Details

Time bar (total: 5.5s)

sample25.0ms

Algorithm
intervals
Results
8.0ms250×body80valid
2.0ms14×body640valid
1.0ms15×body320valid
1.0ms9×body160valid
0.0ms3×body1280valid
0.0ms1×body2560valid

simplify73.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0236
1446
21226
33276
48686
517276
635446
750016

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
3.7b
(* (- y z) (/ (- t x) (- a z)))
4.3b
(+ x (* (- y z) (/ (- t x) (- a z))))

rewrite54.0ms

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:
11.0ms
(/ (- t x) (- a z))
35.0ms
(* (- y z) (/ (- t x) (- a z)))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))

series323.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(/ (- t x) (- a z))
124.0ms
(* (- y z) (/ (- t x) (- a z)))
149.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))

simplify53.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0473869
12012820
25001820

prune327.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.8b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.2b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite93.0ms

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))
79.0ms
(* (/ (- 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)))))

series743.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(cbrt (- a z))
148.0ms
(cbrt (- a z))
294.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
152.0ms
(+ 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

prune470.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- a z))
0.3b
(* (- t x) (/ 1 (- a z)))
3.7b
(* (- y z) (* (- t x) (/ 1 (- a z))))
5.0b
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

rewrite76.0ms

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:
6.0ms
(/ 1 (- a z))
25.0ms
(* (- t x) (/ 1 (- a z)))
37.0ms
(* (- y z) (* (- t x) (/ 1 (- a z))))
3.0ms
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

series372.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ 1 (- a z))
54.0ms
(* (- t x) (/ 1 (- a z)))
130.0ms
(* (- y z) (* (- t x) (/ 1 (- a z))))
152.0ms
(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

simplify76.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05851027
12810910
25002865

prune380.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 3.6b

localize14.0ms

Local error

Found 4 expressions with local error:

5.7b
(cbrt (/ (- t x) (- a z)))
5.7b
(cbrt (/ (- t x) (- a z)))
5.7b
(cbrt (/ (- t x) (- a z)))
8.4b
(+ x (* (- y z) (* (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z)))) (cbrt (/ (- t x) (- a z))))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt *-un-lft-identity
93×cbrt-prod
75×times-frac
37×add-cube-cbrt
30×distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×cbrt-div flip3-- pow1/3 flip-- div-inv
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 131
Calls
4 calls:
6.0ms
(cbrt (/ (- t x) (- a z)))
6.0ms
(cbrt (/ (- t x) (- a z)))
6.0ms
(cbrt (/ (- t x) (- a z)))
3.0ms
(+ x (* (- y z) (* (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z)))) (cbrt (/ (- t x) (- a z))))))

series593.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(cbrt (/ (- t x) (- a z)))
147.0ms
(cbrt (/ (- t x) (- a z)))
149.0ms
(cbrt (/ (- t x) (- a z)))
150.0ms
(+ x (* (- y z) (* (* (cbrt (/ (- t x) (- a z))) (cbrt (/ (- t x) (- a z)))) (cbrt (/ (- t x) (- a z))))))

simplify118.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 3 (103.0ms)

IterNodesCost
03871616
19741538
240981507
350021473

prune517.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.1b

regimes319.0ms

Accuracy

52.2% (4.4b remaining)

Error of 7.6b against oracle of 3.2b and baseline of 12.4b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03436
13436

end0.0ms

sample672.0ms

Algorithm
intervals
Results
248.0ms7794×body80valid
55.0ms460×body640valid
37.0ms435×body320valid
36.0ms255×body1280valid
19.0ms280×body160valid
2.0ms14×body2560valid