×body1280valid
80.0ms162×body80valid
58.0ms38×body640valid
51.0ms53×body80nan
15.0ms14×body320valid
9.0ms14×body160valid

simplify869.0ms

Calls
1 calls:
Slowest
868.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.2b

localize57.0ms

Local error

Found 4 expressions with local error:

18.0b
(pow (fma 2 x (fma F F 2)) -1/2)
9.1b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.1b
(/ x (tan B))
0.1b
(/ (sin B) F)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
181×times-frac
108×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
45×unpow-prod-down
22×associate-/r* add-exp-log
16×associate-/l*
15×sqr-pow
13×add-cbrt-cube
11×div-exp div-inv
10×associate-/r/
5×pow1 cbrt-undiv
4×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow pow-exp
1×pow-pow tan-quot
Calls
4 calls:
Slowest
20.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
15.0ms
(/ (sin B) F)
10.0ms
(/ x (tan B))
7.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series734.0ms

Calls
4 calls:
Slowest
274.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
232.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
184.0ms
(/ x (tan B))
44.0ms
(/ (sin B) F)

simplify55.6s

Calls
285 calls:
Slowest
719.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
688.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
649.0ms
(/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (* (cbrt (/ (sin B) F)) (cbrt (/ (sin B) F))))
597.0ms
(/ (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))) (sqrt F)))
562.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) 1)

prune4.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.0b

localize12.0ms

Local error

Found 4 expressions with local error:

18.0b
(pow (fma 2 x (fma F F 2)) -1/2)
0.3b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
0.3b
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
0.1b
(/ x (tan B))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
883×times-frac
413×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
144×unpow-prod-down
56×add-exp-log
48×sqr-pow
45×associate-/l*
43×div-inv
40×div-exp
25×associate-/r*
20×add-cbrt-cube
13×associate-/l/
10×cbrt-undiv associate-/r/
6×pow-to-exp pow-exp
5×pow1 clear-num frac-2neg
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow
1×pow-pow tan-quot
Calls
4 calls:
Slowest
34.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
19.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
6.0ms
(/ x (tan B))
2.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series823.0ms

Calls
4 calls:
Slowest
280.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
223.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
185.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
134.0ms
(/ x (tan B))

simplify4.9m

Calls
825 calls:
Slowest
1.2s
(/ (/ (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (cbrt (sin B))) (/ (cbrt 1) (cbrt F)))
1.1s
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (cbrt (sin B))) (/ (cbrt 1) F))
1.1s
(/ (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B)) (/ (sqrt 1) (sqrt F)))
1.0s
(/ (/ (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) 1) (* (cbrt (/ 1 F)) (cbrt (/ 1 F))))
990.0ms
(/ (/ (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)))) (/ (sqrt 1) 1))

prune9.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.0b

localize16.0ms

Local error

Found 4 expressions with local error:

18.0b
(pow (fma 2 x (fma F F 2)) -1/2)
0.3b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
0.3b
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
0.2b
(/ (* x (cos B)) (sin B))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
910×times-frac
438×add-sqr-sqrt
430×*-un-lft-identity add-cube-cbrt
144×unpow-prod-down
59×add-exp-log
54×associate-/l*
48×sqr-pow
43×div-inv
41×div-exp
25×associate-/r*
23×add-cbrt-cube
13×associate-/l/
12×associate-*r* associate-*l*
11×cbrt-undiv
9×associate-/r/
6×pow-to-exp pow-exp
5×pow1 clear-num frac-2neg
4×expm1-log1p-u rec-exp 1-exp *-commutative insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-unpow
1×pow-pow prod-exp cbrt-unprod
Calls
4 calls:
Slowest
33.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
18.0ms
(/ (* x (cos B)) (sin B))
15.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series853.0ms

Calls
4 calls:
Slowest
260.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
229.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
189.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
176.0ms
(/ (* x (cos B)) (sin B))