Details

Time bar (total: 6.6s)

sample24.0ms

Algorithm
intervals
Results
8.0ms242×body80valid
2.0ms11×body1280valid
1.0ms15×body320valid
1.0ms9×body640valid
0.0ms2×body2560valid
0.0ms4×body160valid

simplify69.0ms

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: 15.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
1.7b
(+ x (* (- y z) (/ (- t x) (- a z))))
7.2b
(* (- 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))))
31.0ms
(* (- y z) (/ (- t x) (- a z)))

series324.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(/ (- t x) (- a z))
151.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
125.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify56.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0473869
12012820
25001820

prune309.0ms

Filtered
128 candidates to 88 candidates (68.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
1.7b
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
8.3b
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
33×cbrt-prod *-un-lft-identity
26×cbrt-div
24×add-exp-log
21×associate-*r*
15×add-cube-cbrt flip3-- flip--
14×add-cbrt-cube
13×pow1 associate-*l*
10×frac-times swap-sqr prod-exp cbrt-unprod
8×associate-/r/ distribute-lft-out--
7×pow1/3
6×associate-*l/ add-log-exp difference-of-squares unswap-sqr
5×associate-*r/
4×cbrt-undiv div-exp
3×pow-prod-down
2×times-frac pow-sqr *-commutative pow-prod-up
1×+-commutative pow2 flip3-+ pow-plus sum-log flip-+ div-inv
Counts
4 → 126
Calls
4 calls:
2.0ms
(cbrt (- a z))
22.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
55.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
3.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series688.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(cbrt (- a z))
123.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
273.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
151.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify100.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07621695
134341466
250021408

prune456.0ms

Filtered
138 candidates to 93 candidates (67.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
2.6b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.6b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
78×*-un-lft-identity
60×cbrt-prod
54×associate-*r*
52×times-frac
34×add-cube-cbrt
28×cbrt-div
27×add-exp-log
25×associate-*l*
21×distribute-lft-out--
19×difference-of-squares
18×add-cbrt-cube
14×flip3-- flip--
13×pow1
10×swap-sqr associate-/r/ unswap-sqr
9×frac-times prod-exp cbrt-unprod
7×cbrt-undiv pow1/3 div-exp
6×add-log-exp
5×associate-*r/ associate-*l/
3×pow-prod-down
2×pow-sqr *-commutative pow-prod-up div-inv
1×+-commutative pow2 flip3-+ pow-plus sum-log flip-+
Counts
4 → 175
Calls
4 calls:
2.0ms
(cbrt (- a z))
20.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
77.0ms
(* (/ (- 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)))))

series708.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(cbrt (- a z))
123.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
289.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
153.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify118.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
08442163
141931974
250021855

prune512.0ms

Filtered
187 candidates to 125 candidates (66.8%)
Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
0.6b
(* (cbrt (- a z)) (cbrt (- a z)))
1.2b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
7.3b
(+ 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))))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
59×cbrt-prod
56×cbrt-div
54×*-un-lft-identity
44×add-exp-log
33×associate-*l*
32×associate-*r*
24×add-cube-cbrt flip3-- flip--
22×add-cbrt-cube
20×pow1 swap-sqr
17×frac-times prod-exp cbrt-unprod
16×times-frac associate-/r/
14×unswap-sqr
13×distribute-lft-out--
12×cbrt-undiv pow1/3 div-exp
9×associate-*r/ associate-*l/ difference-of-squares
6×add-log-exp
5×pow-prod-down
4×pow-sqr pow-prod-up
3×*-commutative
2×pow2 pow-plus div-inv
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 192
Calls
4 calls:
20.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
22.0ms
(* (cbrt (- a z)) (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))))))

series776.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
179.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
313.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
153.0ms
(+ 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))))))

simplify108.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
08333134
138382760
250032650

prune766.0ms

Filtered
204 candidates to 132 candidates (64.7%)
Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.7b

regimes384.0ms

Accuracy

54.3% (3.7b remaining)

Error of 8.1b against oracle of 4.4b and baseline of 12.5b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05153
15153

end0.0ms

sample716.0ms

Algorithm
intervals
Results
259.0ms7767×body80valid
59.0ms473×body640valid
41.0ms433×body320valid
40.0ms272×body1280valid
18.0ms291×body160valid
3.0ms15×body2560valid