Details

Time bar (total: 5.0s)

sample25.0ms

Algorithm
intervals
Results
8.0ms248×body80valid
2.0ms17×body640valid
1.0ms9×body1280valid
1.0ms16×body160valid
1.0ms9×body320valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0236
1465
21285
33625
410245
522965
650015

prune10.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.0b

Counts
2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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:
8.0ms
(/ (- t x) (- a z))
1.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

series136.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(/ (- t x) (- a z))
89.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

simplify58.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0268450
1733425
22490423
35001421

prune200.0ms

Filtered
70 candidates to 51 candidates (72.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New601070
Fresh011
Picked101
Done000
Total611172

Merged error: 5.3b

Counts
72 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
4.3b
(+ x (* (- y z) (/ (- t x) (- a z))))
7.5b
(* (- y z) (/ (- t x) (- a z)))

rewrite34.0ms

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:
9.0ms
(/ (- t x) (- a z))
4.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
16.0ms
(* (- y z) (/ (- t x) (- a z)))

series328.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(/ (- t x) (- a z))
145.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
132.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify60.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0488901
12066849
25001847

prune308.0ms

Filtered
137 candidates to 95 candidates (69.3%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1289137
Fresh5510
Picked101
Done000
Total13414148

Merged error: 3.3b

Counts
148 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- t x))
0.6b
(cbrt (- t x))
1.0b
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
9.5b
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
18×add-sqr-sqrt
16×cbrt-div
15×*-un-lft-identity
14×add-cbrt-cube
13×associate-*r*
10×cbrt-prod flip3-- flip--
9×add-cube-cbrt prod-exp cbrt-unprod
8×associate-/r/
6×pow1 frac-times add-log-exp
5×associate-*l*
4×cbrt-undiv expm1-log1p-u div-exp associate-*l/ log1p-expm1-u
3×fma-def associate-*r/ distribute-lft-out-- difference-of-squares
2×times-frac pow1/3 unswap-sqr
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+ div-inv
Counts
4 → 96
Calls
4 calls:
3.0ms
(cbrt (- t x))
3.0ms
(cbrt (- t x))
27.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
4.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series708.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(cbrt (- t x))
141.0ms
(cbrt (- t x))
269.0ms
(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
152.0ms
(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify74.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
07041444
127441230
250011149

prune570.0ms

Filtered
108 candidates to 85 candidates (78.7%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1071108
Fresh01313
Picked011
Done000
Total10715122

Merged error: 3.3b

Counts
122 → 15

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.7b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.2b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
60×*-un-lft-identity
52×times-frac
46×associate-*r*
37×cbrt-prod
28×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
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r/ associate-*l/
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 145
Calls
4 calls:
3.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
39.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
4.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series721.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(cbrt (- a z))
143.0ms
(cbrt (- a z))
285.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
149.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify89.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07571897
133391727
250021624

prune394.0ms

Filtered
157 candidates to 114 candidates (72.6%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1561157
Fresh01313
Picked101
Done011
Total15715172

Merged error: 3.3b

Counts
172 → 15

regimes327.0ms

Accuracy

30.8% (5.9b remaining)

Error of 9.7b against oracle of 3.8b and baseline of 12.3b

bsearch82.0ms

Steps
ItersRangePoint
7
2.3171177227223138e+151
7.1007851833342075e+152
3.025594917682983e+152
7
-5.5353460225548844e+147
-2.2422785610801346e+146
-5.247565116560335e+147

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03324
13324

end0.0ms

sample675.0ms

Algorithm
intervals
Results
243.0ms7702×body80valid
60.0ms512×body640valid
42.0ms269×body1280valid
41.0ms395×body320valid
22.0ms284×body160valid
5.0ms15×body2560valid