Details

Time bar (total: 9.9m)

sample774.0ms

Algorithm
intervals
Results
474.0ms53×body1280valid
77.0ms47×body640valid
56.0ms144×body80valid
18.0ms18×body320valid
18.0ms51×body80nan
9.0ms11×body160valid

simplify430.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
429.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize50.0ms

Local error

Found 4 expressions with local error:

17.6b
(pow (fma 2 x (fma F F 2)) -1/2)
6.7b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.2b
(/ x (tan B))
0.1b
(/ (sin B) F)

rewrite37.0ms

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
10.0ms
(/ (sin B) F)
9.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
5.0ms
(/ x (tan B))
5.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series795.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
310.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
252.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
182.0ms
(/ x (tan B))
51.0ms
(/ (sin B) F)

simplify52.9s

Counts
278 → 226
Calls
278 calls:
Slowest
692.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
610.0ms
(/ (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (/ 1 (* (cbrt F) (cbrt F))))
598.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
598.0ms
(/ (* (cbrt (pow (fma 2 x (fma F F 2)) -1/2)) (cbrt (pow (fma 2 x (fma F F 2)) -1/2))) 1)
596.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (sqrt (sin B)) 1))

prune3.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.0b

localize72.0ms

Local error

Found 4 expressions with local error:

17.6b
(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 (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/
Counts
4 → 497
Calls
4 calls:
Slowest
28.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
21.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
10.0ms
(/ x (tan B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series840.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
301.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
207.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
192.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
140.0ms
(/ x (tan B))

simplify4.8m

Counts
808 → 509
Calls
808 calls:
Slowest
1.3s
(/ (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (* (cbrt (sin B)) (cbrt (sin B)))) (/ (sqrt 1) 1))
1.1s
(/ (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B)) (/ (sqrt 1) (sqrt F)))
1.1s
(/ (/ (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (cbrt (sin B))) (/ (cbrt 1) (sqrt F)))
1.1s
(/ (/ (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (sin B)) (/ (cbrt 1) (cbrt F)))
1.1s
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (cbrt (sin B))) (/ (sqrt 1) (cbrt F)))

prune9.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.0b

localize58.0ms

Local error

Found 4 expressions with local error:

17.6b
(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))
0.2b
(/ x (tan B))

rewrite49.0ms

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
17.0ms
(/ (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) (/ 1 F))
15.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
9.0ms
(/ x (tan B))
2.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series852.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
288.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
245.0ms
(/ (* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B))) (/ 1 F))
196.0ms
(* (pow (fma 2 x (fma F F 2)) -1/2) (/ 1 (sin B)))
124.0ms
(/ x (tan B))

simplify35.9s

Counts
198 → 220
Calls
198 calls:
Slowest
652.0ms
(- (+ (log (pow (fma 2 x (fma F F 2)) -1/2)) (- (log (sin B)))) (log (/ 1 F)))
608.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
593.0ms
(/ (* (* (* (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)))
574.0ms
(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sqrt (/ 1 (sin B))))
540.0ms
(* (* (* (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))))

prune3.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.0b

localize59.0ms

Local error

Found 4 expressions with local error:

17.6b
(sqrt (fma 2 x (fma F F 2)))
17.6b
(sqrt (fma 2 x (fma F F 2)))
0.4b
(* (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B)) (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F)))
0.4b
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
631×times-frac
491×add-sqr-sqrt
275×*-un-lft-identity
255×add-cube-cbrt
236×unpow-prod-down
201×add-exp-log
135×associate-*r*
129×div-exp
124×sqrt-prod
65×unswap-sqr
58×sqr-pow
52×prod-exp
34×associate-*l*
33×pow-to-exp pow-exp
30×add-cbrt-cube
24×div-inv
15×rec-exp 1-exp
13×associate-/r*
12×cbrt-undiv
10×associate-/l*
8×pow1
6×cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 520
Calls
4 calls:
Slowest
58.0ms
(* (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B)) (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F)))
25.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F))
2.0ms
(sqrt (fma 2 x (fma F F 2)))
2.0ms
(sqrt (fma 2 x (fma F F 2)))

series916.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
371.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F))
200.0ms
(* (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B)) (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F)))
182.0ms
(sqrt (fma 2 x (fma F F 2)))
163.0ms
(sqrt (fma 2 x (fma F F 2)))

simplify3.1m

Counts
678 → 532
Calls
678 calls:
Slowest
738.0ms
(* (/ (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (* (* (sin B) (sin B)) (sin B))) (/ (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (* (* (/ 1 F) (/ 1 F)) (/ 1 F))))
713.0ms
(+ (log (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sin B))) (- (log (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (- (log 1) (log F))))
687.0ms
(/ (pow (sqrt (sqrt (fma 2 x (fma F F 2)))) -1/2) (/ (sqrt 1) (sqrt F)))
687.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) (/ -1/2 2)) (/ (cbrt 1) (sqrt F)))
682.0ms
(* (/ (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (* (* (sin B) (sin B)) (sin B))) (* (* (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F)) (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F))) (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 F))))

prune10.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 11.0b

regimes487.0ms

bsearch6.0ms

end0.0ms