Details

Time bar (total: 2.5min)

sample2.7s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 11.712646%

Guaranteed chance to sample good point: 40.200484%

Results
13.0ms208×body80valid
2.0ms10×body1280valid
2.0ms11×body640valid
1.0ms12×body320valid
1.0ms15×body160valid
1.0ms30×body80invalid

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: 13.7b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
4.8b
(+ x (* (- y z) (/ (- t x) (- a z))))
5.3b
(* (- y z) (/ (- t x) (- a z)))

rewrite31.0ms

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:
7.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
16.0ms
(* (- y z) (/ (- t x) (- a z)))

series95.0ms

Counts
3 → 9
Calls
3 calls:
12.0ms
(/ (- t x) (- a z))
46.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
37.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify54.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0473869
12012820
25002820

prune192.0ms

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

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New11315128
Fresh000
Picked011
Done000
Total11316129

Merged error: 4.6b

Counts
129 → 16

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.5b
(cbrt (- a z))
2.0b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.5b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite53.0ms

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))
38.0ms
(* (/ (- 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)))))

series154.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(cbrt (- a z))
28.0ms
(cbrt (- a z))
51.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
50.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify86.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07521839
133201671
250011580

prune183.0ms

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

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1451146
Fresh21214
Picked011
Done011
Total14715162

Merged error: 4.6b

Counts
162 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- y z))
0.5b
(cbrt (- y z))
1.2b
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
4.5b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
35×add-cbrt-cube
32×prod-exp cbrt-unprod
22×cbrt-undiv div-exp
15×cbrt-prod add-sqr-sqrt *-un-lft-identity
14×associate-*l*
9×pow1 add-cube-cbrt
8×times-frac
6×cbrt-div add-log-exp
5×frac-times associate-*r/
3×flip3-- pow-prod-down associate-*l/ flip-- distribute-lft-out-- difference-of-squares
2×pow1/3 associate-/r/
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ div-inv
Counts
4 → 103
Calls
4 calls:
3.0ms
(cbrt (- y z))
3.0ms
(cbrt (- y z))
34.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
5.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series155.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(cbrt (- y z))
27.0ms
(cbrt (- y z))
52.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
50.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06602069
125211616
250011458

prune150.0ms

Filtered
68 candidates to 115 candidates (-69.1%)
Pruning

17 alts after pruning (14 fresh and 3 done)

PrunedKeptTotal
New1123115
Fresh11112
Picked011
Done022
Total11317130

Merged error: 4.6b

Counts
130 → 17

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- y z))
0.6b
(pow (cbrt (- y z)) 3)
3.2b
(/ (/ (pow (cbrt (- y z)) 3) (cbrt (- a z))) (/ (cbrt (- a z)) (/ (- t x) (cbrt (- a z)))))
6.7b
(+ x (pow (/ (/ (pow (cbrt (- y z)) 3) (cbrt (- a z))) (/ (cbrt (- a z)) (/ (- t x) (cbrt (- a z))))) 1))

rewrite35.9s

Algorithm
rewrite-expression-head
Rules
259614×times-frac
159967×*-un-lft-identity
159965×add-sqr-sqrt
149765×cbrt-prod
76635×add-cube-cbrt
41665×distribute-lft-out-- difference-of-squares
23944×unpow-prod-down cube-prod
3860×associate-/r/
3680×cbrt-div
2993×cube-mult unpow3 sqr-pow
2022×div-inv
1840×flip3-- flip--
373×associate-/r*
182×associate-/l*
47×add-exp-log
33×div-exp
16×add-cbrt-cube
15×cbrt-undiv
6×add-log-exp
5×pow1
4×pow-to-exp pow-exp
3×pow-unpow
2×cube-div pow-pow pow1/3
1×+-commutative frac-2neg flip3-+ clear-num sum-log flip-+ associate-/l/ distribute-lft-out rem-cube-cbrt
Counts
4 → 68534
Calls
4 calls:
3.0ms
(cbrt (- y z))
5.0ms
(pow (cbrt (- y z)) 3)
1.5s
(/ (/ (pow (cbrt (- y z)) 3) (cbrt (- a z))) (/ (cbrt (- a z)) (/ (- t x) (cbrt (- a z)))))
19.1s
(+ x (pow (/ (/ (pow (cbrt (- y z)) 3) (cbrt (- a z))) (/ (cbrt (- a z)) (/ (- t x) (cbrt (- a z))))) 1))

series168.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(cbrt (- y z))
35.0ms
(pow (cbrt (- y z)) 3)
51.0ms
(/ (/ (pow (cbrt (- y z)) 3) (cbrt (- a z))) (/ (cbrt (- a z)) (/ (- t x) (cbrt (- a z)))))
56.0ms
(+ x (pow (/ (/ (pow (cbrt (- y z)) 3) (cbrt (- a z))) (/ (cbrt (- a z)) (/ (- t x) (cbrt (- a z))))) 1))

simplify24.6s

Algorithm
egg-herbie
Counts
68546 → 68546
Iterations

Useful iterations: 0 (768.0ms)

IterNodesCost
0316152493718

prune1.4min

Filtered
22291 candidates to 68546 candidates (-207.5%)

Profiling

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