Details

Time bar (total: 2.8s)

sample34.0ms

Algorithm
intervals
Results
14.0ms282×body80valid
4.0ms91×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

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: 26.1b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.3b
(* (* x y) z)
8.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.4b
(sqrt (- (* z z) (* t a)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms
(sqrt (- (* z z) (* t a)))

series203.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
82.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0346584
11863515
25001510

prune203.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New80888
Fresh000
Picked101
Done000
Total81889

Merged error: 3.9b

Counts
89 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
2.1b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.4b
(sqrt (- (* z z) (* t a)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
4.0ms
(- (* z z) (* t a))
12.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ z (sqrt (- (* z z) (* t a))))
32.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04311015
12166912
25002893

prune249.0ms

Filtered
124 candidates to 82 candidates (66.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1213124
Fresh257
Picked011
Done000
Total1239132

Merged error: 3.9b

Counts
132 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.7b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.0b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
26.4b
(sqrt (- (* z z) (* t a)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×sqrt-div pow-prod-down
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
11.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
13.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
56.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
83.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
57.0ms
(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0403775
11781676
25001667

prune200.0ms

Filtered
104 candidates to 67 candidates (64.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1031104
Fresh167
Picked011
Done011
Total1049113

Merged error: 3.9b

Counts
113 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.3b
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
26.4b
(sqrt (- (* z z) (* t a)))
26.4b
(sqrt (- (* z z) (* t a)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
48×add-sqr-sqrt times-frac
35×add-cube-cbrt *-un-lft-identity
33×associate-*r*
30×add-exp-log add-cbrt-cube
16×sqrt-div
15×associate-*l*
9×cbrt-undiv div-exp prod-exp associate-/r* cbrt-unprod
8×pow1
6×associate-/r/
5×flip3-- flip--
4×add-log-exp unswap-sqr
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 141
Calls
4 calls:
9.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
24.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
3.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
84.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
61.0ms
(sqrt (- (* z z) (* t a)))
59.0ms
(sqrt (- (* z z) (* t a)))

simplify84.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
06291951
133621738
250011614

prune358.0ms

Filtered
153 candidates to 101 candidates (66.0%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1530153
Fresh066
Picked011
Done022
Total1539162

Merged error: 3.9b

Counts
162 → 9

regimes367.0ms

bsearch3.0ms

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