Details

Time bar (total: 5.2s)

sample27.0ms

Algorithm
intervals
Results
8.0ms239×body80valid
2.0ms19×body640valid
2.0ms10×body1280valid
1.0ms14×body320valid
0.0ms7×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0236
1465
21285
33625
410245
522965
650015

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 13.8b

Counts
2 → 2

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
13.9b
(fma (- y z) (/ (- t x) (- a z)) x)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
9.0ms
(/ (- t x) (- a z))
1.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

series139.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ (- t x) (- a z))
90.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

simplify57.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
0268450
1733425
22490423
35001421

prune193.0ms

Filtered
70 candidates to 51 candidates (72.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New61970
Fresh011
Picked101
Done000
Total621072

Merged error: 4.9b

Counts
72 → 10

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
2.6b
(+ x (* (- y z) (/ (- t x) (- a z))))
3.0b
(* (- y z) (/ (- t x) (- a z)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
74×*-un-lft-identity
51×times-frac
31×associate-*r*
28×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/
3×expm1-log1p-u fma-def log1p-expm1-u
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 → 128
Calls
3 calls:
9.0ms
(/ (- t x) (- a z))
4.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
16.0ms
(* (- y z) (/ (- t x) (- a z)))

series333.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(/ (- t x) (- a z))
150.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
130.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify57.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0488901
12066849
25001847

prune294.0ms

Filtered
137 candidates to 95 candidates (69.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1316137
Fresh459
Picked011
Done000
Total13512147

Merged error: 3.8b

Counts
147 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.9b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.9b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
60×*-un-lft-identity
52×times-frac
46×associate-*r*
37×cbrt-prod
28×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
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r/ associate-*l/
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 145
Calls
4 calls:
6.0ms
(cbrt (- a z))
6.0ms
(cbrt (- a z))
48.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
4.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series752.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(cbrt (- a z))
151.0ms
(cbrt (- a z))
301.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
157.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify94.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07571897
133391727
250021624

prune437.0ms

Filtered
157 candidates to 115 candidates (73.2%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1552157
Fresh01010
Picked101
Done011
Total15613169

Merged error: 3.8b

Counts
169 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.9b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
11.8b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
55×*-un-lft-identity
52×times-frac
46×associate-*r*
33×cbrt-prod
27×add-cube-cbrt
25×add-exp-log
18×add-cbrt-cube
17×associate-*l*
14×cbrt-div distribute-lft-out-- difference-of-squares
10×associate-/r/
8×prod-exp cbrt-unprod
7×cbrt-undiv flip3-- div-exp flip--
6×pow1 unswap-sqr
5×frac-times
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/
2×pow1/3 div-inv
1×pow-prod-down *-commutative fma-udef
Counts
4 → 131
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
35.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
1.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series847.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(cbrt x)
184.0ms
(cbrt x)
305.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
153.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify81.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06501734
129081538
250021462

prune426.0ms

Filtered
143 candidates to 109 candidates (76.2%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1403143
Fresh11011
Picked101
Done011
Total14214156

Merged error: 3.8b

Counts
156 → 14

regimes464.0ms

Accuracy

48.4% (5.0b remaining)

Error of 8.6b against oracle of 3.6b and baseline of 13.2b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03668
13668

end0.0ms

sample704.0ms

Algorithm
intervals
Results
265.0ms7788×body80valid
59.0ms483×body640valid
41.0ms423×body320valid
40.0ms258×body1280valid
20.0ms277×body160valid
3.0ms18×body2560valid