Details

analyze104.0ms (1.9%)

Algorithm

1×

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample28.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	66×	body	1024	valid
6.0ms	142×	body	128	valid
3.0ms	27×	body	512	valid
1.0ms	16×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

prune2.0ms (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

Error

28.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	3.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite153.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

1322×	`*-un-lft-identity_binary64`
1012×	`times-frac_binary64`
869×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
533×	`add-cube-cbrt_binary64`

Counts

3 → 783

Calls

3 calls:

43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
4.0ms	(/.f64 x (+.f64 x 1))

series11.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
4.0ms	(/.f64 x (+.f64 x 1))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify1.0s (19%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-neg_binary64`
367×	`unsub-neg_binary64`
299×	`fma-udef_binary64`
213×	`sub-neg_binary64`
202×	`associate-+r-_binary64`

Counts

819 → 1621

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	545	54602
1	1290	31108
2	3043	22839
3	4323	22837
4	4983	22837
5	4991	22837
6	4742	22837

prune838.0ms (15.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	1615	6	1621
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1616	6	1622

Error

0.0b

Counts

1622 → 6

Alt Table

Status	Error	Program
	47.2b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 x (sqrt.f64 (+.f64 x 1))) (neg.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1))) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)) (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)))))
	32.6b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
▶	28.5b	(/.f64 (-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
	29.0b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
	32.7b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
	31.6b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))

Compiler

Compiled 30680 to 22609 computations (26.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	0.0b	(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
✓	0.0b	(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	3.2b	(-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

rewrite107.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

448×	`*-un-lft-identity_binary64`
284×	`times-frac_binary64`
236×	`add-sqr-sqrt_binary64`
108×	`add-cube-cbrt_binary64`
96×	`distribute-lft-out_binary64`

Counts

4 → 327

Calls

4 calls:

29.0ms	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
27.0ms	(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
15.0ms	(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
11.0ms	(-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

series20.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

11.0ms	(-.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
3.0ms	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
3.0ms	(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
3.0ms	(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))

simplify227.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

369×	`associate-l_binary64`
349×	`associate-r_binary64`
331×	`associate-*r/_binary64`
314×	`associate-*l/_binary64`
280×	`associate-/l*_binary64`

Counts

375 → 706

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	410	10195
1	1231	9124
2	4633	8649
3	4952	8649

prune531.0ms (9.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	705	1	706
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	706	6	712

Error

0.0b

Counts

712 → 6

Alt Table

Status	Error	Program
	47.2b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 x (sqrt.f64 (+.f64 x 1))) (neg.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1))) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)) (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)))))
	32.6b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
▶	29.0b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
	32.7b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
	29.8b	(/.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (+.f64 x -1) (+.f64 x -1))) (pow.f64 (+.f64 1 x) 4)) (.f64 (fma.f64 x x -1) (fma.f64 x x -1))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
	31.6b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))

Compiler

Compiled 21290 to 15285 computations (28.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 (-.f64 -1 x) (+.f64 x -1))
✓	28.9b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out_binary64`

Counts

3 → 103

Calls

3 calls:

7.0ms	(/.f64 (-.f64 -1 x) (+.f64 x -1))
4.0ms	(/.f64 1 (+.f64 x 1))
0.0ms	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
2.0ms	(/.f64 (-.f64 -1 x) (+.f64 x -1))
2.0ms	(/.f64 1 (+.f64 x 1))

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

593×	`div-sub_binary64`
585×	`fma-neg_binary64`
396×	`fma-def_binary64`
220×	`distribute-rgt-in_binary64`
164×	`times-frac_binary64`

Counts

139 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	2228
1	476	2034
2	1162	2028
3	3488	2028
4	5150	2028

prune165.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	237	6	243

Error

0.0b

Counts

243 → 6

Alt Table

Status	Error	Program
	31.6b	(fma.f64 3 (+.f64 x (pow.f64 x 3)) (fma.f64 x x 1))
✓	29.0b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
	47.2b	(+.f64 (fma.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 x (sqrt.f64 (+.f64 x 1))) (neg.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1))))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1))) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)) (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (sqrt.f64 x) 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (+.f64 (sqrt.f64 x) 1)))))
	32.6b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	32.7b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
▶	29.8b	(/.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (+.f64 x -1) (+.f64 x -1))) (pow.f64 (+.f64 1 x) 4)) (.f64 (fma.f64 x x -1) (fma.f64 x x -1))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

Compiler

Compiled 3814 to 2824 computations (26% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 1 x) 4)
✓	0.1b	(.f64 (.f64 x x) (*.f64 (+.f64 x -1) (+.f64 x -1)))
✓	0.1b	(*.f64 (fma.f64 x x -1) (fma.f64 x x -1))
✓	25.2b	(-.f64 (.f64 (.f64 x x) (*.f64 (+.f64 x -1) (+.f64 x -1))) (pow.f64 (+.f64 1 x) 4))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`pow1_binary64`
20×	`*-un-lft-identity_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 126

Calls

4 calls:

