Details

Time bar (total: 24.1s)

sample83.0ms

Algorithm
intervals
Results
20.0ms318×body80valid
19.0ms315×body80nan

simplify14.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11410
22110
33610
46210
513310
619110
737310
8154110
done500010

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize17.0ms

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)))

rewrite59.0ms

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×flip3-- associate-*l* flip-- difference-of-squares
2×associate-*r/ unswap-sqr
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
3 → 54
Calls
3 calls:
33.0ms
(* x (sqrt (- (* y y) (* z z))))
10.0ms
(- (* y y) (* z z))
14.0ms
(sqrt (- (* y y) (* z z)))

series191.0ms

Counts
3 → 9
Calls
3 calls:
99.0ms
(* x (sqrt (- (* y y) (* z z))))
35.0ms
(- (* y y) (* z z))
57.0ms
(sqrt (- (* y y) (* z z)))

simplify1.1s

Counts
63 → 63
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
085765
1185697
2443613
31486613
done5001613

prune154.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

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)))

rewrite52.0ms

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 flip3-- sqrt-div add-cbrt-cube flip-- difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 58
Calls
4 calls:
9.0ms
(- (* y y) (* z z))
9.0ms
(- (* y y) (* z z))
15.0ms
(sqrt (- (* y y) (* z z)))
18.0ms
(sqrt (- (* y y) (* z z)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* y y) (* z z))
46.0ms
(- (* y y) (* z z))
71.0ms
(sqrt (- (* y y) (* z z)))
60.0ms
(sqrt (- (* y y) (* z z)))

simplify3.4s

Counts
70 → 70
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
055808
1120744
2301640
3975640
44860640
done5000640

prune318.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune4.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize17.0ms

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)))

rewrite103.0ms

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×sqrt-pow1 pow1/2 *-commutative add-log-exp
1×sqrt-unprod distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
2 → 67
Calls
2 calls:
58.0ms
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
42.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

series196.0ms

Counts
2 → 6
Calls
2 calls:
119.0ms
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
76.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

simplify2.9s

Counts
73 → 73
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01371064
1308955
2912911
33399903
done5002903

prune242.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes535.0ms

bsearch42.0ms