Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
5.0ms	9×	body	1280	valid
1.0ms	11×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	1×	body	2560	valid

simplify73.0ms

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: 14.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
5.0b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.2b	(* (- y z) (/ (- t x) (- a z)))

rewrite55.0ms

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:

11.0ms	(/ (- t x) (- a z))
3.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
33.0ms	(* (- y z) (/ (- t x) (- a z)))

series326.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- t x) (- a z))
150.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
127.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (12.0ms)

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

prune322.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.4b	(/ 1 (/ (- a z) (- t x)))
5.7b	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
6.2b	(* (- y z) (/ 1 (/ (- a z) (- t x))))

rewrite116.0ms

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:

13.0ms	(/ (- a z) (- t x))
15.0ms	(/ 1 (/ (- a z) (- t x)))
2.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
63.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))

series699.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (- a z) (- t x))
199.0ms	(/ 1 (/ (- a z) (- t x)))
147.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
303.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))

simplify60.0ms

Algorithm

egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1010	3037
1	5002	2740

prune773.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- y z) (- a z))
0.2b	(/ (sqrt 1) (/ 1 (- t x)))
1.5b	(* (/ (- y z) (- a z)) (/ (sqrt 1) (/ 1 (- t x))))
5.2b	(+ x (* (/ (- y z) (- a z)) (/ (sqrt 1) (/ 1 (- t x)))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

537×	`times-frac`
421×	`add-sqr-sqrt`
365×	`*-un-lft-identity`
231×	`add-cube-cbrt`
141×	`sqrt-prod`
131×	`associate-r`
61×	`distribute-lft-out--` `difference-of-squares`
50×	`add-exp-log`
32×	`associate-/r/` `add-cbrt-cube`
31×	`associate-l`
26×	`associate-/r*`
24×	`div-exp`
20×	`unswap-sqr`
17×	`div-inv`
16×	`flip3--` `flip--`
13×	`cbrt-undiv`
11×	`associate-/l*`
10×	`prod-exp`
6×	`pow1` `cbrt-unprod` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `frac-times` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative` `flip-+`

Counts

4 → 443

Calls

4 calls:

13.0ms	(/ (- y z) (- a z))
12.0ms	(/ (sqrt 1) (/ 1 (- t x)))
112.0ms	(* (/ (- y z) (- a z)) (/ (sqrt 1) (/ 1 (- t x))))
2.0ms	(+ x (* (/ (- y z) (- a z)) (/ (sqrt 1) (/ 1 (- t x)))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (- y z) (- a z))
24.0ms	(/ (sqrt 1) (/ 1 (- t x)))
306.0ms	(* (/ (- y z) (- a z)) (/ (sqrt 1) (/ 1 (- t x))))
160.0ms	(+ x (* (/ (- y z) (- a z)) (/ (sqrt 1) (/ 1 (- t x)))))

simplify80.0ms

Algorithm

egg-herbie

Counts

455 → 455

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1509	4610
1	5002	3503

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
0.7b	(/ (- y z) (/ (* (cbrt (- a z)) (cbrt (- a z))) (* (cbrt (- t x)) (cbrt (- t x)))))
7.4b	(+ x (* (/ (- y z) (/ (* (cbrt (- a z)) (cbrt (- a z))) (* (cbrt (- t x)) (cbrt (- t x))))) (/ (sqrt 1) (/ (cbrt (- a z)) (cbrt (- t x))))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

76×	`cbrt-div`
71×	`times-frac`
58×	`add-sqr-sqrt` `*-un-lft-identity`
49×	`associate-/r/`
39×	`flip3--` `flip--`
26×	`add-cube-cbrt`
24×	`frac-times`
22×	`add-exp-log`
16×	`distribute-lft-out--` `difference-of-squares`
14×	`add-cbrt-cube`
13×	`associate-/r*`
12×	`associate-r/` `associate-l/`
10×	`cbrt-prod`
9×	`cbrt-undiv` `div-exp`
7×	`div-inv`
6×	`add-log-exp`
5×	`associate-/l*`
4×	`pow1` `prod-exp` `cbrt-unprod`
2×	`pow1/3` `associate-/l/`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `clear-num` `sum-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

2.0ms	(cbrt (- t x))
2.0ms	(cbrt (- t x))
29.0ms	(/ (- y z) (/ (* (cbrt (- a z)) (cbrt (- a z))) (* (cbrt (- t x)) (cbrt (- t x)))))
2.0ms	(+ x (* (/ (- y z) (/ (* (cbrt (- a z)) (cbrt (- a z))) (* (cbrt (- t x)) (cbrt (- t x))))) (/ (sqrt 1) (/ (cbrt (- a z)) (cbrt (- t x))))))

series865.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- t x))
154.0ms	(cbrt (- t x))
407.0ms	(/ (- y z) (/ (* (cbrt (- a z)) (cbrt (- a z))) (* (cbrt (- t x)) (cbrt (- t x)))))
157.0ms	(+ x (* (/ (- y z) (/ (* (cbrt (- a z)) (cbrt (- a z))) (* (cbrt (- t x)) (cbrt (- t x))))) (/ (sqrt 1) (/ (cbrt (- a z)) (cbrt (- t x))))))

simplify101.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	926	3000
1	3524	2783
2	5002	2752

prune608.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.1b

regimes319.0ms

Accuracy

56.7% (3.3b remaining)

Error of 7.4b against oracle of 4.2b and baseline of 11.7b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	27
1	42	27

end0.0ms

sample678.0ms

Algorithm

intervals

Results

248.0ms	7756×	body	80	valid
60.0ms	492×	body	640	valid
43.0ms	278×	body	1280	valid
34.0ms	393×	body	320	valid
18.0ms	263×	body	160	valid
4.0ms	19×	body	2560	valid