Details

sample96.0ms

Algorithm

intervals

Results

35.0ms	760×	body	80	nan
9.0ms	180×	body	80	valid
8.0ms	29×	body	640	valid
7.0ms	12×	body	1280	valid
4.0ms	21×	body	320	valid
1.0ms	14×	body	160	valid

simplify38.0ms

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

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 9.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.1b	(fma (log y) x (- (* z (log (- 1.0 y))) t))
4.0b	(log (- 1.0 y))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`log-prod`
14×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log`
5×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
4×	`associate-r`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`log-div` `log-pow`
1×	`flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 59

Calls

3 calls:

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

series227.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* z (log (- 1.0 y)))
114.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
45.0ms	(log (- 1.0 y))

simplify111.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	332	427
1	1128	376
2	4553	369
3	5001	366

prune182.0ms

Filtered

68 candidates to 52 candidates (76.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 0.1b

Counts

69 → 4

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b

(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)

0.0b

(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

0.1b

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

51×	`prod-diff`
46×	`associate--l+`
42×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
38×	`add-cube-cbrt`
34×	`distribute-rgt-in` `distribute-lft-in`
18×	`pow1`
13×	`log-pow`
12×	`log-prod`
6×	`associate-r`
5×	`add-exp-log` `sub-neg` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--`
1×	`fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `difference-of-squares` `unswap-sqr`

Counts

3 → 121

Calls

3 calls:

13.0ms

(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)

11.0ms

(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

1.0ms

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

series377.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms

(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)

101.0ms

(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

160.0ms

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

simplify68.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	428	2727
1	1620	1650
2	5001	1591

prune375.0ms

Filtered

130 candidates to 79 candidates (60.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	129	5	134

Merged error: 0.1b

Counts

134 → 5

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
0.1b	(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

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

series273.0ms

Counts

2 → 6

Calls

2 calls:

106.0ms	(fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
167.0ms	(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

simplify139.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	102	342
1	272	291
2	951	291
3	4792	291
4	5001	291

prune114.0ms

Filtered

26 candidates to 24 candidates (92.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	26	5	31

Merged error: 0.1b

Counts

31 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b	(fma (log y) x (- (cbrt (pow (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 3)) t))
0.3b	(pow (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 3)
23.0b	(cbrt (pow (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
24×	`add-cube-cbrt` `prod-diff`
17×	`distribute-rgt-in` `distribute-lft-in`
16×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod`
7×	`log-pow`
6×	`log-prod` `associate-r/` `associate-r*` `associate--l+`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `flip3--` `associate-l` `flip--`
2×	`cube-mult` `sub-neg` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `*-commutative` `rem-cbrt-cube` `fma-udef` `difference-of-squares` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

10.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms	(fma (log y) x (- (cbrt (pow (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 3)) t))
8.0ms	(pow (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 3)
3.0ms	(cbrt (pow (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 3))

series639.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
234.0ms	(fma (log y) x (- (cbrt (pow (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 3)) t))
182.0ms	(pow (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 3)
115.0ms	(cbrt (pow (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) 3))

simplify91.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	573	2417
1	2620	1713
2	5001	1698

prune385.0ms

Filtered

128 candidates to 78 candidates (60.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	128	5	133

Merged error: 0.1b

Counts

133 → 5

regimes129.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	24311×	body	80	nan
273.0ms	5525×	body	80	valid
256.0ms	878×	body	640	valid
230.0ms	384×	body	1280	valid
136.0ms	796×	body	320	valid
47.0ms	445×	body	160	valid