Details

analyze6.0ms (0.1%)

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 (13.9%)

Results

663.0ms	2059×	body	1024	valid
435.0ms	4365×	body	128	valid
265.0ms	1105×	body	512	valid
86.0ms	501×	body	256	valid
86.0ms	226×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify92.0ms (0.8%)

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

25.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	25.3b	(-.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 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	1.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 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 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite232.0ms (2%)

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:

46.0ms	(-.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))

simplify1.4s (11.6%)

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

prune907.0ms (7.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	615	4	619
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	616	4	620

Error

0.0b

Counts

620 → 4

Alt Table

Status	Error	Program
	44.7b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 x (+.f64 x 1))) (sqrt.f64 (/.f64 x (+.f64 x 1))) (neg.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 x 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (fma.f64 (neg.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 x 1))) (/.f64 (sqrt.f64 (+.f64 x 1)) 1) (.f64 (/.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 x 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) 1))))
	36.2b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
	26.3b	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
▶	25.3b	(.f64 (.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))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

Compiler

Compiled 30548 to 22511 computations (26.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.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))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
✓	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)))))
✓	0.0b	(cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
	1.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series15.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

6.0ms

(*.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)))))

5.0ms

(cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

4.0ms

(*.f64 (*.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))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

rewrite324.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

912×	`*-un-lft-identity_binary64`
344×	`times-frac_binary64`
248×	`distribute-lft-out--_binary64`
217×	`cbrt-prod_binary64`
171×	`cbrt-div_binary64`

Counts

3 → 297

Calls

3 calls:

103.0ms

(*.f64 (*.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))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

73.0ms

(*.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)))))

30.0ms

(cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

simplify612.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
348×	`fma-neg_binary64`
336×	`*-commutative_binary64`
250×	`associate-l_binary64`
215×	`times-frac_binary64`

Counts

333 → 349

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	368	20281
1	737	19756
2	1902	16994
3	4571	16791
4	4784	16750
5	4746	16750
6	4959	16750

prune4.3s (36%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1853	3	1856
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	1856	4	1860

Error

Counts

1860 → 4

Alt Table

Status	Error	Program
	36.2b	(-.f64 (/.f64 -3 x) (pow.f64 x -2))
	26.3b	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
	26.3b	(/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))) (cbrt.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)))) (cbrt.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3)))) (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (+.f64 (.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))))))) (cbrt.f64 (+.f64 (.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (+.f64 (.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))))))))
▶	23.1b	(/.f64 (-.f64 (fma.f64 x (+.f64 (+.f64 x -1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (+.f64 x -1)))

Compiler

Compiled 154947 to 114796 computations (25.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 x (+.f64 (+.f64 x -1) (-.f64 -1 x)) -1) x)
✓	0.0b	(*.f64 (+.f64 1 x) (+.f64 x -1))
✓	1.0b	(+.f64 (+.f64 x -1) (-.f64 -1 x))
✓	13.3b	(/.f64 (-.f64 (fma.f64 x (+.f64 (+.f64 x -1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (+.f64 x -1)))

series9.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.f64 (-.f64 (fma.f64 x (+.f64 (+.f64 x -1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (+.f64 x -1)))
2.0ms	(*.f64 (+.f64 1 x) (+.f64 x -1))
2.0ms	(-.f64 (fma.f64 x (+.f64 (+.f64 x -1) (-.f64 -1 x)) -1) x)
1.0ms	(+.f64 (+.f64 x -1) (-.f64 -1 x))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
18×	`add-log-exp_binary64`

Counts

4 → 146

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (fma.f64 x (+.f64 (+.f64 x -1) (-.f64 -1 x)) -1) x) (*.f64 (+.f64 1 x) (+.f64 x -1)))
8.0ms	(+.f64 (+.f64 x -1) (-.f64 -1 x))
8.0ms	(*.f64 (+.f64 1 x) (+.f64 x -1))
3.0ms	(-.f64 (fma.f64 x (+.f64 (+.f64 x -1) (-.f64 -1 x)) -1) x)

simplify118.0ms (1%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-neg_binary64`
357×	`sub-neg_binary64`
303×	`div-sub_binary64`
277×	`distribute-rgt-in_binary64`
248×	`distribute-lft-in_binary64`

Counts

194 → 243

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	3592
1	727	2746
2	3008	2699
3	4484	2699
4	5109	2699

prune258.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	241	2	243
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	244	3	247

Error

Counts

247 → 3

Alt Table

Status	Error	Program
▶	23.7b	(.f64 (/.f64 (-.f64 (fma.f64 x (+.f64 x (-.f64 -2 x)) -1) x) (.f64 (+.f64 x -1) (-.f64 1 (*.f64 x x)))) (-.f64 1 x))
	25.8b	(/.f64 (-.f64 (fma.f64 x (+.f64 (+.f64 x -1) (-.f64 -1 x)) -1) x) (/.f64 (.f64 (+.f64 1 (pow.f64 x 3)) (+.f64 (pow.f64 x 3) -1)) (.f64 (fma.f64 x (+.f64 x -1) 1) (fma.f64 x x (+.f64 1 x)))))
	36.2b	(-.f64 (/.f64 -3 x) (pow.f64 x -2))

