Details

Time bar (total: 5.8s)

sample24.0ms

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

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0236
1465
21285
33625
410245
522965
650015

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
15.1b
(fma (- y z) (/ (- t x) (- a z)) x)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
12.0ms
(/ (- t x) (- a z))
0.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

series140.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ (- t x) (- a z))
91.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

simplify54.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0268450
1733425
22490423
35001421

prune209.0ms

Filtered
70 candidates to 51 candidates (72.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

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)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
74×*-un-lft-identity
51×times-frac
31×associate-*r*
28×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/
3×expm1-log1p-u fma-def log1p-expm1-u
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 → 128
Calls
3 calls:
12.0ms
(/ (- t x) (- a z))
3.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
37.0ms
(* (- y z) (/ (- t x) (- a z)))

series337.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(/ (- t x) (- a z))
155.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
129.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify55.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0488901
12066849
25001847

prune362.0ms

Filtered
137 candidates to 96 candidates (70.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

localize13.0ms

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)))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
79×*-un-lft-identity
60×cbrt-prod
54×associate-*r*
52×times-frac
35×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/
4×expm1-log1p-u log1p-expm1-u
3×fma-def pow-prod-down
2×pow-sqr *-commutative pow-prod-up div-inv
1×+-commutative pow2 flip3-+ pow-plus sum-log flip-+
Counts
4 → 186
Calls
4 calls:
2.0ms
(cbrt (- a z))
23.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
84.0ms
(* (/ (- 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)))))

series756.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(cbrt (- a z))
127.0ms
(* (cbrt (- a z)) (cbrt (- a z)))
313.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
155.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify119.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
08602235
142582044
250011974

prune676.0ms

Filtered
198 candidates to 148 candidates (74.7%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
2.6b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.6b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
55×*-un-lft-identity
52×times-frac
46×associate-*r*
33×cbrt-prod
27×add-cube-cbrt
25×add-exp-log
18×add-cbrt-cube
17×associate-*l*
14×cbrt-div distribute-lft-out-- difference-of-squares
10×associate-/r/
8×prod-exp cbrt-unprod
7×cbrt-undiv flip3-- div-exp flip--
6×pow1 unswap-sqr
5×frac-times
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ associate-*l/
2×pow1/3 div-inv
1×pow-prod-down *-commutative fma-udef
Counts
4 → 131
Calls
4 calls:
0.0ms
(cbrt x)
1.0ms
(cbrt x)
84.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
172.0ms
(cbrt x)
370.0ms
(cbrt x)
309.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
161.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify81.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06501734
129081538
250021462

prune497.0ms

Filtered
143 candidates to 109 candidates (76.2%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.1b

regimes434.0ms

Accuracy

51.3% (4.7b remaining)

Error of 8.5b against oracle of 3.8b and baseline of 13.4b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04140
14140

end0.0ms

sample670.0ms

Algorithm
intervals
Results
246.0ms7767×body80valid
56.0ms473×body640valid
41.0ms272×body1280valid
37.0ms433×body320valid
17.0ms291×body160valid
3.0ms15×body2560valid