Details

Time bar (total: 6.2s)

sample26.0ms

Algorithm
intervals
Results
10.0ms251×body80valid
1.0ms14×body320valid
1.0ms7×body1280valid
1.0ms6×body640valid
1.0ms9×body160valid
0.0ms1×body2560valid

simplify72.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
3.5b
(+ x (* (- y z) (/ (- t x) (- a z))))
6.1b
(* (- y z) (/ (- t x) (- a z)))

rewrite53.0ms

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:
13.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
32.0ms
(* (- y z) (/ (- t x) (- a z)))

series322.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(/ (- t x) (- a z))
149.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
126.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify52.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0473869
12012820
25001820

prune321.0ms

Filtered
128 candidates to 88 candidates (68.8%)
Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 2.7b

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))))
6.7b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite96.0ms

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:
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
82.0ms
(* (/ (- 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)))))

series734.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(cbrt (- a z))
147.0ms
(cbrt (- a z))
293.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
151.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify88.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07441831
132871663
250011576

prune456.0ms

Filtered
146 candidates to 103 candidates (70.5%)
Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 2.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
0.8b
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.3b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite102.0ms

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:
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
90.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series770.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(cbrt (- a z))
155.0ms
(cbrt (- a z))
302.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
158.0ms
(+ 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 (57.0ms)

IterNodesCost
06302051
124661604
250011462

prune349.0ms

Filtered
115 candidates to 70 candidates (60.9%)
Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 2.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
0.8b
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))
4.7b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))))))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
112×add-exp-log
54×add-cbrt-cube
52×prod-exp cbrt-unprod
35×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 → 115
Calls
4 calls:
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
136.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))
3.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))))))

series780.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(cbrt (- a z))
155.0ms
(cbrt (- a z))
318.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))
157.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (* (cbrt (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (cbrt (- a z))))))))

simplify103.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07473380
133062502
250012327

prune402.0ms

Filtered
127 candidates to 73 candidates (57.5%)
Pruning

15 alts after pruning (11 fresh and 4 done)

Merged error: 2.7b

regimes455.0ms

Accuracy

58.5% (3.4b remaining)

Error of 7.4b against oracle of 4.0b and baseline of 12.1b

bsearch6.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04338
14338

end0.0ms

sample674.0ms

Algorithm
intervals
Results
248.0ms7789×body80valid
51.0ms447×body640valid
43.0ms261×body1280valid
40.0ms424×body320valid
16.0ms274×body160valid
3.0ms17×body2560valid