Details

analyze1.6s (19.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0.4%	99.4%	0.2%	10
4.3%	95.5%	0.2%	11
6.4%	93.3%	0.2%	12
7.9%	91.9%	0.2%	13
13.7%	86%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.4s (16.4%)

Results

1.2s	8254×	body	128	valid
79.0ms	505×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
683×	`sub-neg_binary64`
438×	`neg-mul-1_binary64`
412×	`neg-sub0_binary64`
378×	`distribute-rgt-out--_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	28	19
2	66	19
3	158	17
4	344	17
5	846	17
6	2066	17
7	3773	17
8	4182	17
9	4701	17
10	4906	17
11	4923	17

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

2.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
	3.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))

Compiler

Compiled 100 to 63 computations (37% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series56.0ms (0.7%)

Counts

1 → 60

Calls

1 calls:

56.0ms

(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

simplify89.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

506×	`cancel-sign-sub-inv_binary64`
309×	`times-frac_binary64`
302×	`fma-neg_binary64`
286×	`sub-neg_binary64`
276×	`neg-mul-1_binary64`

Counts

70 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	2955
1	665	2920
2	2846	2265
3	4687	2265
4	5172	2265

prune63.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	59	4	63

Error

0.0b

Counts

63 → 4

Alt Table

Status	Error	Program
✓	3.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
▶	3.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	35.9b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
	9.3b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 2264 to 1163 computations (48.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
✓	10.0b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series152.0ms (1.8%)

Counts

3 → 144

Calls

3 calls:

78.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
63.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
11.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite202.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

1052×	`*-un-lft-identity_binary64`
883×	`times-frac_binary64`
649×	`add-sqr-sqrt_binary64`
448×	`add-cube-cbrt_binary64`
300×	`prod-diff_binary64`

Counts

3 → 600

Calls

3 calls:

43.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
11.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
6.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify898.0ms (10.8%)

Algorithm

1×	egg-herbie

Rules

435×	`times-frac_binary64`
336×	`sub-neg_binary64`
248×	`fma-def_binary64`
208×	`fma-udef_binary64`
196×	`neg-sub0_binary64`

Counts

744 → 670

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1050	52563
1	3195	48069
2	4814	47566
3	4994	47566

prune605.0ms (7.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	668	2	670
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	669	5	674

Error

Counts

674 → 5

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
	0.7b	(+.f64 x (neg.f64 (pow.f64 (/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (-.f64 (+.f64 1 t) z)) (cbrt.f64 a))) 3)))
✓	3.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	3.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	9.3b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 34690 to 14904 computations (57% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
✓	0.0b	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
✓	0.7b	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)

series398.0ms (4.8%)

Counts

3 → 144

Calls

3 calls:

215.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
127.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
55.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
29×	`add-cube-cbrt_binary64`

Counts

3 → 126

Calls

3 calls:

11.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
9.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
3.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))

simplify202.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

516×	`times-frac_binary64`
374×	`associate-/l*_binary64`
277×	`associate-/r*_binary64`
246×	`+-commutative_binary64`
207×	`sub-neg_binary64`

Counts

270 → 292

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	658	10133
1	1956	9941
2	4965	9941
3	4992	9941

prune288.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	293	4	297

Error

Counts

297 → 4

Alt Table

Status	Error	Program
	10.9b	(-.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z)) 3)) a))
✓	3.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	3.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	9.3b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 10917 to 5213 computations (52.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	3.7b	(/.f64 (*.f64 y a) (-.f64 (+.f64 1 t) z))
✓	7.2b	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))

series176.0ms (2.1%)

Counts

4 → 135

Calls

4 calls:

75.0ms	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
42.0ms	(/.f64 (*.f64 y a) (-.f64 (+.f64 1 t) z))
31.0ms	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))
28.0ms	(+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x)

rewrite66.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
48×	`prod-diff_binary64`
48×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`

Counts

4 → 172

Calls

4 calls:

20.0ms	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
15.0ms	(+.f64 (/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z)) x)
8.0ms	(/.f64 (*.f64 a z) (-.f64 (+.f64 1 t) z))
6.0ms	(/.f64 (*.f64 y a) (-.f64 (+.f64 1 t) z))

simplify487.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

503×	`times-frac_binary64`
428×	`associate-/l*_binary64`
229×	`associate-/r*_binary64`
197×	`+-commutative_binary64`
193×	`sub-neg_binary64`

Counts

307 → 341

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	636	13467
1	1910	11552
2	5028	11552

prune355.0ms (4.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	341	4	345

Error

Counts

345 → 4

Alt Table

Status	Error	Program
	10.9b	(-.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 y z) (-.f64 (+.f64 1 t) z)) 3)) a))
✓	3.0b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
✓	3.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
✓	9.3b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))

Compiler

Compiled 15508 to 7941 computations (48.8% saved)

regimes1.0s (12.2%)

Accuracy

Total 0.2b remaining (95.2%)

Threshold costs 0.2b (95.2%)

Counts

126 → 1

Compiler

Compiled 18134 to 12148 computations (33% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`*-commutative_binary64`
7×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	25	19
2	40	19
3	54	19
4	73	19
5	81	19
6	82	19
7	78	19

end82.0ms (1%)

Compiler: Compiled 118 to 79 computations (33.1% saved)

Details

analyze1.6s (19.6%)

sample1.4s (16.4%)

simplify102.0ms (1.2%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series56.0ms (0.7%)

rewrite3.0ms (0%)

simplify89.0ms (1.1%)

prune63.0ms (0.8%)

localize9.0ms (0.1%)

series152.0ms (1.8%)

rewrite202.0ms (2.4%)

simplify898.0ms (10.8%)

prune605.0ms (7.3%)

localize9.0ms (0.1%)

series398.0ms (4.8%)

rewrite33.0ms (0.4%)

simplify202.0ms (2.4%)

prune288.0ms (3.5%)

localize13.0ms (0.2%)

series176.0ms (2.1%)

rewrite66.0ms (0.8%)

simplify487.0ms (5.9%)

prune355.0ms (4.3%)

regimes1.0s (12.2%)

simplify4.0ms (0%)

end82.0ms (1%)

Profiling