Details

Time bar (total: 3.2s)

sample59.0ms

Algorithm
intervals
Results
24.0ms338×body80valid
18.0ms324×body80nan

simplify104.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0155
1225
2395
3715
41675
52985
65455
721425
850015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
3.0b
(- (* y y) (* z z))
24.6b
(sqrt (- (* y y) (* z z)))

rewrite20.0ms

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:
11.0ms
(* x (sqrt (- (* y y) (* z z))))
3.0ms
(- (* y y) (* z z))
5.0ms
(sqrt (- (* y y) (* z z)))

series172.0ms

Counts
3 → 9
Calls
3 calls:
85.0ms
(* x (sqrt (- (* y y) (* z z))))
34.0ms
(- (* y y) (* z z))
53.0ms
(sqrt (- (* y y) (* z z)))

simplify96.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (89.0ms)

IterNodesCost
0202397
1786374
23192368
35001364

prune185.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

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

prune9.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×*-un-lft-identity sqrt-prod
18×sqrt-div
15×associate-*r*
13×pow1
11×add-exp-log add-cube-cbrt add-cbrt-cube
10×associate-*r/
5×flip3-+ flip-+
4×expm1-log1p-u frac-times flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
1×hypot-def
Counts
4 → 98
Calls
4 calls:
4.0ms
(sqrt (+ y z))
5.0ms
(sqrt (- y z))
24.0ms
(* (* x (sqrt (+ y z))) (sqrt (- y z)))
11.0ms
(* x (sqrt (+ y z)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(sqrt (+ y z))
73.0ms
(sqrt (- y z))
108.0ms
(* (* x (sqrt (+ y z))) (sqrt (- y z)))
72.0ms
(* x (sqrt (+ y z)))

simplify63.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0419663
11652602
25001579

prune288.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (- y z)))
0.2b
(* (* (* x (sqrt (+ y z))) (sqrt (sqrt (- y z)))) (sqrt (sqrt (- y z))))
0.2b
(* x (sqrt (+ y z)))
0.2b
(* (* x (sqrt (+ y z))) (sqrt (sqrt (- y z))))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
114×sqrt-div
45×sqrt-prod
36×associate-*r/
32×frac-times
29×associate-*r*
27×add-sqr-sqrt
23×*-un-lft-identity
22×pow1 flip3-- flip--
20×add-exp-log add-cbrt-cube
16×associate-*l/
15×add-cube-cbrt
13×flip3-+ flip-+
10×pow-prod-down prod-exp cbrt-unprod
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×*-commutative distribute-lft-out-- difference-of-squares
2×rem-sqrt-square pow1/2 unswap-sqr
1×distribute-lft-out
Counts
4 → 145
Calls
4 calls:
5.0ms
(sqrt (sqrt (- y z)))
91.0ms
(* (* (* x (sqrt (+ y z))) (sqrt (sqrt (- y z)))) (sqrt (sqrt (- y z))))
11.0ms
(* x (sqrt (+ y z)))
29.0ms
(* (* x (sqrt (+ y z))) (sqrt (sqrt (- y z))))

series549.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(sqrt (sqrt (- y z)))
108.0ms
(* (* (* x (sqrt (+ y z))) (sqrt (sqrt (- y z)))) (sqrt (sqrt (- y z))))
71.0ms
(* x (sqrt (+ y z)))
204.0ms
(* (* x (sqrt (+ y z))) (sqrt (sqrt (- y z))))

simplify104.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
07851677
134851504
250011473

prune484.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes480.0ms

bsearch46.0ms