Details

Time bar (total: 2.2s)

sample37.0ms

Algorithm
intervals
Results
11.0ms309×body80nan
9.0ms316×body80valid

simplify93.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0155
1225
2395
3715
41675
52985
65455
721425
850015

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 23.4b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
1.8b
(- (* y y) (* z z))
22.5b
(sqrt (- (* y y) (* z z)))

rewrite16.0ms

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:
7.0ms
(* x (sqrt (- (* y y) (* z z))))
4.0ms
(- (* y y) (* z z))
4.0ms
(sqrt (- (* y y) (* z z)))

series164.0ms

Counts
3 → 9
Calls
3 calls:
80.0ms
(* x (sqrt (- (* y y) (* z z))))
37.0ms
(- (* y y) (* z z))
47.0ms
(sqrt (- (* y y) (* z z)))

simplify83.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0202397
1786374
23192368
35001364

prune181.0ms

Filtered
71 candidates to 54 candidates (76.1%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New67471
Fresh000
Picked101
Done000
Total68472

Merged error: 0.3b

Counts
72 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (* y y) (* z z))
1.8b
(- (* y y) (* z z))
23.3b
(cbrt (- (* y y) (* z z)))
23.3b
(cbrt (- (* y y) (* z z)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod add-log-exp
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg fma-neg pow1/3 diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
4.0ms
(- (* y y) (* z z))
4.0ms
(- (* y y) (* z z))
4.0ms
(cbrt (- (* y y) (* z z)))
3.0ms
(cbrt (- (* y y) (* z z)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* y y) (* z z))
34.0ms
(- (* y y) (* z z))
119.0ms
(cbrt (- (* y y) (* z z)))
110.0ms
(cbrt (- (* y y) (* z z)))

simplify64.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0172482
1568444
21862432
35002420

prune277.0ms

Filtered
78 candidates to 66 candidates (84.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New78078
Fresh033
Picked011
Done000
Total78482

Merged error: 0.3b

Counts
82 → 4

localize2.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

prune4.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New000
Fresh022
Picked011
Done011
Total044

Merged error: 0.3b

Counts
4 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- y z))
0.0b
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
0.0b
(sqrt (+ y z))
0.3b
(* (sqrt (+ y z)) (sqrt (- y z)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
27×add-sqr-sqrt
22×sqrt-prod
19×*-un-lft-identity
15×pow1
12×associate-*r/
11×add-exp-log add-cube-cbrt add-cbrt-cube
10×associate-*l*
9×associate-*r*
8×frac-times
7×flip3-- flip3-+ flip-- flip-+
6×pow-prod-down
4×expm1-log1p-u sqrt-pow1 pow1/2 associate-*l/ prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×rem-sqrt-square *-commutative distribute-lft-out distribute-lft-out-- difference-of-squares
1×sqrt-unprod hypot-def
Counts
4 → 109
Calls
4 calls:
4.0ms
(sqrt (- y z))
12.0ms
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
3.0ms
(sqrt (+ y z))
11.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (- y z))
108.0ms
(* x (* (sqrt (+ y z)) (sqrt (- y z))))
36.0ms
(sqrt (+ y z))
78.0ms
(* (sqrt (+ y z)) (sqrt (- y z)))

simplify50.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0374767
11280721
25001705

prune310.0ms

Filtered
121 candidates to 89 candidates (73.6%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1210121
Fresh011
Picked011
Done022
Total1214125

Merged error: 0.3b

Counts
125 → 4

regimes244.0ms

bsearch10.0ms