Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	178×	body	80	valid
5.0ms	25×	body	1280	valid
3.0ms	109×	body	80	nan
3.0ms	22×	body	640	valid
2.0ms	13×	body	1280	nan
2.0ms	19×	body	320	valid
2.0ms	15×	body	640	nan
1.0ms	12×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	4×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

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))
2.6b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.8b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite109.0ms

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:

26.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
12.0ms	(/ (- x y) (- 1.0 y))
27.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
32.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
37.0ms	(/ (- x y) (- 1.0 y))
54.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
84.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify106.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (69.0ms)

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

prune428.0ms

Filtered

239 candidates to 126 candidates (52.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- x y))
0.6b	(cbrt (- x y))
3.8b	(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
11.9b	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 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:

5.0ms	(cbrt (- x y))
2.0ms	(cbrt (- x y))
2.0ms	(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
3.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- x y))
148.0ms	(cbrt (- x y))
83.0ms	(log (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y)))))
50.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

simplify107.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	342	988
1	996	844
2	4583	772
3	5001	751

prune253.0ms

Filtered

82 candidates to 72 candidates (87.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

3.5b	(log (sqrt (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))))
3.5b	(log (sqrt (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))))
11.9b	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))
11.9b	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `fma-neg` `prod-diff` `sqrt-prod` `log-pow`
4×	`expm1-log1p-u` `log-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `rem-log-exp`

Counts

4 → 82

Calls

4 calls:

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

series352.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(log (sqrt (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))))
125.0ms	(log (sqrt (- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))))
53.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))
50.0ms	(- 1.0 (* (* (cbrt (- x y)) (cbrt (- x y))) (/ (cbrt (- x y)) (- 1.0 y))))

simplify97.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	246	1794
1	773	1526
2	3704	1470
3	5002	1434

prune337.0ms

Filtered

94 candidates to 74 candidates (78.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ x (pow y 2)) (/ 1 y))
2.2b	(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
4.3b	(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
10.0b	(/ x (pow y 2))

rewrite100.0ms

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))

series152.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ x (pow y 2)) (/ 1 y))
60.0ms	(log (fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y)))
37.0ms	(fma 1.0 (- (/ x (pow y 2)) (/ 1 y)) (/ x y))
22.0ms	(/ x (pow y 2))

simplify134.0ms

Algorithm

egg-herbie

Counts

512 → 512

Iterations

Useful iterations: 2 (59.0ms)

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

prune500.0ms

Filtered

512 candidates to 134 candidates (26.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes105.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 17.5b

bsearch125.0ms

Steps

Iters	Range		Point
11	0.04032056371688071	1.4819289714344828e+28	73789365.95162582
8	-1398402063.149054	-3875183.9477288676	-73256728.01718603

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	36
1	36	36

end0.0ms

sample1.0s

Algorithm

intervals

Results

226.0ms	5679×	body	80	valid
165.0ms	837×	body	1280	valid
112.0ms	772×	body	640	valid
103.0ms	3645×	body	80	nan
57.0ms	365×	body	1280	nan
50.0ms	405×	body	640	nan
49.0ms	463×	body	320	valid
21.0ms	239×	body	320	nan
17.0ms	249×	body	160	valid
10.0ms	109×	body	160	nan