Compiler

Compiled 7362 to 4959 computations (32.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (+.f64 x -1) (-.f64 1 (.f64 x x)))
✓	1.0b	(+.f64 x (-.f64 -2 x))
✓	4.8b	(/.f64 (-.f64 (fma.f64 x (+.f64 x (-.f64 -2 x)) -1) x) (.f64 (+.f64 x -1) (-.f64 1 (.f64 x x))))
✓	12.7b	(.f64 (/.f64 (-.f64 (fma.f64 x (+.f64 x (-.f64 -2 x)) -1) x) (.f64 (+.f64 x -1) (-.f64 1 (*.f64 x x)))) (-.f64 1 x))

series10.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.f64 (-.f64 (fma.f64 x (+.f64 x (-.f64 -2 x)) -1) x) (.f64 (+.f64 x -1) (-.f64 1 (.f64 x x))))
3.0ms	(.f64 (/.f64 (-.f64 (fma.f64 x (+.f64 x (-.f64 -2 x)) -1) x) (.f64 (+.f64 x -1) (-.f64 1 (*.f64 x x)))) (-.f64 1 x))
2.0ms	(.f64 (+.f64 x -1) (-.f64 1 (.f64 x x)))
1.0ms	(+.f64 x (-.f64 -2 x))

rewrite57.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
50×	`add-sqr-sqrt_binary64`
35×	`add-cube-cbrt_binary64`
33×	`prod-diff_binary64`
22×	`associate-l_binary64`

Counts

4 → 185

Calls

4 calls:

17.0ms	(.f64 (/.f64 (-.f64 (fma.f64 x (+.f64 x (-.f64 -2 x)) -1) x) (.f64 (+.f64 x -1) (-.f64 1 (*.f64 x x)))) (-.f64 1 x))
10.0ms	(/.f64 (-.f64 (fma.f64 x (+.f64 x (-.f64 -2 x)) -1) x) (.f64 (+.f64 x -1) (-.f64 1 (.f64 x x))))
7.0ms	(.f64 (+.f64 x -1) (-.f64 1 (.f64 x x)))
7.0ms	(+.f64 x (-.f64 -2 x))

simplify139.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

445×	`fma-neg_binary64`
327×	`associate-l_binary64`
269×	`distribute-rgt-in_binary64`
267×	`associate-r_binary64`
240×	`distribute-lft-in_binary64`

Counts

233 → 279

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	349	6746
1	873	6074
2	3872	6074
3	4946	6074

prune261.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	278	1	279
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	279	3	282

Error

Counts

282 → 3

Alt Table

Status	Error	Program
	24.3b	(*.f64 (/.f64 (-.f64 (fma.f64 x (+.f64 x (-.f64 -2 x)) -1) x) (-.f64 (fma.f64 x x x) (+.f64 1 (pow.f64 x 3)))) (-.f64 1 x))
✓	23.7b	(.f64 (/.f64 (-.f64 (fma.f64 x (+.f64 x (-.f64 -2 x)) -1) x) (.f64 (+.f64 x -1) (-.f64 1 (*.f64 x x)))) (-.f64 1 x))
	36.2b	(-.f64 (/.f64 -3 x) (pow.f64 x -2))

Compiler

Compiled 10267 to 6336 computations (38.3% saved)

regimes1.3s (11.2%)

Accuracy

Total 0.0b remaining (45.2%)

Threshold costs 0.0b (45.2%)

Counts

395 → 3

Compiler

Compiled 24701 to 18317 computations (25.8% saved)

bsearch23.0ms (0.2%)

Steps

Iters	Range		Point
1	617105423371050.1	85042801574652220.0	7377809056377330.0
1	-8471382980568.733	-375002230.904208	-57091482545.71593

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`cancel-sign-sub-inv_binary64`
14×	`+-commutative_binary64`
13×	`sub-neg_binary64`
7×	`distribute-rgt-neg-in_binary64`
6×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	91
1	57	90
2	74	88
3	80	88
4	90	88
5	98	88
6	100	88
7	95	88

end87.0ms (0.7%)

Compiler: Compiled 181 to 118 computations (34.8% saved)

Details

analyze6.0ms (0.1%)

sample1.6s (13.9%)

simplify92.0ms (0.8%)

prune2.0ms (0%)

localize6.0ms (0%)

series8.0ms (0.1%)

rewrite232.0ms (2%)

simplify1.4s (11.6%)

prune907.0ms (7.6%)

localize12.0ms (0.1%)

series15.0ms (0.1%)

rewrite324.0ms (2.7%)

simplify612.0ms (5.2%)

prune4.3s (36%)

localize11.0ms (0.1%)

series9.0ms (0.1%)

rewrite41.0ms (0.3%)

simplify118.0ms (1%)

prune258.0ms (2.2%)

localize14.0ms (0.1%)

series10.0ms (0.1%)

rewrite57.0ms (0.5%)

simplify139.0ms (1.2%)

prune261.0ms (2.2%)

regimes1.3s (11.2%)

bsearch23.0ms (0.2%)

simplify5.0ms (0%)

end87.0ms (0.7%)

Profiling