Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample28.0ms

Algorithm

intervals

Results

14.0ms	86×	body	1280	valid
5.0ms	140×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	70	7
1	70	7

prune2.0ms

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: 13.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.0b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-atan_binary64`

Counts

2 → 21

Calls

2 calls:

1.0ms	(atan.f64 (+.f64 N 1))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series6.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan.f64 (+.f64 N 1))
5.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify68.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4923	236
1	4923	236

prune15.0ms

Filtered

19 candidates to 27 candidates (-42.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Merged error: 0.5b

Counts

28 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.6b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-l_binary64`
2×	`add-log-exp_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

2 → 30

Calls

2 calls:

6.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series11.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(*.f64 N (+.f64 N 1))
6.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify66.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5066	260

prune27.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	33	5	38

Merged error: 0.5b

Counts

38 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 1 N))
0.3b	(cbrt.f64 (+.f64 N 1))
0.3b	(*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))
0.6b	(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))) (cbrt.f64 (+.f64 N 1)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64` `cbrt-prod_binary64`
22×	`add-sqr-sqrt_binary64`
16×	`cbrt-div_binary64`
14×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`swap-sqr_binary64`
8×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `flip-+_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 1 N))
3.0ms	(cbrt.f64 (+.f64 N 1))
13.0ms	(*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))
1.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))) (cbrt.f64 (+.f64 N 1)))))

series19.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cbrt.f64 (+.f64 1 N))
5.0ms	(cbrt.f64 (+.f64 N 1))
6.0ms	(*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))
3.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))) (cbrt.f64 (+.f64 N 1)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4837	952
1	4837	952

prune84.0ms

Filtered

73 candidates to 100 candidates (-37.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	99	6	105

Merged error: 0.5b

Counts

105 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 1 N))
0.3b	(.f64 (cbrt.f64 (+.f64 1 N)) (/.f64 (cbrt.f64 (-.f64 1 (.f64 N N))) (cbrt.f64 (-.f64 1 N))))
0.6b	(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (.f64 (cbrt.f64 (+.f64 1 N)) (/.f64 (cbrt.f64 (-.f64 1 (.f64 N N))) (cbrt.f64 (-.f64 1 N))))) (cbrt.f64 (+.f64 N 1)))))
14.5b	(cbrt.f64 (-.f64 1 (*.f64 N N)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

121×	`cbrt-prod_binary64`
108×	`add-sqr-sqrt_binary64`
82×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
78×	`associate-r_binary64`
43×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`
10×	`cbrt-div_binary64` `unswap-sqr_binary64`
9×	`add-exp-log_binary64` `distribute-lft-out--_binary64`
7×	`associate-l_binary64`
6×	`pow1_binary64`
5×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `associate-/r/_binary64` `prod-exp_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 151

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 1 N))
34.0ms	(.f64 (cbrt.f64 (+.f64 1 N)) (/.f64 (cbrt.f64 (-.f64 1 (.f64 N N))) (cbrt.f64 (-.f64 1 N))))
1.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (.f64 (cbrt.f64 (+.f64 1 N)) (/.f64 (cbrt.f64 (-.f64 1 (.f64 N N))) (cbrt.f64 (-.f64 1 N))))) (cbrt.f64 (+.f64 N 1)))))
3.0ms	(cbrt.f64 (-.f64 1 (*.f64 N N)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt.f64 (-.f64 1 N))
9.0ms	(.f64 (cbrt.f64 (+.f64 1 N)) (/.f64 (cbrt.f64 (-.f64 1 (.f64 N N))) (cbrt.f64 (-.f64 1 N))))
6.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (.f64 (cbrt.f64 (+.f64 1 N)) (/.f64 (cbrt.f64 (-.f64 1 (.f64 N N))) (cbrt.f64 (-.f64 1 N))))) (cbrt.f64 (+.f64 N 1)))))
11.0ms	(cbrt.f64 (-.f64 1 (*.f64 N N)))

simplify72.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4918	2837
1	4918	2837

prune237.0ms

Filtered

137 candidates to 163 candidates (-19.0%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	163	6	169

Merged error: 0.5b

Counts

169 → 6

regimes48.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	9
1	10	9

end0.0ms

sample848.0ms

Algorithm

intervals

Results

463.0ms	2775×	body	1280	valid
151.0ms	4123×	body	80	valid
84.0ms	636×	body	640	valid
32.0ms	301×	body	320	valid
12.0ms	165×	body	160	valid

Details

analyze1.0ms

sample28.0ms

simplify8.0ms

prune2.0ms

localize6.0ms

rewrite5.0ms

series6.0ms

simplify68.0ms

prune15.0ms

localize6.0ms

rewrite8.0ms

series11.0ms

simplify66.0ms

prune27.0ms

localize11.0ms

rewrite23.0ms

series19.0ms

simplify87.0ms

prune84.0ms

localize18.0ms

rewrite50.0ms

series31.0ms

simplify72.0ms

prune237.0ms

regimes48.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample848.0ms

Profiling