Details

Time bar (total: 5.8s)

sample29.0ms

Algorithm
intervals
Results
9.0ms244×body80valid
2.0ms15×body640valid
2.0ms18×body320valid
2.0ms10×body1280valid
0.0ms5×body160valid

simplify79.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0236
1446
21226
33276
48686
517276
635446
750016

prune2.0ms

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: 14.3b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
2.7b
(+ x (* (- y z) (/ (- t x) (- a z))))
5.2b
(* (- y z) (/ (- t x) (- a z)))

rewrite37.0ms

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

series338.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(/ (- t x) (- a z))
157.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
132.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify61.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0473869
12012820
25002820

prune321.0ms

Filtered
128 candidates to 88 candidates (68.8%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New11612128
Fresh000
Picked011
Done000
Total11613129

Merged error: 4.7b

Counts
129 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
0.9b
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
8.5b
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
17×add-sqr-sqrt
16×cbrt-div
14×*-un-lft-identity add-cbrt-cube
13×associate-*r*
10×cbrt-prod flip3-- flip--
9×prod-exp cbrt-unprod
8×add-cube-cbrt associate-/r/
6×pow1 frac-times add-log-exp
5×associate-*l*
4×cbrt-undiv div-exp associate-*l/
3×associate-*r/ distribute-lft-out-- difference-of-squares
2×times-frac pow1/3 unswap-sqr
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+ div-inv
Counts
4 → 85
Calls
4 calls:
3.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
23.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
4.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series742.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(cbrt (- a z))
153.0ms
(cbrt (- a z))
285.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
156.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify80.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06681363
126151151
250011129

prune358.0ms

Filtered
97 candidates to 74 candidates (76.3%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New95297
Fresh01111
Picked101
Done011
Total9614110

Merged error: 4.7b

Counts
110 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.0b
(sqrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
9.5b
(+ x (* (* (* (- y z) (fabs (/ (cbrt (- t x)) (cbrt (- a z))))) (sqrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
16×cbrt-div
13×sqrt-prod
12×add-sqr-sqrt
11×*-un-lft-identity
10×cbrt-prod
8×flip3-- associate-/r/ flip--
7×add-cube-cbrt
6×add-log-exp
5×pow1
4×add-exp-log frac-times add-cbrt-cube
2×rem-sqrt-square times-frac pow1/3 associate-*r/ associate-*l/ distribute-lft-out-- difference-of-squares
1×+-commutative sqrt-pow1 flip3-+ pow1/2 sqrt-div sum-log flip-+ div-inv
Counts
4 → 66
Calls
4 calls:
7.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
17.0ms
(sqrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms
(+ x (* (* (* (- y z) (fabs (/ (cbrt (- t x)) (cbrt (- a z))))) (sqrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series692.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(cbrt (- a z))
146.0ms
(cbrt (- a z))
153.0ms
(sqrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
240.0ms
(+ x (* (* (* (- y z) (fabs (/ (cbrt (- t x)) (cbrt (- a z))))) (sqrt (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
05421221
114211062
250021025

prune387.0ms

Filtered
78 candidates to 68 candidates (87.2%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New78078
Fresh01212
Picked011
Done011
Total781492

Merged error: 4.7b

Counts
92 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.4b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.6b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite55.0ms

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)))))

series756.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(cbrt (- a z))
150.0ms
(cbrt (- a z))
307.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
153.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify94.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07441831
132871663
250011576

prune366.0ms

Filtered
146 candidates to 103 candidates (70.5%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1433146
Fresh11011
Picked101
Done022
Total14515160

Merged error: 4.7b

Counts
160 → 15

regimes418.0ms

Accuracy

42.2% (4.7b remaining)

Error of 8.8b against oracle of 4.1b and baseline of 12.2b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04452
14452

end0.0ms

sample782.0ms

Algorithm
intervals
Results
310.0ms7731×body80valid
68.0ms464×body640valid
49.0ms274×body1280valid
47.0ms434×body320valid
22.0ms276×body160valid
4.0ms17×body2560valid

Profiling

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