Details

sample107.0ms

Algorithm

intervals

Results

30.0ms	46×	body	1280	valid
19.0ms	35×	body	10240	exit
12.0ms	42×	body	640	valid
7.0ms	114×	body	80	valid
7.0ms	37×	body	320	valid
3.0ms	2×	body	2560	valid
3.0ms	76×	body	80	nan
3.0ms	14×	body	640	nan
2.0ms	16×	body	160	valid
1.0ms	4×	body	1280	nan
1.0ms	3×	body	320	nan
1.0ms	6×	body	160	nan

simplify247.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1551	7
11	1886	7
12	4545	7
13	5001	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 23.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
2.6b	(log (+ (- 1.0 y) (* y (exp z))))
2.7b	(+ (- 1.0 y) (* y (exp z)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1` `associate-+l+`
10×	`add-exp-log`
9×	`prod-diff` `add-log-exp`
8×	`add-cbrt-cube` `distribute-lft-out`
7×	`log-prod` `associate-l`
5×	`fma-def` `log-pow` `distribute-lft-out--`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `associate-/l*`
3×	`flip3-+` `associate-r` `associate-/r*` `flip-+`
2×	`div-sub` `prod-exp` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

5.0ms	(* y (exp z))
15.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
11.0ms	(log (+ (- 1.0 y) (* y (exp z))))
11.0ms	(+ (- 1.0 y) (* y (exp z)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* y (exp z))
157.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
77.0ms	(log (+ (- 1.0 y) (* y (exp z))))
36.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify66.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	496	959
1	1999	815
2	5002	791

prune290.0ms

Filtered

123 candidates to 92 candidates (74.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	7	124

Merged error: 4.3b

Counts

124 → 7

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.0b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.6b	(log (+ 1.0 (* y (expm1 z))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`times-frac`
10×	`pow1`
8×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`log-prod` `log-pow`
4×	`log-div` `associate-l` `associate-/l*`
3×	`expm1-log1p-u` `associate-r` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+` `distribute-lft-out`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 73

Calls

3 calls:

3.0ms	(* y (expm1 z))
11.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
6.0ms	(log (+ 1.0 (* y (expm1 z))))

series271.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* y (expm1 z))
152.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
77.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	424	641
1	1690	586
2	5002	576

prune195.0ms

Filtered

82 candidates to 62 candidates (75.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 4.2b

Counts

89 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (* y (expm1 z))))
0.0b	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
3.6b	(log (sqrt (+ 1.0 (* y (expm1 z)))))
3.6b	(log (sqrt (+ 1.0 (* y (expm1 z)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

94×	`log-pow`
92×	`*-un-lft-identity`
78×	`times-frac`
73×	`pow1`
62×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
40×	`distribute-rgt-out`
38×	`distribute-lft-out`
27×	`sqrt-pow1` `pow1/2`
26×	`associate-/l*`
16×	`log-prod`
15×	`sqrt-prod`
10×	`sqrt-div`
8×	`add-exp-log` `log-div` `distribute-lft1-in` `distribute-rgt1-in`
6×	`flip3-+` `add-cbrt-cube` `flip-+`
4×	`expm1-log1p-u` `count-2` `div-sub` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r*`
2×	`associate-+l-` `associate-+r-` `rem-log-exp` `hypot-def` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv` `unswap-sqr`

Counts

4 → 194

Calls

4 calls:

7.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
26.0ms	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
7.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
7.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

380.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
1.5s	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
349.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
339.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1254	3131
1	5001	2623

prune524.0ms

Filtered

206 candidates to 122 candidates (59.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	201	5	206
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	204	9	213

Merged error: 3.4b

Counts

213 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (* y (expm1 z))))
0.0b	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (* 1/2 (log (+ 1.0 (* y (expm1 z)))))) t)
3.6b	(log (+ 1.0 (* y (expm1 z))))
3.6b	(log (sqrt (+ 1.0 (* y (expm1 z)))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
48×	`log-pow`
42×	`times-frac`
36×	`pow1`
33×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
26×	`distribute-lft-out`
24×	`distribute-rgt-out`
18×	`pow1/2`
16×	`associate-r`
14×	`sqrt-pow1` `associate-/l*`
13×	`log-prod`
11×	`associate-l`
10×	`sqrt-prod`
8×	`add-exp-log`
6×	`log-div` `sqrt-div` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`associate-+l-` `div-sub` `rem-log-exp` `hypot-def` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv` `unswap-sqr`

Counts

4 → 139

Calls

4 calls:

7.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
29.0ms	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (* 1/2 (log (+ 1.0 (* y (expm1 z)))))) t)
7.0ms	(log (+ 1.0 (* y (expm1 z))))
7.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

377.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
1.7s	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (* 1/2 (log (+ 1.0 (* y (expm1 z)))))) t)
81.0ms	(log (+ 1.0 (* y (expm1 z))))
361.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1337	2241
1	5001	2016

prune424.0ms

Filtered

151 candidates to 98 candidates (64.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	145	6	151
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	151	9	160

Merged error: 3.4b

Counts

160 → 9

regimes338.0ms

Accuracy

15.4% (6.6b remaining)

Error of 10.5b against oracle of 3.8b and baseline of 11.7b

bsearch468.0ms

Steps

Iters	Range		Point
10	5.552852886699997e+156	3.588125464269834e+171	2.18513934236594e+168
9	5.083153231761579e-69	9.114080464594191e-62	1.200322686089934e-65
4	-1.0033589185616838e-167	-5.135396417901946e-168	-6.551981243054993e-168
9	-3.788194238971983e-59	-5.071317957157481e-65	-6.684826227676744e-61

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	105
1	87	105

end0.0ms

sample3.2s

Algorithm

intervals

Results

766.0ms	1431×	body	1280	valid
738.0ms	1472×	body	10240	exit
473.0ms	1570×	body	640	valid
223.0ms	3577×	body	80	valid
173.0ms	906×	body	320	valid
118.0ms	91×	body	2560	valid
94.0ms	2518×	body	80	nan
57.0ms	274×	body	640	nan
52.0ms	449×	body	160	valid
32.0ms	108×	body	1280	nan
27.0ms	198×	body	320	nan
11.0ms	128×	body	160	nan