Details

analyze488.0ms (15.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample112.0ms (3.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
6.0ms	40×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify52.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

823×	`div-sub_binary64`
529×	`fma-neg_binary64`
475×	`distribute-rgt-in_binary64`
409×	`fma-def_binary64`
380×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	50	11
3	156	11
4	331	11
5	666	11
6	1744	11
7	3988	11
8	4953	11

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

9.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.4b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Compiler

Compiled 44 to 26 computations (40.9% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 y z) 1)
✓	0.0b	(*.f64 x (+.f64 (-.f64 y z) 1))
✓	8.8b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

series23.0ms (0.7%)

Counts

3 → 96

Calls

3 calls:

13.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
7.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))
3.0ms	(+.f64 (-.f64 y z) 1)

rewrite36.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`associate-+l+_binary64`
10×	`add-cbrt-cube_binary64`

Counts

3 → 86

Calls

3 calls:

19.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
7.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))
6.0ms	(+.f64 (-.f64 y z) 1)

simplify92.0ms (3%)

Algorithm

1×	egg-herbie

Rules

623×	`distribute-rgt-in_binary64`
606×	`distribute-lft-in_binary64`
412×	`fma-def_binary64`
265×	`fma-neg_binary64`
175×	`exp-prod_binary64`

Counts

182 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	2086
1	327	1649
2	1464	1590
3	4612	1590
4	4990	1590

prune114.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	153	7	160
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	7	161

Error

0.0b

Counts

161 → 7

Alt Table

Status	Error	Program
	38.1b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 x (-.f64 y z) x) 3)) z)
	36.2b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (+.f64 (-.f64 y z) 1) (sqrt.f64 z)))
	3.4b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	36.6b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
▶	2.8b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))
	9.6b	(.f64 (.f64 x (+.f64 (-.f64 y z) 1)) (/.f64 1 z))
	2.9b	(*.f64 x (/.f64 (-.f64 (+.f64 1 y) z) z))

Compiler

Compiled 2591 to 1157 computations (55.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (-.f64 y z) 1)
✓	0.0b	(/.f64 z (+.f64 (-.f64 y z) 1))
✓	2.6b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))

series29.0ms (1%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))
14.0ms	(/.f64 z (+.f64 (-.f64 y z) 1))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

150×	`*-un-lft-identity_binary64`
138×	`times-frac_binary64`
70×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`
32×	`distribute-lft-out_binary64`

Counts

2 → 143

Calls

2 calls:

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

simplify169.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
653×	`fma-def_binary64`
173×	`fma-neg_binary64`
164×	`associate-/r/_binary64`
142×	`distribute-neg-in_binary64`

Counts

203 → 240

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	292	4769
1	700	4591
2	2636	4422
3	4765	4413
4	4988	4413
5	4967	4413

prune178.0ms (5.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	296	3	299
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	301	5	306

Error

Counts

306 → 5

Alt Table

Status	Error	Program
	9.6b	(*.f64 (/.f64 1 z) (fma.f64 x (-.f64 y z) x))
✓	2.8b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))
	36.2b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (+.f64 (-.f64 y z) 1) (sqrt.f64 z)))
▶	2.8b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
	11.5b	(*.f64 (/.f64 x z) (+.f64 (-.f64 y z) 1))

Compiler

Compiled 6173 to 3056 computations (50.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
✓	2.7b	(fma.f64 (/.f64 y z) x (/.f64 x z))

series40.0ms (1.3%)

Counts

2 → 72

Calls

2 calls:

22.0ms	(fma.f64 (/.f64 y z) x (/.f64 x z))
18.0ms	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 41

Calls

2 calls:

3.0ms	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
0.0ms	(fma.f64 (/.f64 y z) x (/.f64 x z))

simplify82.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

532×	`fma-neg_binary64`
432×	`fma-def_binary64`
410×	`associate-r_binary64`
323×	`distribute-rgt-out_binary64`
297×	`exp-prod_binary64`

Counts

113 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1550
1	160	1503
2	620	1466
3	2489	1152
4	4207	1152
5	4908	1152

prune43.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	74	5	79

Error

Counts

79 → 5

Alt Table

Status	Error	Program
	9.6b	(*.f64 (/.f64 1 z) (fma.f64 x (-.f64 y z) x))
✓	2.8b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))
▶	2.9b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
✓	2.8b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
	11.5b	(*.f64 (/.f64 x z) (+.f64 (-.f64 y z) 1))

Compiler

Compiled 1435 to 310 computations (78.4% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1)
✓	0.0b	(+.f64 (/.f64 y z) (/.f64 1 z))
✓	2.7b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)

series36.0ms (1.2%)

Counts

3 → 45

Calls

3 calls:

17.0ms	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
12.0ms	(-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1)
6.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite52.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`

Counts

3 → 137

Calls

3 calls:

14.0ms	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
14.0ms	(-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1)
12.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

simplify116.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-neg_binary64`
500×	`times-frac_binary64`
399×	`associate-l_binary64`
375×	`distribute-rgt-in_binary64`
366×	`distribute-lft-in_binary64`

Counts

182 → 184

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	2354
1	271	2128
2	775	1816
3	3167	1810
4	4715	1808
5	5115	1808

prune152.0ms (4.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	184	5	189

Error

Counts

189 → 5

Alt Table

Status	Error	Program
	9.6b	(*.f64 (/.f64 1 z) (fma.f64 x (-.f64 y z) x))
✓	2.8b	(/.f64 x (/.f64 z (+.f64 (-.f64 y z) 1)))
✓	2.9b	(*.f64 (-.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) 1) x)
✓	2.8b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
	11.5b	(*.f64 (/.f64 x z) (+.f64 (-.f64 y z) 1))

Compiler

Compiled 3637 to 2317 computations (36.3% saved)

regimes483.0ms (15.6%)

Accuracy

Total 0.1b remaining (89.6%)

Threshold costs 0.1b (89.6%)

Counts

79 → 3

Compiler

Compiled 4668 to 2901 computations (37.9% saved)

bsearch23.0ms (0.7%)

Steps

Iters	Range		Point
2	1.1137173536738116e-15	6.059325759944901	0.0007078159893443644
9	-4.3883636007686663e-13	-4.1746428062801183e-19	-2.236168945046539e-18

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	36	55
2	43	55
3	47	55
4	49	55
5	47	55

end1.0ms (0%)

Compiler: Compiled 41 to 23 computations (43.9% saved)

sample699.0ms (22.6%)

Algorithm

1×

intervals

Results

320.0ms	8000×	body	128	valid
40.0ms	1042×	body	128	invalid

Compiler

Compiled 121 to 76 computations (37.2% saved)

Details

analyze488.0ms (15.8%)

sample112.0ms (3.6%)

simplify52.0ms (1.7%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series23.0ms (0.7%)

rewrite36.0ms (1.2%)

simplify92.0ms (3%)

prune114.0ms (3.7%)

localize6.0ms (0.2%)

series29.0ms (1%)

rewrite29.0ms (0.9%)

simplify169.0ms (5.5%)

prune178.0ms (5.8%)

localize6.0ms (0.2%)

series40.0ms (1.3%)

rewrite5.0ms (0.2%)

simplify82.0ms (2.7%)

prune43.0ms (1.4%)

localize11.0ms (0.3%)

series36.0ms (1.2%)

rewrite52.0ms (1.7%)

simplify116.0ms (3.7%)

prune152.0ms (4.9%)

regimes483.0ms (15.6%)

bsearch23.0ms (0.7%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample699.0ms (22.6%)

Profiling