Details

sample37.0ms

Algorithm

intervals

Results

12.0ms	52×	body	1280	valid
9.0ms	34×	body	640	valid
5.0ms	146×	body	80	valid
2.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	31	5
3	54	5
4	119	5
5	333	5
6	1646	5
7	5001	5

prune2.0ms

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: 25.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
7×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`add-exp-log` `add-cbrt-cube` `div-inv`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `distribute-lft-out--`

Counts

3 → 141

Calls

3 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
12.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series132.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
37.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
79.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	398	1645
1	1287	1235
2	5001	1212

prune210.0ms

Filtered

150 candidates to 86 candidates (57.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	2	151

Merged error: 0.0b

Counts

151 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.4b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
26.3b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
42×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`sqrt-prod`
14×	`associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u`
3×	`pow-flip` `fma-def` `flip3-+` `div-exp` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
1×	`+-commutative` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `sum-log` `fma-udef` `inv-pow`

Counts

4 → 127

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
6.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
6.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
1.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series336.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ 1.0 (exp (* -2.0 x)))
65.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
46.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
209.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	378	1222
1	1335	1083
2	5001	1031

prune246.0ms

Filtered

139 candidates to 85 candidates (61.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	137	4	141

Merged error: 0.0b

Counts

141 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
0.0b	(* 0.33333333333333337 (pow x 3))
10.1b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`associate-r`
8×	`add-exp-log`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 53

Calls

3 calls:

1.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
6.0ms	(* 0.33333333333333337 (pow x 3))
1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series175.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
34.0ms	(* 0.33333333333333337 (pow x 3))
94.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify194.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	170	298
1	655	262
2	4021	262
3	5002	262

prune137.0ms

Filtered

62 candidates to 43 candidates (69.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

10.1b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))
14.9b	(cbrt (fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))))
14.9b	(cbrt (fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))))
14.9b	(cbrt (fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))
1.0ms	(cbrt (fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))))
1.0ms	(cbrt (fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))))
1.0ms	(cbrt (fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))))

series545.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))
149.0ms	(cbrt (fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))))
151.0ms	(cbrt (fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))))
152.0ms	(cbrt (fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	198	845
1	603	785
2	2393	701
3	5001	674

prune240.0ms

Filtered

61 candidates to 56 candidates (91.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

regimes239.0ms

Accuracy

98.5% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 30.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	47
1	36	47

end0.0ms

sample1.0s

Algorithm

intervals

Results

424.0ms	1735×	body	1280	valid
201.0ms	1237×	body	640	valid
128.0ms	4060×	body	80	valid
72.0ms	634×	body	320	valid
27.0ms	334×	body	160	valid

Details

sample37.0ms

simplify62.0ms

prune2.0ms

localize6.0ms

rewrite27.0ms

series132.0ms

simplify52.0ms

prune210.0ms

localize13.0ms

rewrite20.0ms

series336.0ms

simplify43.0ms

prune246.0ms

localize10.0ms

rewrite9.0ms

series175.0ms

simplify194.0ms

prune137.0ms

localize14.0ms

rewrite5.0ms

series545.0ms

simplify70.0ms

prune240.0ms

regimes239.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling