Details

Time bar (total: 10.4s)

sample30.0ms

Algorithm
intervals
Results
8.0ms329×body80valid
7.0ms278×body80nan

simplify6.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0810
11510
22210
33910
47010
512710
623310
745510
8189610
done500010

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
2.6b
(- (* y y) (* z z))
25.9b
(sqrt (- (* y y) (* z z)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
7×add-cube-cbrt *-un-lft-identity associate-*r*
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div
3×expm1-log1p-u flip3-- associate-*l* flip-- log1p-expm1-u difference-of-squares
2×associate-*r/ unswap-sqr
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
3 → 62
Calls
3 calls:
15.0ms
(* x (sqrt (- (* y y) (* z z))))
3.0ms
(- (* y y) (* z z))
4.0ms
(sqrt (- (* y y) (* z z)))

series151.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(* x (sqrt (- (* y y) (* z z))))
31.0ms
(- (* y y) (* z z))
46.0ms
(sqrt (- (* y y) (* z z)))

simplify1.1s

Counts
71 → 71
Iterations

Useful iterations: done (1.1s)

IterNodesCost
094839
1201760
2569676
32169676
done5001675

prune166.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (sqrt (* (+ y z) (- y z))))
25.9b
(sqrt (* (+ y z) (- y z)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div
12×associate-*r/
8×frac-times
7×pow1
6×add-sqr-sqrt flip3-- flip3-+ flip-- flip-+
4×add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* associate-*l/ add-cbrt-cube
3×associate-*l*
2×expm1-log1p-u sqrt-pow1 pow-prod-down sqrt-prod log1p-expm1-u add-log-exp
1×pow1/2 prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 50
Calls
2 calls:
22.0ms
(* x (sqrt (* (+ y z) (- y z))))
12.0ms
(sqrt (* (+ y z) (- y z)))

series145.0ms

Counts
2 → 6
Calls
2 calls:
88.0ms
(* x (sqrt (* (+ y z) (- y z))))
57.0ms
(sqrt (* (+ y z) (- y z)))

simplify1000.0ms

Counts
56 → 56
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
099758
1215685
2659659
32450659
done5000659

prune143.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (/ (fabs (* (+ y z) (- y z))) (sqrt (* (- y z) (+ y z)))))
25.9b
(sqrt (* (- y z) (+ y z)))
25.9b
(/ (fabs (* (+ y z) (- y z))) (sqrt (* (- y z) (+ y z))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×times-frac
24×sqrt-div associate-*r*
21×add-cube-cbrt *-un-lft-identity
16×associate-/r/
12×frac-times
10×add-exp-log add-cbrt-cube
9×flip3-- flip3-+ flip-- flip-+
8×pow1 sqrt-prod
7×associate-*r/
6×associate-*l/
4×associate-/r*
3×expm1-log1p-u associate-*l* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv sqrt-pow1 div-exp pow-prod-down prod-exp cbrt-unprod div-inv unswap-sqr
1×frac-2neg pow1/2 clear-num *-commutative
Counts
3 → 107
Calls
3 calls:
30.0ms
(* x (/ (fabs (* (+ y z) (- y z))) (sqrt (* (- y z) (+ y z)))))
6.0ms
(sqrt (* (- y z) (+ y z)))
8.0ms
(/ (fabs (* (+ y z) (- y z))) (sqrt (* (- y z) (+ y z))))

series230.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(* x (/ (fabs (* (+ y z) (- y z))) (sqrt (* (- y z) (+ y z)))))
62.0ms
(sqrt (* (- y z) (+ y z)))
89.0ms
(/ (fabs (* (+ y z) (- y z))) (sqrt (* (- y z) (+ y z))))

simplify842.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (143.0ms)

IterNodesCost
01702514
13852409
212632241
done50002241

prune362.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize2.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes147.0ms

bsearch12.0ms