Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	251×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	7×	body	1280	valid
0.0ms	5×	body	160	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	44	6
2	122	6
3	327	6
4	868	6
5	1727	6
6	3544	6
7	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.4b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite100.0ms

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:

25.0ms	(/ (- t x) (- a z))
8.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
62.0ms	(* (- y z) (/ (- t x) (- a z)))

series302.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- t x) (- a z))
138.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
118.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify53.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	473	869
1	2012	820
2	5001	820

prune330.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
8.7b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
8.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series560.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (- a z))
140.0ms	(cbrt (- a z))
139.0ms	(cbrt (- a z))
142.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify33.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	258	689
1	784	601
2	5002	590

prune323.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.4b	(/ 1 (/ (- a z) (- t x)))
4.8b	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
5.7b	(* (- y z) (/ 1 (/ (- a z) (- t x))))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log` `associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 344

Calls

4 calls:

22.0ms	(/ (- a z) (- t x))
28.0ms	(/ 1 (/ (- a z) (- t x)))
7.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
93.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (- a z) (- t x))
184.0ms	(/ 1 (/ (- a z) (- t x)))
141.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
284.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))

simplify53.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1010	3037
1	5002	2740

prune808.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cbrt 1) (/ 1 (- t x)))
0.2b	(* (- y z) (/ (* (cbrt 1) (cbrt 1)) (- a z)))
2.3b	(* (* (- y z) (/ (* (cbrt 1) (cbrt 1)) (- a z))) (/ (cbrt 1) (/ 1 (- t x))))
4.1b	(+ x (* (* (- y z) (/ (* (cbrt 1) (cbrt 1)) (- a z))) (/ (cbrt 1) (/ 1 (- t x)))))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

453×	`times-frac`
297×	`add-sqr-sqrt`
293×	`*-un-lft-identity`
211×	`add-cube-cbrt`
142×	`associate-r`
129×	`cbrt-prod`
112×	`add-exp-log`
54×	`add-cbrt-cube`
44×	`prod-exp`
42×	`div-exp`
41×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/r/`
28×	`cbrt-unprod`
23×	`cbrt-undiv`
21×	`associate-/r*`
20×	`flip3--` `flip--`
16×	`div-inv`
11×	`pow1` `frac-times` `associate-*l/`
6×	`associate-l` `associate-/l*` `add-log-exp`
5×	`rec-exp` `1-exp`
4×	`associate-*r/` `pow-prod-down`
2×	`*-commutative` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+`

Counts

4 → 404

Calls

4 calls:

20.0ms	(/ (cbrt 1) (/ 1 (- t x)))
53.0ms	(* (- y z) (/ (* (cbrt 1) (cbrt 1)) (- a z)))
150.0ms	(* (* (- y z) (/ (* (cbrt 1) (cbrt 1)) (- a z))) (/ (cbrt 1) (/ 1 (- t x))))
8.0ms	(+ x (* (* (- y z) (/ (* (cbrt 1) (cbrt 1)) (- a z))) (/ (cbrt 1) (/ 1 (- t x)))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (cbrt 1) (/ 1 (- t x)))
48.0ms	(* (- y z) (/ (* (cbrt 1) (cbrt 1)) (- a z)))
279.0ms	(* (* (- y z) (/ (* (cbrt 1) (cbrt 1)) (- a z))) (/ (cbrt 1) (/ 1 (- t x))))
144.0ms	(+ x (* (* (- y z) (/ (* (cbrt 1) (cbrt 1)) (- a z))) (/ (cbrt 1) (/ 1 (- t x)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

416 → 416

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1616	5163
1	5001	4535

prune1.1s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.8b

regimes361.0ms

Accuracy

61.5% (2.8b remaining)

Error of 7.3b against oracle of 4.5b and baseline of 11.7b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	44
1	49	44

end0.0ms

sample750.0ms

Algorithm

intervals

Results

232.0ms	7839×	body	80	valid
50.0ms	482×	body	640	valid
37.0ms	263×	body	1280	valid
36.0ms	427×	body	320	valid
13.0ms	246×	body	160	valid
1.0ms	9×	body	2560	valid