Details

Time bar (total: 6.6m)

sample451.0ms

Algorithm
intervals
Results
94.0ms34×body1280valid
83.0ms51×body640valid
68.0ms175×body80valid
60.0ms16×body320valid
15.0ms42×body80nan
7.0ms9×body160valid

simplify485.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
485.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

localize44.0ms

Local error

Found 4 expressions with local error:

14.6b
(pow (fma 2 x (fma F F 2)) -1/2)
4.1b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.1b
(/ (sin B) F)
0.1b
(/ x (tan B))

rewrite33.0ms

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
Counts
4 → 214
Calls
4 calls:
Slowest
8.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
7.0ms
(/ (sin B) F)
5.0ms
(/ x (tan B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series761.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
319.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
209.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
178.0ms
(/ x (tan B))
54.0ms
(/ (sin B) F)

simplify54.3s

Counts
278 → 226
Calls
278 calls:
Slowest
699.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
633.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (cbrt (sin B)) (sqrt F)))
605.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
599.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
588.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))

prune3.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.4b

localize55.0ms

Local error

Found 4 expressions with local error:

14.6b
(pow (fma 2 x (fma F F 2)) -1/2)
0.4b
(/ (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))

rewrite54.0ms

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/
Counts
4 → 497
Calls
4 calls:
Slowest
13.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
11.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
5.0ms
(/ x (tan B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
634.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
209.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
174.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
147.0ms
(/ x (tan B))

simplify4.7m

Counts
808 → 509
Calls
808 calls:
Slowest
1.1s
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sqrt (sin B))) (/ (sqrt 1) F))
1.1s
(/ (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (cbrt (sin B))) (/ (sqrt 1) (cbrt F)))
1.1s
(/ (/ (pow (cbrt (fma 2 x (fma F F 2))) -1/2) (sqrt (sin B))) (/ (sqrt 1) (cbrt F)))
1.0s
(/ (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B)) (/ (cbrt 1) (sqrt F)))
1.0s
(/ (/ (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) 1))

prune8.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.4b

localize50.0ms

Local error

Found 4 expressions with local error:

14.6b
(pow (fma 2 x (fma F F 2)) -1/2)
0.4b
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
0.3b
(/ (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) (/ 1 F))
0.1b
(/ x (tan B))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
191×add-exp-log
109×div-exp
60×prod-exp
55×add-sqr-sqrt times-frac
40×*-un-lft-identity
37×add-cube-cbrt
32×add-cbrt-cube
28×rec-exp 1-exp
21×pow-to-exp pow-exp
16×associate-/r*
13×cbrt-undiv associate-*r*
9×unpow-prod-down unswap-sqr
7×associate-*l*
6×cbrt-unprod
5×pow1 div-inv sqr-pow
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×pow-unpow
2×clear-num frac-2neg associate-*r/ associate-/r/ un-div-inv associate-/l/
1×pow-pow tan-quot *-commutative
Counts
4 → 208
Calls
4 calls:
Slowest
33.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
26.0ms
(/ (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) (/ 1 F))
5.0ms
(/ x (tan B))
2.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series824.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
272.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
233.0ms
(/ (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) (/ 1 F))
172.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
147.0ms
(/ x (tan B))

simplify36.1s

Counts
198 → 220
Calls
198 calls:
Slowest
688.0ms
(- (+ (* (log (fma 2 x (fma F F 2))) -1/2) (- (log (sin B)))) (- (log 1) (log F)))
635.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
574.0ms
(* (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)) (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))))
567.0ms
(/ (* (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)) (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B)))) (* (* (/ 1 F) (/ 1 F)) (/ 1 F)))
549.0ms
(/ (* (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)) (/ (* (* 1 1) 1) (* (* (sin B) (sin B)) (sin B)))) (* (* (/ 1 F) (/ 1 F)) (/ 1 F)))

prune3.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.4b

localize49.0ms

Local error

Found 4 expressions with local error:

14.6b
(pow (fma 2 x (fma F F 2)) -1/2)
0.4b
(/ (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))

rewrite70.0ms

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/
Counts
4 → 490
Calls
4 calls:
Slowest
30.0ms
(/ (/ (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))
12.0ms
(/ (* x (cos B)) (sin B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series830.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
301.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
227.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
163.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
139.0ms
(/ (* x (cos B)) (sin B))