Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	192×	body	80	valid
4.0ms	22×	body	1280	valid
3.0ms	23×	body	640	valid
3.0ms	95×	body	80	nan
2.0ms	15×	body	640	nan
1.0ms	14×	body	320	valid
1.0ms	8×	body	1280	nan
0.0ms	5×	body	320	nan
0.0ms	5×	body	160	valid
0.0ms	1×	body	160	nan

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 16.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
2.4b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
27×	`times-frac`
16×	`add-cube-cbrt` `difference-of-squares`
14×	`distribute-lft-out--`
6×	`add-exp-log` `log-prod`
5×	`associate-/r` `add-cbrt-cube` `associate-/l` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`log-div` `div-sub` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `log-pow` `div-inv` `associate--r-`

Counts

3 → 85

Calls

3 calls:

10.0ms	(/ (- x y) (- 1.0 y))
19.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
22.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series178.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (- x y) (- 1.0 y))
54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
86.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify43.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	397	707
1	1115	663
2	5001	658

prune230.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- 1.0 y))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
3.9b	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
5.1b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`times-frac`
25×	`add-cube-cbrt`
21×	`associate-r`
18×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`flip3--` `flip--` `add-log-exp`
5×	`associate-l` `associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`log-prod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `log-div` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `clear-num` `log-pow` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 117

Calls

4 calls:

5.0ms	(/ 1 (- 1.0 y))
24.0ms	(* (- x y) (/ 1 (- 1.0 y)))
5.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
2.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (- 1.0 y))
37.0ms	(* (- x y) (/ 1 (- 1.0 y)))
87.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
57.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify60.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	480	836
1	2036	736
2	5001	688

prune262.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- 1.0 (/ (- x y) (- 1.0 y))) 3)
2.4b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.9b	(log (cbrt (pow (- 1.0 (/ (- x y) (- 1.0 y))) 3)))
11.6b	(cbrt (pow (- 1.0 (/ (- x y) (- 1.0 y))) 3))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
36×	`cbrt-prod`
28×	`*-un-lft-identity`
21×	`log-prod`
18×	`unpow-prod-down` `cube-prod`
14×	`add-cube-cbrt` `difference-of-squares`
7×	`times-frac` `distribute-lft-out--`
6×	`pow1` `add-exp-log` `cube-div` `add-log-exp`
5×	`add-cbrt-cube`
4×	`cbrt-div` `flip3--` `flip--`
3×	`cube-mult` `pow-unpow` `unpow3` `sqr-pow`
2×	`log-div` `pow1/3` `log-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `div-sub` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `associate--r-` `rem-cube-cbrt`

Counts

4 → 109

Calls

4 calls:

40.0ms	(pow (- 1.0 (/ (- x y) (- 1.0 y))) 3)
19.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
43.0ms	(log (cbrt (pow (- 1.0 (/ (- x y) (- 1.0 y))) 3)))
42.0ms	(cbrt (pow (- 1.0 (/ (- x y) (- 1.0 y))) 3))

series303.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow (- 1.0 (/ (- x y) (- 1.0 y))) 3)
59.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
88.0ms	(log (cbrt (pow (- 1.0 (/ (- x y) (- 1.0 y))) 3)))
52.0ms	(cbrt (pow (- 1.0 (/ (- x y) (- 1.0 y))) 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	385	1177
1	1371	1078
2	5001	1062

prune248.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))
2.4b	(- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))))
3.1b	(log (- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))))
3.8b	(log (+ 1.0 (/ (- x y) (- 1.0 y))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

240×	`*-un-lft-identity`
166×	`add-sqr-sqrt`
152×	`times-frac`
76×	`distribute-lft-out--`
58×	`add-cube-cbrt`
55×	`swap-sqr`
50×	`difference-of-squares`
31×	`associate-r` `associate-l`
18×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`pow1`
8×	`log-prod` `associate-/r/`
6×	`flip3--` `flip--` `add-log-exp`
4×	`cbrt-undiv` `log-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`rem-log-exp` `log-pow`
1×	`pow2` `frac-times` `sub-neg` `flip3-+` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `distribute-lft-out`

Counts

4 → 188

Calls

4 calls:

56.0ms	(* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))
3.0ms	(- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))))
3.0ms	(log (- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))))
19.0ms	(log (+ 1.0 (/ (- x y) (- 1.0 y))))

series574.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))
105.0ms	(- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y))))
332.0ms	(log (- (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (/ (- x y) (- 1.0 y)))))
86.0ms	(log (+ 1.0 (/ (- x y) (- 1.0 y))))

simplify115.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	899	2342
1	4077	2154
2	5002	2099

prune463.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes140.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 17.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

end0.0ms

sample1000.0ms

Algorithm

intervals

Results

214.0ms	5689×	body	80	valid
149.0ms	779×	body	1280	valid
108.0ms	807×	body	640	valid
107.0ms	3853×	body	80	nan
54.0ms	363×	body	1280	nan
53.0ms	427×	body	640	nan
45.0ms	472×	body	320	valid
18.0ms	224×	body	320	nan
16.0ms	253×	body	160	valid
6.0ms	106×	body	160	nan