Details

sample52.0ms

Algorithm

intervals

Results

11.0ms	172×	body	80	valid
7.0ms	28×	body	1280	valid
6.0ms	134×	body	80	nan
5.0ms	23×	body	320	valid
5.0ms	29×	body	640	valid
2.0ms	10×	body	1280	nan
2.0ms	13×	body	640	nan
1.0ms	9×	body	320	nan
0.0ms	5×	body	160	nan
0.0ms	4×	body	160	valid

simplify19.0ms

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: 21.1b

localize8.0ms

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))
1.7b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

23.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
13.0ms	(/ (- x y) (- 1.0 y))
21.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
20.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
36.0ms	(/ (- x y) (- 1.0 y))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify44.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	488	942
1	1388	894
2	5001	876

prune287.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.3b	(* (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)))))
14.3b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
37×	`cbrt-prod`
34×	`*-un-lft-identity`
15×	`difference-of-squares`
14×	`add-cube-cbrt` `cbrt-div`
12×	`pow1` `times-frac`
10×	`swap-sqr`
9×	`log-prod` `flip3--` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`add-exp-log` `pow1/3`
6×	`add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`log-div` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `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 → 110

Calls

4 calls:

2.0ms	(cbrt (- 1.0 y))
21.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
63.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
63.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (- 1.0 y))
102.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
83.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
53.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

simplify54.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	511	1461
1	1611	1335
2	5001	1234

prune345.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

1.7b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
18×	`log-prod`
15×	`*-un-lft-identity`
8×	`difference-of-squares`
7×	`pow1` `add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`flip3--` `times-frac` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`rem-log-exp` `log-pow`
1×	`sub-neg` `diff-log` `div-sub` `associate--r-`

Counts

4 → 67

Calls

4 calls:

21.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
20.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
20.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
22.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
82.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
86.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify56.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	194	742
1	481	673
2	1890	661
3	5002	661

prune246.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

1.7b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
18×	`log-prod`
15×	`*-un-lft-identity`
8×	`difference-of-squares`
7×	`pow1` `add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`flip3--` `times-frac` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`rem-log-exp` `log-pow`
1×	`sub-neg` `diff-log` `div-sub` `associate--r-`

Counts

4 → 67

Calls

4 calls:

20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
23.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
20.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
20.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
87.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify55.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	194	742
1	481	673
2	1890	661
3	5002	661

prune267.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes239.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 17.4b

bsearch158.0ms

Steps

Iters	Range		Point
9	0.24914757354793585	42942575.54555991	36683682.57368248
9	-8.085901714425178e+20	-317207061041.6537	-325586491895.52155

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	22
1	36	22

end0.0ms

sample1.4s

Algorithm

intervals

Results

394.0ms	5624×	body	80	valid
189.0ms	813×	body	1280	valid
173.0ms	3628×	body	80	nan
138.0ms	805×	body	640	valid
68.0ms	360×	body	1280	nan
66.0ms	486×	body	320	valid
61.0ms	409×	body	640	nan
26.0ms	272×	body	160	valid
24.0ms	210×	body	320	nan
11.0ms	131×	body	160	nan