Details

analyze5.0ms (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)

sample123.0ms (2.4%)

Algorithm

1×

intervals

Results

9.0ms	59×	body	1024	valid
5.0ms	137×	body	128	valid
4.0ms	37×	body	512	valid
2.0ms	18×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify87.0ms (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

30.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.1%)

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

series8.0ms (0.2%)

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))

rewrite219.0ms (4.2%)

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:

42.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

simplify950.0ms (18.2%)

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

prune980.0ms (18.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	616	3	619
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	617	3	620

Error

0.0b

Counts

620 → 3

Alt Table

Status	Error	Program
	32.0b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1))) (/.f64 (cbrt.f64 x) (sqrt.f64 (+.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))))
	31.2b	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
▶	31.1b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))

Compiler

Compiled 30480 to 22459 computations (26.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
✓	0.3b	(/.f64 1 (*.f64 x x))
✓	0.3b	(/.f64 3 (pow.f64 x 3))
✓	6.5b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))

series14.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

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

rewrite77.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

178×	`*-un-lft-identity_binary64`
136×	`times-frac_binary64`
101×	`add-sqr-sqrt_binary64`
96×	`add-cube-cbrt_binary64`
78×	`prod-diff_binary64`

Counts

4 → 245

Calls

4 calls:

27.0ms	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
19.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
4.0ms	(/.f64 3 (pow.f64 x 3))
4.0ms	(/.f64 1 (*.f64 x x))

simplify219.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

508×	`unswap-sqr_binary64`
388×	`cancel-sign-sub-inv_binary64`
372×	`fma-neg_binary64`
185×	`associate-l_binary64`
185×	`associate-/r*_binary64`

Counts

281 → 274

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	8270
1	610	6566
2	2500	5026
3	4684	5026
4	4880	5026

prune240.0ms (4.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	273	1	274
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	273	4	277

Error

Counts

277 → 4

Alt Table

Status	Error	Program
	32.0b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1))) (/.f64 (cbrt.f64 x) (sqrt.f64 (+.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))))
▶	31.2b	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
	31.4b	(fma.f64 (/.f64 (.f64 (cbrt.f64 -3) (cbrt.f64 -3)) 1) (/.f64 (cbrt.f64 -3) x) (-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (.f64 x x))))
✓	31.1b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))

Compiler

Compiled 9503 to 6596 computations (30.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 x) (-.f64 -1 x))
✓	0.0b	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
✓	31.3b	(fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

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

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 96

Calls

3 calls:

9.0ms	(*.f64 (+.f64 1 x) (-.f64 -1 x))
2.0ms	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
0.0ms	(fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x)))

simplify97.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

795×	`distribute-rgt-in_binary64`
696×	`distribute-lft-in_binary64`
603×	`fma-neg_binary64`
160×	`associate-l_binary64`
149×	`associate-r_binary64`

Counts

132 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	2768
1	465	2474
2	1647	2284
3	4716	2272
4	4988	2272

prune148.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	166	3	169

Error

Counts

169 → 3

Alt Table

Status	Error	Program
▶	13.7b	(/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))
	32.0b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1))) (/.f64 (cbrt.f64 x) (sqrt.f64 (+.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))))
✓	31.1b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))

Compiler

Compiled 4677 to 3061 computations (34.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x -3 -1)
✓	13.7b	(/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))
2.0ms	(fma.f64 x -3 -1)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))
0.0ms	(fma.f64 x -3 -1)

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
370×	`distribute-rgt-in_binary64`
362×	`div-sub_binary64`
336×	`neg-mul-1_binary64`
289×	`distribute-lft-in_binary64`

Counts

63 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	89	997
1	188	875
2	506	871
3	1616	868
4	4434	860
5	4943	860

prune50.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Status	Error	Program
	14.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 x -3 -1)) (cbrt.f64 (fma.f64 x -3 -1))) (/.f64 (cbrt.f64 (fma.f64 x -3 -1)) (fma.f64 x x -1)))
✓	13.7b	(/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))
✓	31.1b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))

Compiler

Compiled 984 to 724 computations (26.4% saved)

regimes874.0ms (16.7%)

Accuracy

Total 0.0b remaining (57.1%)

Threshold costs 0.0b (57.1%)

Counts

221 → 3

Compiler

Compiled 14444 to 10842 computations (24.9% saved)

bsearch22.0ms (0.4%)

Steps

Iters	Range		Point
3	41.25954878773936	235868767227552.28	2483722.563740262
3	-8119083230921666000.0	-1110384604261601300.0	-1476318468044825000.0

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	45
1	28	45
2	36	45
3	46	45
4	51	45
5	53	45
6	52	45

end1.0ms (0%)

Compiler: Compiled 32 to 24 computations (25% saved)

sample964.0ms (18.5%)

Algorithm

1×

intervals

Results

317.0ms	1993×	body	1024	valid
192.0ms	4336×	body	128	valid
110.0ms	958×	body	512	valid
45.0ms	487×	body	256	valid
44.0ms	226×	body	2048	valid

Compiler

Compiled 97 to 73 computations (24.7% saved)

Details

analyze5.0ms (0.1%)

sample123.0ms (2.4%)

simplify87.0ms (1.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series8.0ms (0.2%)

rewrite219.0ms (4.2%)

simplify950.0ms (18.2%)

prune980.0ms (18.8%)

localize8.0ms (0.2%)

series14.0ms (0.3%)

rewrite77.0ms (1.5%)

simplify219.0ms (4.2%)

prune240.0ms (4.6%)

localize10.0ms (0.2%)

series9.0ms (0.2%)

rewrite17.0ms (0.3%)

simplify97.0ms (1.9%)

prune148.0ms (2.8%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify67.0ms (1.3%)

prune50.0ms (1%)

regimes874.0ms (16.7%)

bsearch22.0ms (0.4%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample964.0ms (18.5%)

Profiling