Details

Time bar (total: 6.1m)

sample997.0ms

Algorithm
intervals
Results
248.0ms55×body1280valid
157.0ms52×body640valid
69.0ms137×body80valid
41.0ms23×body320valid
24.0ms50×body80nan
12.0ms12×body160valid

simplify705.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
704.0ms
(+ (- (* 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: 13.8b

localize66.0ms

Local error

Found 4 expressions with local error:

19.4b
(pow (fma 2 x (fma F F 2)) -1/2)
6.2b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.2b
(/ x (tan B))
0.1b
(/ (sin B) F)

rewrite64.0ms

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
15.0ms
(/ (sin B) F)
14.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
9.0ms
(/ x (tan B))
6.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series742.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
349.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
227.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
128.0ms
(/ x (tan B))
38.0ms
(/ (sin B) F)

simplify55.8s

Counts
278 → 226
Calls
278 calls:
Slowest
712.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) 1)
704.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
691.0ms
(/ (pow (fma 2 x (fma F F 2)) (/ -1/2 2)) (/ 1 (* (cbrt F) (cbrt F))))
676.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
657.0ms
(/ (* (cbrt (pow (fma 2 x (fma F F 2)) -1/2)) (cbrt (pow (fma 2 x (fma F F 2)) -1/2))) (/ (sqrt (sin B)) (sqrt F)))

prune4.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.1b

localize42.0ms

Local error

Found 4 expressions with local error:

19.4b
(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 (tan B))

rewrite49.0ms

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
16.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
9.0ms
(/ x (tan B))
7.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
2.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series810.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
240.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
234.0ms
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
176.0ms
(/ x (tan B))
161.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))

simplify4.9m

Counts
808 → 509
Calls
808 calls:
Slowest
1.2s
(/ (/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (sqrt (sin B))) (/ (cbrt 1) F))
1.2s
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sqrt (sin B))) (/ (cbrt 1) (sqrt F)))
1.2s
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (cbrt (sin B))) (/ (cbrt 1) F))
1.1s
(/ (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)) (/ 1 F))
1.1s
(/ (/ (pow (cbrt (fma 2 x (fma F F 2))) -1/2) (cbrt (sin B))) (/ 1 F))

prune8.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.1b

localize78.0ms

Local error

Found 4 expressions with local error:

19.4b
(pow (fma 2 x (fma F F 2)) -1/2)
0.5b
(/ 1 (/ (/ 1 F) (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))))
0.3b
(/ (/ 1 F) (/ (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))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
5156×times-frac
2163×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
609×unpow-prod-down
358×associate-/r*
206×add-exp-log
203×sqr-pow
199×div-inv
181×div-exp
36×add-cbrt-cube
33×rec-exp 1-exp
23×associate-/l*
22×cbrt-undiv
18×pow-to-exp pow-exp
6×pow1 associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow clear-num frac-2neg
1×pow-pow pow-flip inv-pow associate-/l/
Counts
4 → 1861
Calls
4 calls:
Slowest
43.0ms
(/ 1 (/ (/ 1 F) (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))))
23.0ms
(/ (/ 1 F) (/ (pow (fma 2 x (fma F F 2)) -1/2) (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)

series846.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
321.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
215.0ms
(/ 1 (/ (/ 1 F) (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))))
156.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B))
154.0ms
(/ (/ 1 F) (/ (pow (fma 2 x (fma F F 2)) -1/2) (sin B)))