Details

Time bar (total: 5.9s)

sample24.0ms

Algorithm
intervals
Results
8.0ms252×body80valid
1.0ms12×body640valid
1.0ms13×body320valid
1.0ms4×body1280valid
0.0ms8×body160valid
0.0ms1×body2560valid

simplify74.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0236
1446
21226
33276
48686
517276
635446
750016

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
3.6b
(+ x (* (- y z) (/ (- t x) (- a z))))
4.1b
(* (- 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:
10.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
35.0ms
(* (- y z) (/ (- t x) (- a z)))

series331.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(/ (- t x) (- a z))
151.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
128.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify53.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0473869
12012820
25001820

prune320.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.3b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
5.3b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite91.0ms

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))
78.0ms
(* (/ (- 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)))))

series770.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(cbrt (- a z))
155.0ms
(cbrt (- a z))
301.0ms
(* (/ (- 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)))))

simplify86.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
07441831
132871663
250011576

prune460.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
4.1b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 56
Calls
4 calls:
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
2.0ms
(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))))))

series614.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(cbrt (- a z))
154.0ms
(cbrt (- a z))
156.0ms
(cbrt (- a z))
155.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify136.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (124.0ms)

IterNodesCost
0262689
1810633
24502622
35003616

prune301.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.1b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
7.8b
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log
36×cbrt-div
26×add-sqr-sqrt
22×add-cbrt-cube
17×associate-*l*
16×*-un-lft-identity times-frac associate-*r* associate-/r/
15×prod-exp cbrt-unprod
14×flip3-- flip--
13×cbrt-prod
12×cbrt-undiv div-exp
10×add-cube-cbrt
9×frac-times
6×pow1 add-log-exp unswap-sqr
5×associate-*r/ associate-*l/
3×distribute-lft-out-- difference-of-squares
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 110
Calls
4 calls:
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
77.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
3.0ms
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series763.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(cbrt (- a z))
155.0ms
(cbrt (- a z))
297.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
162.0ms
(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify95.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
08102470
132412130
250022090

prune500.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.8b

regimes341.0ms

Accuracy

61.2% (3.6b remaining)

Error of 7.0b against oracle of 3.4b and baseline of 12.6b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04137
14137

end0.0ms

sample667.0ms

Algorithm
intervals
Results
251.0ms7769×body80valid
55.0ms486×body640valid
42.0ms453×body320valid
39.0ms270×body1280valid
15.0ms260×body160valid
3.0ms16×body2560valid