Details

Time bar (total: 6.6m)

sample60.0ms

Algorithm
intervals
Results
41.0ms316×body80valid

simplify104.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
104.0ms
(fabs (- (/ (+ x 4) y) (* (/ x y) z)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize17.0ms

Local error

Found 3 expressions with local error:

2.1b
(* (/ x y) z)
0.0b
(- (/ (+ x 4) y) (* (/ x y) z))
0.0b
(/ (+ x 4) y)

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
46×times-frac
41×add-sqr-sqrt
36×add-cube-cbrt
16×fma-neg prod-diff
13×associate-*l*
10×add-cbrt-cube add-exp-log distribute-lft-out
5×pow1 add-log-exp
4×div-inv associate-/l*
3×expm1-log1p-u associate-/r* associate-*r* associate-*l/ insert-posit16 log1p-expm1-u
2×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr associate-/l/
1×clear-num sub-neg frac-2neg flip3-+ flip3-- diff-log pow-prod-down *-commutative frac-sub flip-+ flip-- sub-div
Counts
3 → 120
Calls
3 calls:
Slowest
51.0ms
(- (/ (+ x 4) y) (* (/ x y) z))
26.0ms
(/ (+ x 4) y)
19.0ms
(* (/ x y) z)

series135.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
59.0ms
(- (/ (+ x 4) y) (* (/ x y) z))
41.0ms
(* (/ x y) z)
35.0ms
(/ (+ x 4) y)

simplify6.2s

Counts
115 → 129
Calls
115 calls:
Slowest
328.0ms
(/ (* (* (+ x 4) (+ x 4)) (+ x 4)) (* (* y y) y))
325.0ms
(fma (/ 1 (sqrt y)) (/ (+ x 4) (sqrt y)) (- (* z (/ x y))))
275.0ms
(fma (/ 1 (* (cbrt y) (cbrt y))) (/ (+ x 4) (cbrt y)) (- (* z (/ x y))))
272.0ms
(* (* (* (/ x y) (/ x y)) (/ x y)) (* (* z z) z))
268.0ms
(fma (/ 1 (sqrt y)) (/ (+ x 4) (sqrt y)) (- (* z (/ x y))))

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 3 expressions with local error:

2.1b
(/ z (/ y x))
0.0b
(- (/ (+ 4 x) y) (/ z (/ y x)))
0.0b
(/ (+ 4 x) y)

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
1696×times-frac
1263×*-un-lft-identity
995×add-sqr-sqrt
974×add-cube-cbrt
704×prod-diff
140×distribute-lft-out
115×div-inv
17×associate-/r/
16×associate-/r* fma-neg
10×add-cbrt-cube add-exp-log
7×associate-/l*
6×difference-of-squares
5×add-log-exp
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out--
2×clear-num frac-2neg associate-/l/
1×sub-neg flip3-+ flip3-- diff-log frac-sub flip-+ flip--
Counts
3 → 854
Calls
3 calls:
Slowest
81.0ms
(- (/ (+ 4 x) y) (/ z (/ y x)))
26.0ms
(/ (+ 4 x) y)
12.0ms
(/ z (/ y x))

series131.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
67.0ms
(- (/ (+ 4 x) y) (/ z (/ y x)))
33.0ms
(/ (+ 4 x) y)
31.0ms
(/ z (/ y x))

simplify6.3m

Counts
1581 → 863
Calls
1581 calls:
Slowest
901.0ms
(fma (+ 4 x) (/ 1 y) (- (* (/ z (/ (sqrt y) (cbrt x))) (/ 1 (/ (sqrt y) (* (cbrt x) (cbrt x)))))))
888.0ms
(fma (/ 1 1) (/ (+ 4 x) y) (- (* (/ (cbrt z) (/ y (sqrt x))) (/ (* (cbrt z) (cbrt z)) (/ 1 (sqrt x))))))
861.0ms
(fma (/ (* (cbrt (+ 4 x)) (cbrt (+ 4 x))) (* (cbrt y) (cbrt y))) (/ (cbrt (+ 4 x)) (cbrt y)) (- (* (/ (sqrt z) (/ y (cbrt x))) (/ (sqrt z) (/ 1 (* (cbrt x) (cbrt x)))))))
784.0ms
(fma (/ 1 (sqrt y)) (/ (+ 4 x) (sqrt y)) (- (* (/ (cbrt z) (/ (sqrt y) x)) (/ (* (cbrt z) (cbrt z)) (/ (sqrt y) 1)))))
781.0ms
(fma (* (cbrt (/ (+ 4 x) y)) (cbrt (/ (+ 4 x) y))) (cbrt (/ (+ 4 x) y)) (- (* (/ (cbrt z) (/ y (sqrt x))) (/ (* (cbrt z) (cbrt z)) (/ 1 (sqrt x))))))

prune11.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 3 expressions with local error:

2.1b
(/ z (/ y x))
0.0b
(- (/ (+ x 4) y) (/ z (/ y x)))
0.0b
(/ (+ x 4) y)

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
1696×times-frac
1263×*-un-lft-identity
995×add-sqr-sqrt
974×add-cube-cbrt
704×prod-diff
140×distribute-lft-out
115×div-inv
17×associate-/r/
16×associate-/r* fma-neg
10×add-cbrt-cube add-exp-log
7×associate-/l*
6×difference-of-squares
5×add-log-exp
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out--
2×clear-num frac-2neg associate-/l/
1×sub-neg flip3-+ flip3-- diff-log frac-sub flip-+ flip--
Counts
3 → 854
Calls
3 calls:
Slowest
64.0ms
(- (/ (+ x 4) y) (/ z (/ y x)))
27.0ms
(/ (+ x 4) y)
6.0ms
(/ z (/ y x))

series184.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
81.0ms
(- (/ (+ x 4) y) (/ z (/ y x)))
57.0ms
(/ (+ x 4) y)
46.0ms
(/ z (/ y x))