Details

Time bar (total: 20.4s)

sample41.0ms

Algorithm
intervals
Results
12.0ms318×body80valid
11.0ms315×body80nan

simplify11.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11510
22210
33910
47110
516410
627510
751810
8191210
done500110

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
1.0b
(- (* y y) (* z z))
26.1b
(sqrt (- (* y y) (* z z)))

rewrite104.0ms

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:
54.0ms
(* x (sqrt (- (* y y) (* z z))))
18.0ms
(- (* y y) (* z z))
30.0ms
(sqrt (- (* y y) (* z z)))

series234.0ms

Counts
3 → 9
Calls
3 calls:
107.0ms
(* x (sqrt (- (* y y) (* z z))))
58.0ms
(- (* y y) (* z z))
69.0ms
(sqrt (- (* y y) (* z z)))

simplify1.5s

Counts
71 → 71
Iterations

Useful iterations: done (1.5s)

IterNodesCost
094839
1199758
2491676
31629676
done5002671

prune239.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* y y) (* z z))
1.0b
(- (* y y) (* z z))
26.1b
(sqrt (- (* y y) (* z z)))
26.1b
(sqrt (- (* y y) (* z z)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 70
Calls
4 calls:
9.0ms
(- (* y y) (* z z))
17.0ms
(- (* y y) (* z z))
21.0ms
(sqrt (- (* y y) (* z z)))
17.0ms
(sqrt (- (* y y) (* z z)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* y y) (* z z))
58.0ms
(- (* y y) (* z z))
82.0ms
(sqrt (- (* y y) (* z z)))
65.0ms
(sqrt (- (* y y) (* z z)))

simplify1.5s

Counts
82 → 82
Iterations

Useful iterations: done (1.5s)

IterNodesCost
062912
1132824
2347722
31112722
done5001712

prune475.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize6.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune7.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
0.2b
(* (sqrt (+ y z)) (sqrt (- y z)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-div
17×add-sqr-sqrt
13×sqrt-prod
12×associate-*r/
11×pow1 *-un-lft-identity
10×associate-*l*
9×add-exp-log associate-*r* add-cbrt-cube
8×frac-times
7×add-cube-cbrt
6×flip3-- flip3-+ pow-prod-down flip-- flip-+
4×associate-*l/ prod-exp cbrt-unprod unswap-sqr
2×expm1-log1p-u sqrt-pow1 pow1/2 *-commutative log1p-expm1-u add-log-exp
1×sqrt-unprod distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
2 → 71
Calls
2 calls:
61.0ms
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
60.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

series233.0ms

Counts
2 → 6
Calls
2 calls:
128.0ms
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
105.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

simplify4.1s

Counts
77 → 77
Iterations

Useful iterations: done (4.1s)

IterNodesCost
01411108
1321995
2942945
33537937
done5000935

prune296.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes1.0ms