Details

Time bar (total: 9.9m)

sample113.0ms

Algorithm
intervals
Results
61.0ms105×body1280valid
26.0ms126×body80valid
6.0ms12×body640valid
3.0ms11×body320valid
1.0ms2×body160valid

simplify48.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
48.0ms
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize26.0ms

Local error

Found 1 expressions with local error:

1.1b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
23×add-sqr-sqrt
21×prod-diff
16×sqrt-prod
15×add-cube-cbrt
4×distribute-lft-out difference-of-squares
3×fma-neg distribute-lft-out-- add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u flip--
Counts
1 → 46
Calls
1 calls:
Slowest
51.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series514.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
513.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify4.0s

Counts
61 → 49
Calls
61 calls:
Slowest
296.0ms
(- (+ (* 1/8 (pow x 2)) (* 69/1024 (pow x 6))) (* 11/128 (pow x 4)))
277.0ms
(- (+ (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))) 1) (+ (* 1/4 (/ 1 (* x (sqrt 1/2)))) (sqrt 1/2)))
254.0ms
(- (+ (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))) (+ (* 1/4 (/ 1 (* x (sqrt 1/2)))) 1)) (sqrt 1/2))
200.0ms
(fma 1 1 (- (* (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))))
191.0ms
(fma (sqrt 1) (sqrt 1) (- (* (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))))

prune412.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize33.0ms

Local error

Found 2 expressions with local error:

1.1b
(log (exp (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
1.1b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
47×add-sqr-sqrt
42×prod-diff
32×sqrt-prod
31×add-cube-cbrt
26×log-prod
23×exp-sum
11×log-pow
10×exp-prod
8×distribute-lft-out difference-of-squares
6×distribute-lft-out--
4×add-log-exp
3×pow1 fma-neg
2×expm1-log1p-u sub-neg add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×log-div flip3-- exp-diff diff-log rem-log-exp flip--
Counts
2 → 95
Calls
2 calls:
Slowest
184.0ms
(log (exp (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
40.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

series276.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
140.0ms
(log (exp (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
136.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify8.4s

Counts
101 → 101
Calls
101 calls:
Slowest
357.0ms
(log (exp (fma (sqrt 1) (sqrt 1) (- (* (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))))))
335.0ms
(log (exp (fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (cbrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))))))
334.0ms
(- (+ (* 1/32 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3)))) 1) (+ (* 1/4 (/ 1 (* x (sqrt 1/2)))) (sqrt 1/2)))
315.0ms
(- (+ (* 1/8 (pow x 2)) (* 69/1024 (pow x 6))) (* 11/128 (pow x 4)))
304.0ms
(- (+ (* 1/8 (pow x 2)) (* 69/1024 (pow x 6))) (* 11/128 (pow x 4)))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize71.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
0.5b
(pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)
0.5b
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
241×*-un-lft-identity
240×prod-diff
208×add-sqr-sqrt
190×unpow-prod-down cube-prod
150×sqrt-prod
140×add-cube-cbrt
54×sqrt-div
46×sqr-pow
36×distribute-lft-out difference-of-squares
35×cube-mult
34×unpow3
28×flip3-+ flip-+
22×associate-*r/
21×pow1
16×frac-add
14×distribute-lft-out--
12×frac-times fma-neg
11×swap-sqr
9×sqrt-pow1 pow1/2
8×add-log-exp
7×add-cbrt-cube associate-*r* associate-*l* add-exp-log
6×associate-*l/
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr
2×cube-div
1×pow2 pow-to-exp difference-cubes +-commutative sum-log sub-neg rem-square-sqrt fma-def pow-plus distribute-rgt-out flip3-- sqrt-unprod diff-log pow-exp prod-exp *-commutative cbrt-unprod sqrt-pow2 flip-- rem-cube-cbrt
Counts
4 → 454
Calls
4 calls:
Slowest
96.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
81.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
21.0ms
(+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
11.0ms
(pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)

series552.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
177.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
172.0ms
(+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
142.0ms
(pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)
61.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify3.2m

Counts
743 → 466
Calls
743 calls:
Slowest
779.0ms
(fma (- (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)) (pow (sqrt 1) 3) (* (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3) (pow (sqrt 1) 3)))
744.0ms
(fma 1 (pow 1 3) (- (* (sqrt (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)) (sqrt (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)))))
715.0ms
(fma (pow 1 3) (pow 1 3) (- (* (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3) (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))))
713.0ms
(fma 1 (pow 1 3) (- (* (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3) (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))))
704.0ms
(fma 1 (* 1 1) (- (* (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3) (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))))

prune6.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
0.6b
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
0.6b
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
0.5b
(* (* (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))))

rewrite959.0ms

Algorithm
rewrite-expression-head
Rules
720×prod-diff
659×*-un-lft-identity
601×add-sqr-sqrt
585×unpow-prod-down cube-prod
375×add-cube-cbrt
368×sqrt-prod
147×sqr-pow
144×difference-of-squares
103×cube-mult
99×unpow3
88×distribute-lft-out
57×associate-*r*
56×distribute-lft-out--
55×cbrt-prod
54×cbrt-div
36×fma-neg
30×flip3-- flip--
28×frac-times
23×pow1
14×associate-*l/
10×add-log-exp
9×pow1/3 add-exp-log pow-prod-up
8×associate-*r/
6×pow-plus
5×add-cbrt-cube pow-prod-down
4×expm1-log1p-u difference-cubes insert-posit16 log1p-expm1-u
3×sub-neg diff-log prod-exp pow-sqr cbrt-unprod
2×pow2 unswap-sqr
1×associate-*l* pow3 *-commutative
Counts
4 → 1069
Calls
4 calls:
Slowest
687.0ms
(* (* (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))))
100.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
78.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
51.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))

series830.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
224.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
214.0ms
(* (* (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)))) (cbrt (- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))))
199.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
192.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))

simplify6.2m

Counts
1913 → 1081
Calls
1913 calls:
Slowest
893.0ms
(fma (- (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
773.0ms
(fma (* (cbrt (pow 1 3)) (cbrt (pow 1 3))) (cbrt (pow 1 3)) (- (* (pow (sqrt (cbrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3) (pow (sqrt (* (cbrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (cbrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) 3))))
736.0ms
(fma (pow 1 3) (pow 1 3) (- (* (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3) (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))))
714.0ms
(fma (pow 1 3) (pow 1 3) (- (* (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3) (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))))
684.0ms
(fma (pow 1 3) (pow 1 3) (- (* (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3) (pow (sqrt (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))))