Details

Time bar (total: 3.9s)

sample33.0ms

Algorithm
intervals
Results
8.0ms309×body80valid
7.0ms288×body80nan

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0145
1215
2365
3625
41335
52115
63975
717985
850015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (sqrt (- (* y y) (* z z))))
2.4b
(- (* y y) (* z z))
23.2b
(sqrt (- (* y y) (* z z)))

rewrite47.0ms

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:
29.0ms
(* x (sqrt (- (* y y) (* z z))))
8.0ms
(- (* y y) (* z z))
9.0ms
(sqrt (- (* y y) (* z z)))

series168.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(* x (sqrt (- (* y y) (* z z))))
36.0ms
(- (* y y) (* z z))
58.0ms
(sqrt (- (* y y) (* z z)))

simplify86.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0187365
1732340
23010337
35002337

prune132.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ y z) (- y z))
0.0b
(* x (sqrt (* (+ y z) (- y z))))
23.2b
(sqrt (* (+ y z) (- y z)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div
14×associate-*r/
13×add-sqr-sqrt
12×frac-times
11×*-un-lft-identity
10×pow1
9×flip3-- flip3-+ associate-*r* flip-- flip-+
7×add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
6×associate-*l/
3×pow-prod-down add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
1×pow1/2 distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
3 → 79
Calls
3 calls:
35.0ms
(* (+ y z) (- y z))
42.0ms
(* x (sqrt (* (+ y z) (- y z))))
11.0ms
(sqrt (* (+ y z) (- y z)))

series194.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(* (+ y z) (- y z))
91.0ms
(* x (sqrt (* (+ y z) (- y z))))
58.0ms
(sqrt (* (+ y z) (- y z)))

simplify44.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0300543
11444516
25002514

prune191.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (* (sqrt (sqrt (* (+ y z) (- y z)))) (sqrt (sqrt (* (+ y z) (- y z))))))
0.5b
(* (sqrt (sqrt (* (+ y z) (- y z)))) (sqrt (sqrt (* (+ y z) (- y z)))))
23.2b
(sqrt (* (+ y z) (- y z)))
23.2b
(sqrt (* (+ y z) (- y z)))

rewrite424.0ms

Algorithm
rewrite-expression-head
Rules
592×sqrt-div
280×frac-times
172×associate-*r/
114×flip3-- flip3-+ flip-- flip-+
92×associate-*l/
78×sqrt-pow1
72×pow1
28×sqrt-prod
27×pow-prod-down
26×add-sqr-sqrt
20×pow1/2
14×pow-prod-up
13×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
10×associate-*l*
9×swap-sqr
8×associate-*r* pow-sqr
5×unswap-sqr
4×prod-exp cbrt-unprod add-log-exp
2×*-commutative
1×pow2 pow-plus sqrt-unprod rem-square-sqrt
Counts
4 → 288
Calls
4 calls:
268.0ms
(* x (* (sqrt (sqrt (* (+ y z) (- y z)))) (sqrt (sqrt (* (+ y z) (- y z))))))
102.0ms
(* (sqrt (sqrt (* (+ y z) (- y z)))) (sqrt (sqrt (* (+ y z) (- y z)))))
11.0ms
(sqrt (* (+ y z) (- y z)))
11.0ms
(sqrt (* (+ y z) (- y z)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* x (* (sqrt (sqrt (* (+ y z) (- y z)))) (sqrt (sqrt (* (+ y z) (- y z))))))
64.0ms
(* (sqrt (sqrt (* (+ y z) (- y z)))) (sqrt (sqrt (* (+ y z) (- y z)))))
62.0ms
(sqrt (* (+ y z) (- y z)))
57.0ms
(sqrt (* (+ y z) (- y z)))

simplify91.0ms

Algorithm
egg-herbie
Counts
300 → 300
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
07014351
121374237
250034215

prune988.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- y z) (+ y z))
0.0b
(* x (exp (log (sqrt (* (- y z) (+ y z))))))
5.5b
(exp (log (sqrt (* (- y z) (+ y z)))))
23.2b
(sqrt (* (- y z) (+ y z)))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-div
19×add-sqr-sqrt
16×frac-times log-div exp-diff associate-*r/
15×pow1 *-un-lft-identity
12×flip3-- flip3-+ flip-- flip-+
11×add-cube-cbrt associate-*r*
9×log-prod exp-sum
8×associate-*l* associate-*l/ add-cbrt-cube
7×add-exp-log exp-prod
4×sqrt-pow1 pow-prod-down log-pow add-log-exp
3×sqrt-prod unswap-sqr
2×pow1/2 prod-exp *-commutative cbrt-unprod
1×distribute-rgt-in distribute-lft-in rem-exp-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 108
Calls
4 calls:
35.0ms
(* (- y z) (+ y z))
146.0ms
(* x (exp (log (sqrt (* (- y z) (+ y z))))))
45.0ms
(exp (log (sqrt (* (- y z) (+ y z)))))
12.0ms
(sqrt (* (- y z) (+ y z)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (- y z) (+ y z))
95.0ms
(* x (exp (log (sqrt (* (- y z) (+ y z))))))
59.0ms
(exp (log (sqrt (* (- y z) (+ y z)))))
64.0ms
(sqrt (* (- y z) (+ y z)))

simplify54.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0399799
11720750
25002739

prune304.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

regimes144.0ms

bsearch10.0ms