Details

analyze61.0ms

Algorithm

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

sample23.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	258×	pre	80	true
0.0ms	2×	body	80	invalid

simplify623.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (152.0ms)

Iter	Nodes	Cost
0	4930	13
1	4930	13

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 m (-.f64 1 m))
0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.0b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
10×	`add-cube-cbrt_binary64` `associate-l_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`pow1_binary64` `difference-of-squares_binary64`
6×	`add-log-exp_binary64` `associate-*r/_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-out--_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 98

Calls

4 calls:

7.0ms	(*.f64 m (-.f64 1 m))
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
18.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

series33.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 m (-.f64 1 m))
5.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
17.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

simplify49.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4988	1291
1	4988	1291

prune99.0ms

Filtered

77 candidates to 110 candidates (-42.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	5	111

Merged error: 0.0b

Counts

111 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 v (-.f64 1 m))
0.0b	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
0.0b	(/.f64 m (/.f64 v (-.f64 1 m)))
0.0b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac_binary64`
177×	`add-sqr-sqrt_binary64`
143×	`*-un-lft-identity_binary64`
82×	`add-cube-cbrt_binary64`
46×	`difference-of-squares_binary64`
30×	`associate-/r*_binary64`
19×	`distribute-lft-out--_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
12×	`flip3--_binary64` `flip--_binary64`
11×	`associate-/r/_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `difference-of-sqr-1_binary64` `associate-/l*_binary64` `div-inv_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`sub-neg_binary64`
2×	`associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 217

Calls

4 calls:

6.0ms	(/.f64 v (-.f64 1 m))
32.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
10.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
36.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))

series24.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 v (-.f64 1 m))
5.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
5.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
7.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))

simplify46.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5227	3186

prune141.0ms

Filtered

160 candidates to 229 candidates (-43.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	229	5	234

Merged error: 0.0b

Counts

234 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
0.1b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

32×	`frac-times_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64` `flip3--_binary64` `flip--_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-*l/_binary64`
14×	`associate-r_binary64`
12×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
11×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`
8×	`associate-l_binary64` `difference-of-squares_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `distribute-lft-out--_binary64` `sqrt-prod_binary64`
3×	`associate-/r*_binary64` `sub-neg_binary64` `times-frac_binary64`
2×	`associate-/l/_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 124

Calls

4 calls:

9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
16.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
22.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
12.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))

simplify42.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5047	2632

prune108.0ms

Filtered

100 candidates to 136 candidates (-36.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	135	6	141

Merged error: 0b

Counts

141 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m)))) 1)
0.0b	(.f64 (-.f64 (.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m)))) 1) (-.f64 1 m))
0.3b	(/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m)))
0.4b	(*.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

534×	`times-frac_binary64`
391×	`add-sqr-sqrt_binary64`
357×	`*-un-lft-identity_binary64`
237×	`add-cube-cbrt_binary64`
159×	`sqrt-prod_binary64`
155×	`associate-r_binary64`
80×	`difference-of-squares_binary64`
40×	`distribute-lft-out--_binary64`
28×	`associate-/r/_binary64`
24×	`associate-/r*_binary64`
20×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
15×	`div-inv_binary64`
11×	`unswap-sqr_binary64`
9×	`associate-l_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `associate-*r/_binary64`
2×	`pow-prod-down_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 412

Calls

4 calls:

20.0ms	(-.f64 (*.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m)))) 1)
29.0ms	(.f64 (-.f64 (.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m)))) 1) (-.f64 1 m))
12.0ms	(/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m)))
46.0ms	(*.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(-.f64 (*.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m)))) 1)
16.0ms	(.f64 (-.f64 (.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m)))) 1) (-.f64 1 m))
24.0ms	(/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m)))
16.0ms	(*.f64 (sqrt.f64 m) (/.f64 (sqrt.f64 m) (/.f64 v (-.f64 1 m))))

simplify115.0ms

Algorithm

egg-herbie

Counts

424 → 424

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4983	6212
1	4983	6212

prune225.0ms

Filtered

245 candidates to 424 candidates (-73.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	424	0	424
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	424	6	430

Merged error: 0b

Counts

430 → 6

regimes66.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	13
1	31	13

end0.0ms

sample574.0ms

Algorithm

intervals

Results

283.0ms	8000×	body	80	valid
152.0ms	8057×	pre	80	true
2.0ms	57×	body	80	invalid

Details

analyze61.0ms

sample23.0ms

simplify623.0ms

prune6.0ms

localize9.0ms

rewrite62.0ms

series33.0ms

simplify49.0ms

prune99.0ms

localize10.0ms

rewrite95.0ms

series24.0ms

simplify46.0ms

prune141.0ms

localize15.0ms

rewrite60.0ms

series40.0ms

simplify42.0ms

prune108.0ms

localize10.0ms

rewrite137.0ms

series68.0ms

simplify115.0ms

prune225.0ms

regimes66.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample574.0ms

Profiling