Details

sample104.0ms

Algorithm

intervals

Results

28.0ms	59×	body	10240	exit
23.0ms	47×	body	1280	valid
13.0ms	49×	body	640	valid
6.0ms	97×	body	80	nan
6.0ms	111×	body	80	valid
5.0ms	27×	body	320	valid
2.0ms	22×	body	160	valid
2.0ms	6×	body	1280	nan
1.0ms	5×	body	640	nan
1.0ms	6×	body	320	nan
1.0ms	8×	body	160	nan

simplify209.0ms

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: 26.5b

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)
2.2b	(log (+ (- 1.0 y) (* y (exp z))))
3.8b	(+ (- 1.0 y) (* y (exp z)))

rewrite28.0ms

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)
5.0ms	(log (+ (- 1.0 y) (* y (exp z))))
7.0ms	(+ (- 1.0 y) (* y (exp z)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (exp z))
177.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
69.0ms	(log (+ (- 1.0 y) (* y (exp z))))
39.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify64.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (49.0ms)

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

prune335.0ms

Filtered

114 candidates to 91 candidates (79.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Merged error: 3.6b

Counts

115 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.3b	(log (+ 1.0 (* y (expm1 z))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`pow1`
8×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`expm1-log1p-u` `log-prod` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `div-sub` `flip-+`
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 → 71

Calls

3 calls:

3.0ms	(* y (expm1 z))
5.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
3.0ms	(log (+ 1.0 (* y (expm1 z))))

series269.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* y (expm1 z))
161.0ms	(/ (log (+ 1.0 (* y (expm1 z)))) t)
72.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify47.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	429	631
1	1711	580
2	5002	571

prune216.0ms

Filtered

80 candidates to 62 candidates (77.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	79	6	85

Merged error: 3.5b

Counts

85 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (expm1 z))
0.1b	(/ t (log (+ 1.0 (* y (expm1 z)))))
0.1b	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
3.3b	(log (+ 1.0 (* y (expm1 z))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 159

Calls

4 calls:

3.0ms	(* y (expm1 z))
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))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* y (expm1 z))
202.0ms	(/ t (log (+ 1.0 (* y (expm1 z)))))
77.0ms	(/ 1 (/ t (log (+ 1.0 (* y (expm1 z))))))
68.0ms	(log (+ 1.0 (* y (expm1 z))))

simplify82.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	723	1701
1	3451	1541
2	5002	1448

prune337.0ms

Filtered

171 candidates to 102 candidates (59.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	170	7	177

Merged error: 3.5b

Counts

177 → 7

localize186.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (* y (expm1 z))))
0.1b	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
3.4b	(log (sqrt (+ 1.0 (* y (expm1 z)))))
3.4b	(log (sqrt (+ 1.0 (* y (expm1 z)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

94×	`log-pow`
80×	`*-un-lft-identity`
78×	`times-frac`
73×	`pow1`
57×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
40×	`distribute-rgt-out`
32×	`distribute-lft-out`
27×	`sqrt-pow1` `pow1/2`
26×	`associate-/l*`
12×	`log-prod`
10×	`sqrt-div`
9×	`sqrt-prod`
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-/r*`
2×	`associate-+l-` `associate-+r-` `rem-log-exp` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 186

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
12.0ms	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
3.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
3.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

362.0ms	(sqrt (+ 1.0 (* y (expm1 z))))
1.4s	(/ (+ (log (sqrt (+ 1.0 (* y (expm1 z))))) (log (sqrt (+ 1.0 (* y (expm1 z)))))) t)
329.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))
329.0ms	(log (sqrt (+ 1.0 (* y (expm1 z)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1260	3093
1	5001	2585

prune502.0ms

Filtered

198 candidates to 120 candidates (60.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	196	9	205

Merged error: 3.2b

Counts

205 → 9

regimes305.0ms

Accuracy

39.6% (4.5b remaining)

Error of 8.2b against oracle of 3.7b and baseline of 11.2b

bsearch126.0ms

Steps

Iters	Range		Point
8	4.120859846406049e-58	2.66572929097632e-55	4.717741906354947e-57
5	-5.111952297160968e-38	-2.2868282571572898e-38	-4.6972541441660704e-38

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	30
1	42	30

end0.0ms

sample3.1s

Algorithm

intervals

Results

789.0ms	1489×	body	1280	valid
724.0ms	1490×	body	10240	exit
445.0ms	1525×	body	640	valid
207.0ms	3565×	body	80	valid
161.0ms	903×	body	320	valid
90.0ms	2551×	body	80	nan
87.0ms	69×	body	2560	valid
55.0ms	473×	body	160	valid
51.0ms	264×	body	640	nan
38.0ms	134×	body	1280	nan
25.0ms	176×	body	320	nan
8.0ms	97×	body	160	nan