Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample22.0ms

Algorithm

intervals

Results

8.0ms	67×	body	1024	valid
4.0ms	132×	body	128	valid
3.0ms	37×	body	512	valid
1.0ms	16×	body	256	valid
1.0ms	4×	body	2048	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune1.0ms

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: 30.8b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
4.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
20×	`distribute-lft-out_binary64`
18×	`distribute-lft-out--_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64` `difference-of-sqr-1_binary64`
4×	`associate-/r/_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-sub_binary64`

Counts

3 → 113

Calls

3 calls:

10.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))
48.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series124.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
25.0ms	(/.f64 x (+.f64 x 1))
74.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify79.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4942	2299
1	4942	2299

prune133.0ms

Filtered

77 candidates to 122 candidates (-58.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	3	123

Merged error: 0.0b

Counts

123 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.2b	(/.f64 3 (pow.f64 x 3))
0.7b	(/.f64 -1 (*.f64 x x))
7.0b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64` `times-frac_binary64`
39×	`add-sqr-sqrt_binary64`
35×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-/r*_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
9×	`unpow3_binary64`
6×	`distribute-lft-out_binary64` `associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`pow1_binary64` `distribute-rgt-out_binary64` `sqr-pow_binary64` `div-inv_binary64` `cube-mult_binary64`
3×	`cbrt-undiv_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `distribute-rgt1-in_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 128

Calls

4 calls:

35.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
6.0ms	(/.f64 3 (pow.f64 x 3))
5.0ms	(/.f64 -1 (*.f64 x x))
43.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

series210.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
45.0ms	(/.f64 3 (pow.f64 x 3))
34.0ms	(/.f64 -1 (*.f64 x x))
31.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify51.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5319	2247

prune110.0ms

Filtered

87 candidates to 140 candidates (-60.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 0.0b

Counts

143 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (pow.f64 x 3))
0.2b	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
0.7b	(/.f64 -1 (*.f64 x x))
7.0b	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64` `times-frac_binary64`
39×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`
16×	`associate-r_binary64`
13×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
10×	`unpow3_binary64`
7×	`distribute-lft-out_binary64` `div-inv_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-r/_binary64` `associate-/l_binary64`
5×	`distribute-rgt-out_binary64` `div-exp_binary64`
4×	`sqr-pow_binary64` `cube-mult_binary64`
3×	`cbrt-undiv_binary64` `associate-l_binary64` `rec-exp_binary64` `frac-sub_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `associate--r+_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-rgt1-in_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `flip--_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 143

Calls

4 calls:

6.0ms	(/.f64 1 (pow.f64 x 3))
43.0ms	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
5.0ms	(/.f64 -1 (*.f64 x x))
8.0ms	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/.f64 1 (pow.f64 x 3))
94.0ms	(*.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))))
31.0ms	(/.f64 -1 (*.f64 x x))
30.0ms	(-.f64 (/.f64 -1 (.f64 x x)) (.f64 3 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5015	2069

prune108.0ms

Filtered

84 candidates to 155 candidates (-84.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	155	7	162

Merged error: 0.0b

Counts

162 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
4.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
4.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
4.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

956×	`*-un-lft-identity_binary64`
364×	`times-frac_binary64`
261×	`distribute-lft-out--_binary64`
184×	`cbrt-prod_binary64`
168×	`distribute-lft-out_binary64`
104×	`add-sqr-sqrt_binary64`
77×	`swap-sqr_binary64`
28×	`difference-of-squares_binary64`
24×	`cbrt-div_binary64`
19×	`associate-r_binary64` `associate-l_binary64`
12×	`add-cube-cbrt_binary64`
11×	`pow1_binary64` `flip3--_binary64` `flip--_binary64` `frac-sub_binary64`
10×	`add-log-exp_binary64`
9×	`frac-times_binary64`
6×	`pow1/3_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 227

Calls

4 calls:

105.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
48.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
48.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
80.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
72.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
70.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify105.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5116	8730

prune291.0ms

Filtered

106 candidates to 239 candidates (-125.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	239	7	246

Merged error: 0.0b

Counts

246 → 7

regimes61.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.3b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	69
1	84	69

end0.0ms

sample648.0ms

Algorithm

intervals

Results

245.0ms	1941×	body	1024	valid
143.0ms	4345×	body	128	valid
90.0ms	974×	body	512	valid
36.0ms	540×	body	256	valid
32.0ms	200×	body	2048	valid

Details

analyze4.0ms

sample22.0ms

simplify73.0ms

prune1.0ms

localize6.0ms

rewrite76.0ms

series124.0ms

simplify79.0ms

prune133.0ms

localize11.0ms

rewrite102.0ms

series210.0ms

simplify51.0ms

prune110.0ms

localize11.0ms

rewrite77.0ms

series197.0ms

simplify72.0ms

prune108.0ms

localize10.0ms

rewrite317.0ms

series363.0ms

simplify105.0ms

prune291.0ms

regimes61.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample648.0ms

Profiling