Details

sample132.0ms

Algorithm

intervals

Results

33.0ms	51×	body	1280	valid
26.0ms	41×	body	5120	exit
23.0ms	57×	body	640	valid
11.0ms	107×	body	80	valid
7.0ms	29×	body	320	valid
5.0ms	95×	body	80	nan
2.0ms	13×	body	160	valid
2.0ms	7×	body	640	nan
1.0ms	1×	body	2560	valid
1.0ms	4×	body	320	nan
0.0ms	4×	body	160	nan
0.0ms	1×	body	1280	nan

simplify211.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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	1553	7
11	1892	7
12	4682	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: 26.4b

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)
1.6b	(+ (- 1.0 y) (* y (exp z)))
1.7b	(log (+ (- 1.0 y) (* y (exp z))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

5.0ms	(* y (exp z))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
7.0ms	(+ (- 1.0 y) (* y (exp z)))
6.0ms	(log (+ (- 1.0 y) (* y (exp z))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* y (exp z))
145.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
37.0ms	(+ (- 1.0 y) (* y (exp z)))
74.0ms	(log (+ (- 1.0 y) (* y (exp z))))

simplify60.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune311.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	6	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Merged error: 5.0b

Counts

115 → 6

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
4.0b	(log (+ 1.0 (* y (expm1 z))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

9.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
4.0ms	(log (+ 1.0 (* y (expm1 z))))

series227.0ms

Counts

2 → 6

Calls

2 calls:

147.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
80.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify39.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	551
1	1312	506
2	5002	493

prune162.0ms

Filtered

57 candidates to 46 candidates (80.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	57	6	63

Merged error: 5.0b

Counts

63 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
0.1b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
4.0b	(log (+ 1.0 (* y (expm1 z))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
62×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`pow1`
20×	`associate-/r*`
17×	`add-exp-log` `log-pow`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv`
3×	`expm1-log1p-u` `log-prod` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `flip3-+` `rem-log-exp` `associate-/r/` `flip-+` `inv-pow`

Counts

3 → 139

Calls

3 calls:

3.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
6.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series337.0ms

Counts

3 → 9

Calls

3 calls:

189.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
76.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
72.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify71.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	654	1621
1	3051	1467
2	5002	1374

prune281.0ms

Filtered

148 candidates to 86 candidates (58.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	145	9	154

Merged error: 5.0b

Counts

154 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (+ 1.0 (* y (expm1 z))))
0.1b	(cbrt (+ 1.0 (* y (expm1 z))))
4.0b	(log (cbrt (+ 1.0 (* y (expm1 z)))))
4.0b	(log (cbrt (+ 1.0 (* y (expm1 z)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-div`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `log-div` `flip3-+` `pow1/3` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp`

Counts

4 → 70

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
2.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
3.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
3.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
149.0ms	(cbrt (+ 1.0 (* y (expm1 z))))
139.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))
137.0ms	(log (cbrt (+ 1.0 (* y (expm1 z)))))

simplify39.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	318	880
1	1062	820
2	5001	794

prune332.0ms

Filtered

82 candidates to 76 candidates (92.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	82	9	91

Merged error: 5.0b

Counts

91 → 9

regimes340.0ms

Accuracy

42% (4.1b remaining)

Error of 8.4b against oracle of 4.3b and baseline of 11.4b

bsearch94.0ms

Steps

Iters	Range		Point
8	-1.0323301464746194e-49	-1.8237789437890818e-53	-4.754825993747406e-50

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	30
1	36	30

end0.0ms

sample3.6s

Algorithm

intervals

Results

882.0ms	1525×	body	5120	exit
834.0ms	1420×	body	1280	valid
562.0ms	1629×	body	640	valid
254.0ms	3494×	body	80	valid
197.0ms	888×	body	320	valid
126.0ms	2584×	body	80	nan
108.0ms	84×	body	2560	valid
71.0ms	515×	body	160	valid
66.0ms	266×	body	640	nan
40.0ms	113×	body	1280	nan
33.0ms	193×	body	320	nan
11.0ms	106×	body	160	nan