Details

Time bar (total: 4.9s)

analyze2.6s

Algorithm
search
sampling

Space saved by range analysis: 0.243902%

Space saved by search: 1.437274%

Guaranteed chance to sample good point: 35.82592%

sample36.0ms

Algorithm
intervals
Results
8.0ms210×body80valid
2.0ms14×body640valid
1.0ms36×body80invalid
1.0ms11×body320valid
1.0ms16×body160valid
1.0ms5×body1280valid

simplify73.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0236
1446
21226
33276
48686
517276
635446
750016

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.1b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
5.7b
(+ x (* (- y z) (/ (- t x) (- a z))))
6.3b
(* (- y z) (/ (- t x) (- a z)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
73×*-un-lft-identity
51×times-frac
31×associate-*r*
27×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 119
Calls
3 calls:
8.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
16.0ms
(* (- y z) (/ (- t x) (- a z)))

series102.0ms

Counts
3 → 9
Calls
3 calls:
13.0ms
(/ (- t x) (- a z))
50.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
39.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify55.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0473869
12012820
25002820

prune181.0ms

Filtered
88 candidates to 128 candidates (-45.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New11513128
Fresh000
Picked101
Done000
Total11613129

Merged error: 2.9b

Counts
129 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
7.9b
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 56
Calls
4 calls:
3.0ms
(cbrt (- t x))
3.0ms
(cbrt (- t x))
3.0ms
(cbrt (- t x))
3.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series133.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(cbrt (- t x))
26.0ms
(cbrt (- t x))
26.0ms
(cbrt (- t x))
53.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify32.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0260701
1807613
25002579

prune124.0ms

Filtered
57 candidates to 68 candidates (-19.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New67168
Fresh21012
Picked011
Done000
Total691281

Merged error: 1.2b

Counts
81 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
2.3b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.6b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
59×*-un-lft-identity
52×times-frac
46×associate-*r*
37×cbrt-prod
27×add-cube-cbrt
25×add-exp-log
18×cbrt-div add-cbrt-cube
17×associate-*l*
16×distribute-lft-out-- difference-of-squares
10×associate-/r/
9×flip3-- flip--
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×pow1 add-log-exp unswap-sqr
5×frac-times
3×associate-*r/ associate-*l/
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 134
Calls
4 calls:
3.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
39.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series167.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(cbrt (- a z))
27.0ms
(cbrt (- a z))
60.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
51.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify87.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07521839
133201671
250011580

prune185.0ms

Filtered
103 candidates to 146 candidates (-41.7%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1424146
Fresh1910
Picked011
Done011
Total14315158

Merged error: 1.2b

Counts
158 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
4.7b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 56
Calls
4 calls:
5.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
3.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series134.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cbrt (- a z))
28.0ms
(cbrt (- a z))
27.0ms
(cbrt (- a z))
52.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify133.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (125.0ms)

IterNodesCost
0270701
1842645
24609613
35002595

prune75.0ms

Filtered
54 candidates to 68 candidates (-25.9%)
Pruning

16 alts after pruning (13 fresh and 3 done)

PrunedKeptTotal
New67168
Fresh01212
Picked011
Done022
Total671683

Merged error: 1.2b

Counts
83 → 16

regimes676.0ms

bsearch2.0ms

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