Details

Time bar (total: 8.1s)

sample26.0ms

Algorithm
intervals
Results
8.0ms255×body80valid
2.0ms18×body640valid
2.0ms9×body1280valid
1.0ms12×body320valid
0.0ms6×body160valid

simplify72.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0236
1446
21226
33276
48686
517276
635446
750016

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: 13.4b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
2.1b
(+ x (* (- y z) (/ (- t x) (- a z))))
5.3b
(* (- 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))
4.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
17.0ms
(* (- y z) (/ (- t x) (- a z)))

series337.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(/ (- t x) (- a z))
156.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
131.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify55.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0473869
12012820
25001820

prune318.0ms

Filtered
128 candidates to 88 candidates (68.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1208128
Fresh000
Picked011
Done000
Total1209129

Merged error: 3.4b

Counts
129 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.5b
(cbrt (- a z))
2.8b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.9b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite57.0ms

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))
41.0ms
(* (/ (- 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))
153.0ms
(cbrt (- a z))
300.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
156.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify92.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
07441831
132871663
250011576

prune446.0ms

Filtered
146 candidates to 104 candidates (71.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1451146
Fresh167
Picked101
Done011
Total1478155

Merged error: 3.4b

Counts
155 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
0.6b
(cbrt (cbrt (- a z)))
2.6b
(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
7.7b
(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
182×times-frac
164×add-sqr-sqrt
119×cbrt-prod
101×*-un-lft-identity
96×cbrt-div
80×associate-*l*
61×associate-*r*
59×add-cube-cbrt
42×associate-/r/
38×flip3-- flip--
36×add-exp-log
25×frac-times
22×add-cbrt-cube
21×distribute-lft-out-- difference-of-squares
20×unswap-sqr
14×cbrt-undiv div-exp
13×associate-*r/ associate-*l/
10×prod-exp cbrt-unprod
6×pow1 div-inv add-log-exp
2×pow1/3
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 235
Calls
4 calls:
9.0ms
(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
4.0ms
(cbrt (cbrt (- a z)))
100.0ms
(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
3.0ms
(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series753.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(cbrt (* (cbrt (- a z)) (cbrt (- a z))))
149.0ms
(cbrt (cbrt (- a z)))
305.0ms
(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
158.0ms
(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify66.0ms

Algorithm
egg-herbie
Counts
247 → 247
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
014205129
150014883

prune1.3s

Filtered
247 candidates to 204 candidates (82.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2452247
Fresh156
Picked011
Done011
Total2469255

Merged error: 3.4b

Counts
255 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b
(cbrt (/ (- t x) (cbrt (cbrt (- a z)))))
1.3b
(cbrt (/ (- t x) (cbrt (cbrt (- a z)))))
1.5b
(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (* (cbrt (/ (- t x) (cbrt (cbrt (- a z))))) (cbrt (/ (- t x) (cbrt (cbrt (- a z)))))))
8.4b
(+ x (* (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (* (cbrt (/ (- t x) (cbrt (cbrt (- a z))))) (cbrt (/ (- t x) (cbrt (cbrt (- a z))))))) (cbrt (/ (- t x) (cbrt (cbrt (- a z)))))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
271×cbrt-prod
204×times-frac
163×add-sqr-sqrt
156×*-un-lft-identity
86×cbrt-div
84×add-cube-cbrt
80×associate-*l*
44×associate-/r/
36×add-exp-log distribute-lft-out-- difference-of-squares
32×flip3-- flip--
25×frac-times
18×add-cbrt-cube
15×associate-*r/
14×prod-exp cbrt-unprod
13×associate-*l/
10×cbrt-undiv div-exp
9×pow1
7×div-inv
6×add-log-exp
5×unswap-sqr
3×pow-prod-down
2×pow1/3
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+
Counts
4 → 270
Calls
4 calls:
10.0ms
(cbrt (/ (- t x) (cbrt (cbrt (- a z)))))
10.0ms
(cbrt (/ (- t x) (cbrt (cbrt (- a z)))))
60.0ms
(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (* (cbrt (/ (- t x) (cbrt (cbrt (- a z))))) (cbrt (/ (- t x) (cbrt (cbrt (- a z)))))))
3.0ms
(+ x (* (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (* (cbrt (/ (- t x) (cbrt (cbrt (- a z))))) (cbrt (/ (- t x) (cbrt (cbrt (- a z))))))) (cbrt (/ (- t x) (cbrt (cbrt (- a z)))))))

series991.0ms

Counts
4 → 12
Calls
4 calls:
257.0ms
(cbrt (/ (- t x) (cbrt (cbrt (- a z)))))
245.0ms
(cbrt (/ (- t x) (cbrt (cbrt (- a z)))))
333.0ms
(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (* (cbrt (/ (- t x) (cbrt (cbrt (- a z))))) (cbrt (/ (- t x) (cbrt (cbrt (- a z)))))))
155.0ms
(+ x (* (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (* (cbrt (/ (- t x) (cbrt (cbrt (- a z))))) (cbrt (/ (- t x) (cbrt (cbrt (- a z))))))) (cbrt (/ (- t x) (cbrt (cbrt (- a z)))))))

simplify130.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
013456313
139945842
250025795

prune1.4s

Filtered
282 candidates to 219 candidates (77.7%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New2820282
Fresh066
Picked011
Done022
Total2829291

Merged error: 3.4b

Counts
291 → 9

regimes301.0ms

Accuracy

54.6% (3.8b remaining)

Error of 7.9b against oracle of 4.1b and baseline of 12.5b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04239
14239

end0.0ms

sample686.0ms

Algorithm
intervals
Results
261.0ms7849×body80valid
59.0ms477×body640valid
44.0ms275×body1280valid
38.0ms423×body320valid
15.0ms250×body160valid
3.0ms14×body2560valid