Details

analyze5.0ms (0%)

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)

sample1.6s (10.2%)

Results

638.0ms	2046×	body	1024	valid
426.0ms	4447×	body	128	valid
253.0ms	1072×	body	512	valid
85.0ms	515×	body	256	valid
65.0ms	176×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify90.0ms (0.6%)

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

27.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.1b	(-.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%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	3.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series7.0ms (0%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite217.0ms (1.4%)

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:

40.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.0ms	(/.f64 x (+.f64 x 1))

simplify930.0ms (6%)

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 → 619

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

prune752.0ms (4.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	613	6	619
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	614	6	620

Error

0.0b

Counts

620 → 6

Alt Table

Status	Error	Program
	34.4b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	27.2b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
	27.5b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
▶	27.2b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	33.9b	(/.f64 -3 x)
	61.4b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (pow.f64 (sqrt.f64 (/.f64 (+.f64 1 x) (+.f64 x -1))) 4) (*.f64 (/.f64 x (+.f64 1 x)) (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))))

Compiler

Compiled 30522 to 22493 computations (26.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	0.0b	(exp.f64 (/.f64 x (+.f64 x 1)))
✓	3.1b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	4.1b	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))

series8.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
3.0ms	(exp.f64 (/.f64 x (+.f64 x 1)))
2.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))

rewrite293.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

1435×	`*-un-lft-identity_binary64`
1089×	`times-frac_binary64`
985×	`add-sqr-sqrt_binary64`
748×	`prod-diff_binary64`
685×	`log-pow_binary64`

Counts

3 → 884

Calls

3 calls:

47.0ms	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
4.0ms	(log.f64 (exp.f64 (/.f64 x (+.f64 x 1))))
4.0ms	(exp.f64 (/.f64 x (+.f64 x 1)))

simplify736.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-neg_binary64`
415×	`unsub-neg_binary64`
393×	`times-frac_binary64`
306×	`fma-udef_binary64`
231×	`exp-prod_binary64`

Counts

920 → 608

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	607	34067
1	1302	22396
2	2772	22185
3	4140	22183
4	4819	22183

prune848.0ms (5.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	694	0	694
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	694	6	700

Error

0.0b

Counts

700 → 6

Alt Table

Status	Error	Program
	34.4b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
▶	27.2b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
	27.5b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
✓	27.2b	(-.f64 (log.f64 (exp.f64 (/.f64 x (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	33.9b	(/.f64 -3 x)
	61.4b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (pow.f64 (sqrt.f64 (/.f64 (+.f64 1 x) (+.f64 x -1))) 4) (*.f64 (/.f64 x (+.f64 1 x)) (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))))

Compiler

Compiled 36459 to 27296 computations (25.1% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.1b	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
✓	6.2b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))

series8.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
78×	`add-sqr-sqrt_binary64`
68×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
27×	`associate-r_binary64`

Counts

3 → 164

Calls

3 calls:

11.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
10.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
4.0ms	(/.f64 1 (-.f64 x 1))

simplify118.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

679×	`distribute-rgt-in_binary64`
563×	`distribute-lft-in_binary64`
490×	`fma-neg_binary64`
412×	`times-frac_binary64`
150×	`distribute-rgt-neg-in_binary64`

Counts

200 → 271

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3951
1	615	3300
2	2018	2929
3	4657	2927
4	4919	2927

prune270.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	338	1	339
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	340	5	345

Error

0.0b

Counts

345 → 5

Alt Table

Status	Error	Program
	34.4b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
✓	27.2b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
▶	27.1b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (fma.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	33.9b	(/.f64 -3 x)
	27.5b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

Compiler

Compiled 8034 to 5918 computations (26.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
✓	0.0b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (fma.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
✓	0.1b	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
✓	3.0b	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))

series16.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (fma.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
5.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
3.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
2.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)

rewrite1.4s (8.9%)

Algorithm

1×	rewrite-expression-head

Rules

5264×	`*-un-lft-identity_binary64`
3871×	`times-frac_binary64`
2802×	`add-sqr-sqrt_binary64`
2524×	`cube-prod_binary64`
2524×	`unpow-prod-down_binary64`

Counts

4 → 3085

Calls

4 calls:

160.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (fma.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
126.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
8.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
5.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)

simplify4.3s (27.8%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-neg_binary64`
441×	`fma-udef_binary64`
260×	`fma-def_binary64`
248×	`unsub-neg_binary64`
247×	`associate-/l*_binary64`

Counts

3133 → 1132

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1052	287091
1	2179	205380
2	4818	205380
3	5246	205380

prune3.2s (20.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1132	0	1132
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	1132	5	1137

Error

0.0b

Counts

1137 → 5

Alt Table

Status	Error	Program
	34.4b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
✓	27.2b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))
✓	27.1b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (fma.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	33.9b	(/.f64 -3 x)
	27.5b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

Compiler

Compiled 104559 to 78931 computations (24.5% saved)

regimes423.0ms (2.7%)

Accuracy

Total 0.0b remaining (20.6%)

Threshold costs 0.0b (20.6%)

Counts

123 → 3

Compiler

Compiled 6865 to 5135 computations (25.2% saved)

bsearch43.0ms (0.3%)

Steps

Iters	Range		Point
8	24.98942712927663	149845.75484670163	2601.5280327281093
9	-658595127.8552431	-164.1333492973497	-3606.908350404843

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	136
1	51	136
2	66	136
3	81	136
4	88	136
5	90	136
6	87	136

end146.0ms (0.9%)

Compiler: Compiled 290 to 215 computations (25.9% saved)

Details

analyze5.0ms (0%)

sample1.6s (10.2%)

simplify90.0ms (0.6%)

prune2.0ms (0%)

localize6.0ms (0%)

series7.0ms (0%)

rewrite217.0ms (1.4%)

simplify930.0ms (6%)

prune752.0ms (4.9%)

localize10.0ms (0.1%)

series8.0ms (0.1%)

rewrite293.0ms (1.9%)

simplify736.0ms (4.8%)

prune848.0ms (5.5%)

localize7.0ms (0%)

series8.0ms (0.1%)

rewrite37.0ms (0.2%)

simplify118.0ms (0.8%)

prune270.0ms (1.7%)

localize15.0ms (0.1%)

series16.0ms (0.1%)

rewrite1.4s (8.9%)

simplify4.3s (27.8%)

prune3.2s (20.7%)

regimes423.0ms (2.7%)

bsearch43.0ms (0.3%)

simplify5.0ms (0%)

end146.0ms (0.9%)

Profiling