Details

Time bar (total: 5.7s)

sample25.0ms

Algorithm
intervals
Results
8.0ms252×body80valid
2.0ms16×body640valid
2.0ms13×body1280valid
1.0ms15×body320valid
0.0ms4×body160valid

simplify70.0ms

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: 13.4b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
3.0b
(* (- y z) (/ (- t x) (- a z)))
3.2b
(+ x (* (- y z) (/ (- t x) (- a z))))

rewrite35.0ms

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:
10.0ms
(/ (- t x) (- a z))
16.0ms
(* (- y z) (/ (- t x) (- a z)))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))

series321.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(/ (- t x) (- a z))
127.0ms
(* (- y z) (/ (- t x) (- a z)))
146.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))

simplify57.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0473869
12012820
25001820

prune324.0ms

Filtered
128 candidates to 88 candidates (68.8%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New11315128
Fresh000
Picked011
Done000
Total11316129

Merged error: 4.9b

Counts
129 → 16

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- a z))
0.3b
(* (- t x) (/ 1 (- a z)))
3.0b
(* (- y z) (* (- t x) (/ 1 (- a z))))
3.9b
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
44×*-un-lft-identity
32×add-exp-log times-frac
25×add-cube-cbrt
22×associate-*r*
20×frac-times add-cbrt-cube
17×flip3-- flip--
13×prod-exp
12×pow1
10×associate-*r/ associate-*l* associate-*l/
9×distribute-lft-out-- difference-of-squares
7×cbrt-unprod
6×div-exp add-log-exp
5×associate-/r*
4×pow-prod-down associate-/r/ un-div-inv
3×cbrt-undiv rec-exp 1-exp associate-/l* unswap-sqr
2×*-commutative div-inv
1×+-commutative pow-flip frac-2neg flip3-+ clear-num sum-log flip-+ inv-pow
Counts
4 → 146
Calls
4 calls:
5.0ms
(/ 1 (- a z))
13.0ms
(* (- t x) (/ 1 (- a z)))
18.0ms
(* (- y z) (* (- t x) (/ 1 (- a z))))
4.0ms
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

series363.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 1 (- a z))
51.0ms
(* (- t x) (/ 1 (- a z)))
126.0ms
(* (- y z) (* (- t x) (/ 1 (- a z))))
152.0ms
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

simplify73.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05851027
12810910
25002865

prune358.0ms

Filtered
158 candidates to 97 candidates (61.4%)
Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1526158
Fresh6814
Picked011
Done011
Total15816174

Merged error: 4.9b

Counts
174 → 16

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
3.0b
(* (- y z) (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
8.3b
(+ x (* (- y z) (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
65×add-exp-log
35×prod-exp
26×add-cbrt-cube
15×div-exp cbrt-unprod
13×add-sqr-sqrt *-un-lft-identity
10×cbrt-prod
9×pow1 frac-times
7×cbrt-undiv add-cube-cbrt
6×flip3-- associate-*r/ flip-- add-log-exp
5×associate-*l* associate-*l/
4×rec-exp cbrt-div 1-exp
3×pow-prod-down distribute-lft-out-- difference-of-squares
2×pow1/3
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+
Counts
4 → 90
Calls
4 calls:
3.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
27.0ms
(* (- y z) (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
4.0ms
(+ x (* (- y z) (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))))

series744.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(cbrt (- a z))
146.0ms
(cbrt (- a z))
293.0ms
(* (- y z) (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
154.0ms
(+ x (* (- y z) (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))))

simplify73.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06311274
125391073
250031034

prune313.0ms

Filtered
102 candidates to 67 candidates (65.7%)
Pruning

17 alts after pruning (14 fresh and 3 done)

PrunedKeptTotal
New993102
Fresh21113
Picked011
Done022
Total10117118

Merged error: 4.9b

Counts
118 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
1.4b
(* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (/ (- t x) (cbrt (- a z))) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- y z))))
2.0b
(* (/ (/ (- t x) (cbrt (- a z))) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- y z)))
5.1b
(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (/ (- t x) (cbrt (- a z))) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- y z)))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
128×cbrt-div
96×times-frac
88×frac-times
78×add-exp-log
77×add-sqr-sqrt
64×flip3-- flip--
59×associate-*l*
57×*-un-lft-identity
41×cbrt-prod
39×associate-*r/ prod-exp cbrt-unprod
33×add-cbrt-cube
32×associate-*l/
27×add-cube-cbrt
18×pow1 cbrt-undiv div-exp
15×distribute-lft-out-- difference-of-squares
10×associate-/r/
9×associate-*r* pow-prod-down
8×unswap-sqr
6×add-log-exp
2×*-commutative div-inv
1×+-commutative flip3-+ pow1/3 sum-log flip-+
Counts
4 → 215
Calls
4 calls:
3.0ms
(cbrt (- a z))
38.0ms
(* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (/ (- t x) (cbrt (- a z))) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- y z))))
34.0ms
(* (/ (/ (- t x) (cbrt (- a z))) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- y z)))
3.0ms
(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (/ (- t x) (cbrt (- a z))) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- y z)))))

series681.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(cbrt (- a z))
135.0ms
(* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (/ (- t x) (cbrt (- a z))) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- y z))))
249.0ms
(* (/ (/ (- t x) (cbrt (- a z))) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- y z)))
151.0ms
(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (/ (/ (- t x) (cbrt (- a z))) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- y z)))))

simplify125.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
012894483
143443765
250013569

prune830.0ms

Filtered
227 candidates to 135 candidates (59.5%)
Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New2252227
Fresh31013
Picked011
Done123
Total22915244

Merged error: 4.9b

Counts
244 → 15

regimes414.0ms

Accuracy

44.6% (5.9b remaining)

Error of 10.6b against oracle of 4.7b and baseline of 15.3b

bsearch3.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03124
13124

end0.0ms

sample677.0ms

Algorithm
intervals
Results
256.0ms7746×body80valid
59.0ms503×body640valid
41.0ms282×body1280valid
38.0ms432×body320valid
17.0ms281×body160valid
3.0ms16×body2560valid