15.0ms	(-.f64 (.f64 (.f64 x x) (*.f64 (+.f64 x -1) (+.f64 x -1))) (pow.f64 (+.f64 1 x) 4))
11.0ms	(.f64 (.f64 x x) (*.f64 (+.f64 x -1) (+.f64 x -1)))
5.0ms	(*.f64 (fma.f64 x x -1) (fma.f64 x x -1))
3.0ms	(pow.f64 (+.f64 1 x) 4)

series22.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

9.0ms	(*.f64 (fma.f64 x x -1) (fma.f64 x x -1))
6.0ms	(.f64 (.f64 x x) (*.f64 (+.f64 x -1) (+.f64 x -1)))
4.0ms	(-.f64 (.f64 (.f64 x x) (*.f64 (+.f64 x -1) (+.f64 x -1))) (pow.f64 (+.f64 1 x) 4))
2.0ms	(pow.f64 (+.f64 1 x) 4)

simplify143.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

276×	`associate-l_binary64`
246×	`associate-r_binary64`
244×	`exp-prod_binary64`
235×	`unswap-sqr_binary64`
234×	`log-prod_binary64`

Counts

174 → 321

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	3522
1	566	2931
2	2095	2459
3	4326	2404
4	4960	2404
5	4971	2404

prune277.0ms (5.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	318	3	321
Fresh	1	3	4
Picked	1	0	1
Done	1	0	1
Total	321	6	327

Error

0.0b

Counts

327 → 6

Alt Table

Status	Error	Program
	22.4b	(/.f64 (/.f64 (neg.f64 (+.f64 1 (+.f64 (.f64 5 (pow.f64 x 2)) (+.f64 (.f64 4 x) (.f64 6 (pow.f64 x 3)))))) (.f64 (fma.f64 x x -1) (fma.f64 x x -1))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
	29.8b	(/.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (+.f64 x -1) (+.f64 x -1))) (pow.f64 (+.f64 1 x) 4)) (+.f64 (-.f64 (pow.f64 x 4) (.f64 x x)) (-.f64 1 (*.f64 x x)))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
	31.6b	(fma.f64 3 (+.f64 x (pow.f64 x 3)) (fma.f64 x x 1))
	32.6b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	32.7b	(neg.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))))))
	22.4b	(/.f64 (/.f64 (-.f64 (fma.f64 x -4 -1) (.f64 (.f64 x x) (+.f64 5 (.f64 6 x)))) (.f64 (fma.f64 x x -1) (fma.f64 x x -1))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

Compiler

Compiled 10216 to 6916 computations (32.3% saved)

regimes436.0ms (7.9%)

Accuracy

Total 0.0b remaining (74%)

Threshold costs 0.0b (74%)

Compiler

Compiled 7652 to 5664 computations (26% saved)

bsearch24.0ms (0.4%)

Steps

Iters	Range		Point
6	274587220209162.75	3645111812598632.5	3580589034911187.0
4	-10563676.794156242	-800.7477104091652	-15104.003133029944

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

24×	`+-commutative_binary64`
18×	`*-commutative_binary64`
18×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	130
1	70	128
2	96	128
3	133	128
4	168	128
5	183	128
6	190	128
7	192	128
8	186	128

end2.0ms (0%)

Compiler: Compiled 88 to 65 computations (26.1% saved)

sample1.1s (19.2%)

Algorithm

1×

intervals

Results

322.0ms	2039×	body	1024	valid
184.0ms	4296×	body	128	valid
116.0ms	965×	body	512	valid
42.0ms	494×	body	256	valid
40.0ms	206×	body	2048	valid

Compiler

Compiled 293 to 214 computations (27% saved)

Iter	Nodes	Cost
0	47	130
1	70	128
2	96	128
3	133	128
4	168	128
5	183	128
6	190	128
7	192	128
8	186	128

Iter	Nodes	Cost
0	47	130
1	70	128
2	96	128
3	133	128
4	168	128
5	183	128
6	190	128
7	192	128
8	186	128

Details

analyze104.0ms (1.9%)

sample28.0ms (0.5%)

simplify92.0ms (1.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite153.0ms (2.8%)

series11.0ms (0.2%)

simplify1.0s (19%)

prune838.0ms (15.3%)

localize11.0ms (0.2%)

rewrite107.0ms (2%)

series20.0ms (0.4%)

simplify227.0ms (4.1%)

prune531.0ms (9.7%)

localize9.0ms (0.2%)

rewrite15.0ms (0.3%)

series9.0ms (0.2%)

simplify92.0ms (1.7%)

prune165.0ms (3%)

localize20.0ms (0.4%)

rewrite40.0ms (0.7%)

series22.0ms (0.4%)

simplify143.0ms (2.6%)

prune277.0ms (5.1%)

regimes436.0ms (7.9%)

bsearch24.0ms (0.4%)

simplify9.0ms (0.2%)

end2.0ms (0%)

sample1.1s (19.2%)

Profiling

Iter	Nodes	Cost
0	47	130
1	70	128
2	96	128
3	133	128
4	168	128
5	183	128
6	190	128
7	192	128
8	186	128