Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	240×	body	80	valid
2.0ms	17×	body	640	valid
2.0ms	12×	body	1280	valid
1.0ms	13×	body	320	valid
1.0ms	16×	body	160	valid
0.0ms	1×	body	2560	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
16.8b	(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)

series138.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- t x) (- a z))
88.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify58.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune202.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
4.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.1b	(* (- y z) (/ (- t x) (- a z)))

rewrite53.0ms

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))))
33.0ms	(* (- y z) (/ (- t x) (- a z)))

series324.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- t x) (- a z))
149.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
128.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify55.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	488	901
1	2066	849
2	5001	847

prune346.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
2.1b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
10.2b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite114.0ms

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))
20.0ms	(* (cbrt (- a z)) (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)))))

series716.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (- a z))
121.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
295.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
154.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify121.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	860	2235
1	4258	2044
2	5001	1974

prune646.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.1b	(* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))
10.9b	(+ x (* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))

rewrite363.0ms

Algorithm

rewrite-expression-head

Rules

384×	`cbrt-div`
137×	`frac-times`
111×	`flip3--` `flip--`
89×	`associate-l`
82×	`associate-/r/`
68×	`add-sqr-sqrt`
60×	`add-exp-log` `*-un-lft-identity`
47×	`times-frac`
46×	`associate-r`
45×	`associate-r/` `associate-l/`
38×	`add-cbrt-cube`
36×	`cbrt-prod`
28×	`add-cube-cbrt` `prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `unswap-sqr`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 226

Calls

4 calls:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
334.0ms	(* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))

series757.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a z))
145.0ms	(cbrt (- a z))
306.0ms	(* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z))))
158.0ms	(+ x (* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (- a z))))) (/ (- t x) (cbrt (- a z)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1269	4718
1	5001	3854

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.3b

regimes447.0ms

Accuracy

56.8% (4.1b remaining)

Error of 7.5b against oracle of 3.4b and baseline of 12.9b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	99
1	50	99

end0.0ms

sample669.0ms

Algorithm

intervals

Results

247.0ms	7827×	body	80	valid
54.0ms	452×	body	640	valid
41.0ms	290×	body	1280	valid
35.0ms	409×	body	320	valid
16.0ms	272×	body	160	valid
4.0ms	20×	body	2560	valid