Details

sample156.0ms

Algorithm

intervals

Results

55.0ms	822×	body	80	nan
14.0ms	182×	body	80	valid
13.0ms	15×	body	1280	valid
10.0ms	23×	body	640	valid
9.0ms	22×	body	320	valid
3.0ms	15×	body	160	valid

simplify27.0ms

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

prune8.0ms

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: 10.9b

Counts

2 → 2

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))
4.2b	(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))

series231.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* z (log (- 1.0 y)))
117.0ms	(fma (log y) x (- (* z (log (- 1.0 y))) t))
45.0ms	(log (- 1.0 y))

simplify105.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (99.0ms)

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

prune219.0ms

Filtered

68 candidates to 52 candidates (76.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	5	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Merged error: 0.1b

Counts

70 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
0.0b	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
0.1b	(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
9.7b	(* z (pow y 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
25×	`prod-exp`
20×	`associate-r`
19×	`add-sqr-sqrt`
15×	`add-cbrt-cube`
12×	`div-exp`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow-to-exp` `times-frac` `pow-exp`
7×	`unpow-prod-down`
6×	`pow1` `associate-l`
5×	`cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow2` `sqr-pow`
2×	`cbrt-undiv` `*-commutative` `fma-udef`
1×	`associate-*r/` `pow-prod-down` `div-inv`

Counts

4 → 93

Calls

4 calls:

1.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
14.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
1.0ms	(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
6.0ms	(* z (pow y 2))

series364.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2))))
56.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
162.0ms	(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
29.0ms	(* z (pow y 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	380	697
1	1716	603
2	5001	603

prune391.0ms

Filtered

105 candidates to 67 candidates (63.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	105	5	110

Merged error: 0.1b

Counts

110 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
0.0b	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
0.2b	(* (log y) x)
9.7b	(* z (pow y 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
29×	`add-sqr-sqrt`
26×	`prod-exp`
23×	`associate-r`
19×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-cbrt-cube`
12×	`associate-+r+` `div-exp`
10×	`associate-l`
9×	`pow1` `prod-diff` `add-log-exp`
8×	`pow-to-exp` `times-frac` `pow-exp`
7×	`unpow-prod-down`
6×	`cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`*-commutative` `unpow2` `sqr-pow`
2×	`cbrt-undiv` `pow-prod-down` `sum-log`
1×	`+-commutative` `associate-+r-` `sub-neg` `fma-def` `flip3-+` `diff-log` `associate-*r/` `associate--l+` `log-pow` `flip-+` `fma-udef` `div-inv`

Counts

4 → 122

Calls

4 calls:

7.0ms	(+ (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
10.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
4.0ms	(* (log y) x)
6.0ms	(* z (pow y 2))

series313.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(+ (* (log y) x) (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))))) t))
55.0ms	(* 1/2 (/ (* z (pow y 2)) (pow 1.0 2)))
63.0ms	(* (log y) x)
33.0ms	(* z (pow y 2))

simplify75.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	592	1085
1	2452	938
2	5001	933

prune490.0ms

Filtered

134 candidates to 84 candidates (62.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	128	6	134
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	132	7	139

Merged error: 0.1b

Counts

139 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (log y))
0.5b	(cbrt (log y))
0.5b	(* (cbrt (log y)) (cbrt (log y)))
9.7b	(* z (pow y 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
31×	`add-sqr-sqrt`
19×	`pow1` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`associate-r`
11×	`add-exp-log`
10×	`associate-l`
9×	`swap-sqr`
8×	`pow1/3` `log-pow` `unswap-sqr`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `unpow-prod-down` `prod-exp` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unpow2` `sqr-pow`
1×	`pow2` `pow-to-exp` `pow-plus` `pow-exp`

Counts

4 → 104

Calls

4 calls:

1.0ms	(cbrt (log y))
1.0ms	(cbrt (log y))
6.0ms	(* (cbrt (log y)) (cbrt (log y)))
6.0ms	(* z (pow y 2))

series994.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt (log y))
257.0ms	(cbrt (log y))
262.0ms	(* (cbrt (log y)) (cbrt (log y)))
217.0ms	(* z (pow y 2))

simplify38.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	227	563
1	891	478
2	5002	427

prune415.0ms

Filtered

116 candidates to 73 candidates (62.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	114	9	123

Merged error: 0.0b

Counts

123 → 9

regimes240.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	19
1	31	19

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.0s	23996×	body	80	nan
279.0ms	5550×	body	80	valid
255.0ms	872×	body	640	valid
238.0ms	408×	body	1280	valid
130.0ms	758×	body	320	valid
49.0ms	444×	body	160	valid