Details

sample52.0ms

Algorithm

intervals

Results

12.0ms	189×	body	80	valid
7.0ms	21×	body	1280	valid
6.0ms	121×	body	80	nan
4.0ms	16×	body	640	valid
3.0ms	17×	body	320	valid
3.0ms	10×	body	1280	nan
2.0ms	8×	body	640	nan
2.0ms	13×	body	160	valid
1.0ms	9×	body	320	nan
0.0ms	3×	body	160	nan

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	29	6
2	41	6
3	60	6
4	78	6
5	94	6
6	109	6
7	139	6
8	214	6
9	279	6
10	279	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b	(/ (- x y) (- 1.0 y))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.5b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
184×	`*-un-lft-identity`
105×	`prod-diff`
103×	`times-frac`
91×	`add-cube-cbrt`
49×	`difference-of-squares`
47×	`distribute-lft-out--`
12×	`log-prod`
9×	`pow1` `flip3--` `flip--`
8×	`associate-/r/`
7×	`add-exp-log` `add-log-exp`
6×	`fma-neg` `add-cbrt-cube` `associate--r+`
5×	`associate-/r` `log-pow` `associate-/l`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `div-inv`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 227

Calls

4 calls:

22.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
15.0ms	(/ (- x y) (- 1.0 y))
28.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
26.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
37.0ms	(/ (- x y) (- 1.0 y))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify105.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	986	4621
1	3240	3344
2	5003	3134

prune434.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.2b	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
3.1b	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
13.2b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

540×	`times-frac`
506×	`add-sqr-sqrt`
480×	`*-un-lft-identity`
426×	`prod-diff`
310×	`add-cube-cbrt`
308×	`cbrt-div`
292×	`cbrt-prod`
198×	`associate-/r/`
156×	`flip3--` `flip--`
100×	`frac-times`
90×	`difference-of-squares`
84×	`distribute-lft-out--`
50×	`associate-r/` `associate-l/`
27×	`div-inv`
12×	`pow1`
10×	`swap-sqr`
9×	`log-prod`
8×	`associate-r` `associate-l`
7×	`add-exp-log` `pow1/3`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg`
2×	`log-div` `div-sub` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `associate--r-`

Counts

4 → 547

Calls

4 calls:

2.0ms	(cbrt (- 1.0 y))
22.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
89.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
82.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (- 1.0 y))
111.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
89.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
52.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

simplify291.0ms

Algorithm

egg-herbie

Counts

559 → 559

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	3264	32435
1	5001	30574

prune1.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
1.8b	(expm1 (log1p (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))))
13.2b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))
24.7b	(log (expm1 (log1p (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

534×	`times-frac`
489×	`add-sqr-sqrt`
475×	`*-un-lft-identity`
426×	`prod-diff`
309×	`add-cube-cbrt`
306×	`cbrt-div`
285×	`cbrt-prod`
198×	`associate-/r/`
154×	`flip3--` `flip--`
100×	`frac-times`
84×	`difference-of-squares`
82×	`distribute-lft-out--`
50×	`associate-r/` `associate-l/`
27×	`div-inv`
12×	`pow1`
10×	`swap-sqr`
8×	`associate-r` `associate-l`
7×	`add-exp-log`
6×	`pow1/3` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `fma-neg`
2×	`div-sub` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `expm1-log1p` `pow-plus` `diff-log` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `expm1-udef` `associate--r-`

Counts

4 → 533

Calls

4 calls:

22.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
0.0ms	(expm1 (log1p (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))))
83.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))
1.0ms	(log (expm1 (log1p (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
150.0ms	(expm1 (log1p (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))))
57.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))
289.0ms	(log (expm1 (log1p (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))))

simplify286.0ms

Algorithm

egg-herbie

Counts

545 → 545

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	3328	32441
1	5001	30549

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ x (pow y 2)) (/ 1 y))
1.9b	(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
4.5b	(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
12.0b	(/ x (pow y 2))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

636×	`times-frac`
469×	`add-sqr-sqrt`
440×	`*-un-lft-identity`
428×	`add-cube-cbrt`
364×	`prod-diff`
141×	`unpow-prod-down`
49×	`unpow2` `sqr-pow`
44×	`div-inv`
28×	`fma-neg`
15×	`difference-of-squares`
10×	`add-exp-log`
8×	`associate-/r*`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `div-exp` `associate-/l*` `distribute-lft-out--`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `frac-sub` `flip--` `fma-udef`

Counts

4 → 500

Calls

4 calls:

52.0ms	(- (/ x (pow y 2)) (/ 1 y))
1.0ms	(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
0.0ms	(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
4.0ms	(/ x (pow y 2))

series157.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ x (pow y 2)) (/ 1 y))
71.0ms	(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
32.0ms	(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
23.0ms	(/ x (pow y 2))

simplify141.0ms

Algorithm

egg-herbie

Counts

512 → 512

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	1276	10765
1	3395	6095
2	5003	6012

prune552.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 17.0b

bsearch170.0ms

Steps

Iters	Range		Point
11	2.617753675252566e-05	2.2737699151718684e+27	47573649.567421444
7	-1285523271281.5593	-32079174255.072563	-32434980278.36437

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	23
1	35	23

end0.0ms

sample1.6s

Algorithm

intervals

Results

369.0ms	5666×	body	80	valid
264.0ms	810×	body	1280	valid
208.0ms	834×	body	640	valid
201.0ms	3633×	body	80	nan
102.0ms	360×	body	1280	nan
80.0ms	363×	body	640	nan
79.0ms	450×	body	320	valid
36.0ms	213×	body	320	nan
28.0ms	240×	body	160	valid
10.0ms	93×	body	160	nan