Details

sample121.0ms

Algorithm

intervals

Results

47.0ms	829×	body	80	nan
11.0ms	169×	body	80	valid
11.0ms	15×	body	1280	valid
11.0ms	31×	body	640	valid
5.0ms	24×	body	320	valid
2.0ms	18×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	22	7
1	38	6
2	53	6
3	61	6
4	78	6
5	110	6
6	175	6
7	284	6
8	363	6
9	392	6
10	476	6
11	476	6

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 9.4b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.0b	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
0.3b	(* x (log y))
5.0b	(log (- 1.0 y))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
21×	`log-prod`
20×	`add-cube-cbrt`
11×	`pow1`
9×	`add-exp-log` `prod-diff` `add-log-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`fma-neg` `log-pow`
2×	`log-div` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-log-exp` `associate--l+` `sum-log`

Counts

4 → 106

Calls

4 calls:

6.0ms	(* z (log (- 1.0 y)))
7.0ms	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
4.0ms	(* x (log y))
4.0ms	(log (- 1.0 y))

series234.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* z (log (- 1.0 y)))
84.0ms	(- (+ (* x (log y)) (* z (log (- 1.0 y)))) t)
37.0ms	(* x (log y))
46.0ms	(log (- 1.0 y))

simplify59.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	519	871
1	1908	704
2	5001	676

prune278.0ms

Filtered

118 candidates to 80 candidates (67.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	7	120

Merged error: 0.0b

Counts

120 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.0b	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.3b	(* x (log y))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
57×	`prod-diff`
56×	`*-un-lft-identity`
51×	`add-cube-cbrt`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
24×	`log-prod`
22×	`pow1`
14×	`log-pow`
13×	`associate--l+`
11×	`add-log-exp`
10×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-l`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `distribute-lft-out--`
2×	`flip3--` `diff-log` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `-commutative` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `flip-+`

Counts

4 → 170

Calls

4 calls:

7.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
11.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
10.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
5.0ms	(* x (log y))

series460.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
126.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
103.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
43.0ms	(* x (log y))

simplify92.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	644	3156
1	2391	2185
2	5003	2156

prune523.0ms

Filtered

182 candidates to 107 candidates (58.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	182	7	189

Merged error: 0.0b

Counts

189 → 7

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) z (- (* x (log y)) t))
0.0b	(- (* x (log y)) t)
0.3b	(* x (log y))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `log-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `distribute-rgt-in` `distribute-lft-in` `associate--l+`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`associate-r`
3×	`expm1-log1p-u` `associate-l` `prod-diff` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

1.0ms	(fma (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) z (- (* x (log y)) t))
5.0ms	(- (* x (log y)) t)
5.0ms	(* x (log y))

series271.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(fma (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) z (- (* x (log y)) t))
58.0ms	(- (* x (log y)) t)
37.0ms	(* x (log y))

simplify116.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	291	435
1	1003	372
2	4429	355
3	5001	354

prune247.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	71	6	77

Merged error: 0.0b

Counts

77 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (* x (log y)) t)) (cbrt (- (* x (log y)) t)))
0.5b	(cbrt (- (* x (log y)) t))
0.5b	(cbrt (- (* x (log y)) t))
0.5b	(cbrt (- (* x (log y)) t))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

12.0ms	(* (cbrt (- (* x (log y)) t)) (cbrt (- (* x (log y)) t)))
4.0ms	(cbrt (- (* x (log y)) t))
4.0ms	(cbrt (- (* x (log y)) t))
4.0ms	(cbrt (- (* x (log y)) t))

series899.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (cbrt (- (* x (log y)) t)) (cbrt (- (* x (log y)) t)))
219.0ms	(cbrt (- (* x (log y)) t))
216.0ms	(cbrt (- (* x (log y)) t))
228.0ms	(cbrt (- (* x (log y)) t))

simplify49.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	334	1165
1	1295	1100
2	5001	1038

prune480.0ms

Filtered

107 candidates to 83 candidates (77.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	106	7	113

Merged error: 0.0b

Counts

113 → 7

regimes165.0ms

Accuracy

0% (1.3b remaining)

Error of 1.4b against oracle of 0.1b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	22
1	31	22
2	31	22

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	24134×	body	80	nan
358.0ms	5580×	body	80	valid
301.0ms	862×	body	640	valid
280.0ms	415×	body	1280	valid
157.0ms	726×	body	320	valid
58.0ms	433×	body	160	valid