Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	186×	body	80	valid
5.0ms	26×	body	1280	valid
4.0ms	28×	body	640	valid
3.0ms	107×	body	80	nan
2.0ms	12×	body	1280	nan
1.0ms	10×	body	640	nan
1.0ms	10×	body	320	valid
1.0ms	8×	body	320	nan
0.0ms	6×	body	160	valid
0.0ms	2×	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: 17.9b

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))
2.3b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite76.0ms

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:

17.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
9.0ms	(/ (- x y) (- 1.0 y))
19.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
19.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series259.0ms

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)))
83.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify113.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	986	4621
1	3240	3344
2	5001	3134

prune408.0ms

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))
0.2b	(cbrt (- 1.0 y))
3.9b	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
11.8b	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-prod`
9×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `prod-diff`
2×	`log-div` `pow1/3` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 70

Calls

4 calls:

3.0ms	(cbrt (- 1.0 y))
3.0ms	(cbrt (- 1.0 y))
3.0ms	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
3.0ms	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (- 1.0 y))
88.0ms	(cbrt (- 1.0 y))
90.0ms	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
57.0ms	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	378	1088
1	1244	972
2	5001	950

prune281.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (- x y) (- 1.0 y)) 3)
2.2b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
3.9b	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0))))
10.7b	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0)))

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

1473×	`add-sqr-sqrt`
1185×	`*-un-lft-identity`
912×	`times-frac`
816×	`prod-diff`
754×	`unpow-prod-down` `cube-prod`
585×	`add-cube-cbrt`
452×	`difference-of-squares`
300×	`distribute-lft-out--`
162×	`sqr-pow`
103×	`log-prod`
82×	`cube-mult` `unpow3`
52×	`associate-/r/`
33×	`associate-/l*`
28×	`flip3--` `flip--` `div-inv`
12×	`add-exp-log` `fma-neg`
9×	`add-cbrt-cube`
8×	`difference-cubes`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `div-exp` `associate-/r*`
2×	`cbrt-undiv` `rem-log-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`cube-div` `pow-to-exp` `sub-neg` `log-div` `pow-pow` `frac-2neg` `diff-log` `div-sub` `clear-num` `log-pow`

Counts

4 → 1224

Calls

4 calls:

11.0ms	(pow (/ (- x y) (- 1.0 y)) 3)
66.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
52.0ms	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0))))
104.0ms	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0)))

series861.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (/ (- x y) (- 1.0 y)) 3)
182.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
352.0ms	(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0))))
259.0ms	(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (fma (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))) (* 1.0 1.0)))

simplify377.0ms

Algorithm

egg-herbie

Counts

1236 → 1236

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	2071	40517
1	5001	32680

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))
2.3b	(- 1.0 (/ (- x y) (- 1.0 y)))
2.7b	(log1p (expm1 (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))))
3.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

140×	`add-sqr-sqrt`
134×	`*-un-lft-identity`
93×	`prod-diff`
77×	`times-frac`
70×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`distribute-lft-out--`
6×	`log-prod` `associate-/r/` `add-log-exp`
5×	`pow1` `add-exp-log` `flip3--` `flip--` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-cbrt-cube`
3×	`fma-neg` `div-inv`
2×	`log-div`
1×	`sub-neg` `log1p-udef` `expm1-log1p` `diff-log` `div-sub` `log1p-expm1` `rem-log-exp` `log-pow` `expm1-udef` `associate--r-`

Counts

4 → 155

Calls

4 calls:

1.0ms	(expm1 (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))
17.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
1.0ms	(log1p (expm1 (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))))
23.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series450.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(expm1 (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))
56.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
115.0ms	(log1p (expm1 (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))))
92.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify93.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	897	3892
1	2807	2810
2	5001	2596

prune326.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes115.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.3b

bsearch152.0ms

Steps

Iters	Range		Point
10	7.521372480586488e-07	27530559744.528915	76447033.33081697
10	-5.651135004763443e+21	-1608183693.8472729	-1630045945.922767

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	40	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

227.0ms	5752×	body	80	valid
159.0ms	828×	body	1280	valid
107.0ms	757×	body	640	valid
102.0ms	3704×	body	80	nan
57.0ms	365×	body	1280	nan
44.0ms	422×	body	320	valid
42.0ms	368×	body	640	nan
18.0ms	219×	body	320	nan
16.0ms	241×	body	160	valid
9.0ms	113×	body	160	nan