Details

analyze1.3s (25.7%)

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
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.4s (28.8%)

Results

1.3s	8255×	body	128	valid
90.0ms	710×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify116.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1894×	`fma-neg_binary64`
843×	`div-sub_binary64`
750×	`fma-def_binary64`
582×	`times-frac_binary64`
397×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	37	14
3	78	14
4	163	14
5	295	14
6	645	14
7	1554	14
8	3040	14
9	3228	14
10	3469	14
11	3370	14
12	3363	14
13	3398	14
14	4949	14

prune4.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	10.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.7b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series67.0ms (1.4%)

Counts

2 → 96

Calls

2 calls:

46.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
21.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify118.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune95.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	135	5	140

Error

0.0b

Counts

140 → 5

Alt Table

Status	Error	Program
	32.5b	(+.f64 (.f64 (/.f64 y t) (+.f64 a (/.f64 (.f64 a a) t))) (-.f64 (+.f64 x y) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z a) t)))))
	10.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	41.3b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x) 3))
▶	1.8b	(+.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) x)
	2.8b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 3396 to 1149 computations (66.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) x)
	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	2.0b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

series80.0ms (1.6%)

Counts

2 → 108

Calls

2 calls:

47.0ms	(+.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) x)
33.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
31×	`associate-r_binary64`
26×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 66

Calls

2 calls:

11.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
7.0ms	(+.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) x)

simplify100.0ms (2%)

Algorithm

1×	egg-herbie

Rules

459×	`distribute-rgt-in_binary64`
392×	`sub-neg_binary64`
222×	`associate--l+_binary64`
187×	`fma-neg_binary64`
167×	`associate-/l*_binary64`

Counts

174 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	4463
1	797	4053
2	3111	3640
3	5081	3640

prune176.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	246	5	251

Error

Counts

251 → 5

Alt Table

Status	Error	Program
	32.5b	(+.f64 (.f64 (/.f64 y t) (+.f64 a (/.f64 (.f64 a a) t))) (-.f64 (+.f64 x y) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z a) t)))))
	10.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	30.4b	(+.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 z t))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 a t))) x)
✓	1.8b	(+.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) x)
▶	2.8b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 6207 to 1904 computations (69.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	10.8b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series103.0ms (2.1%)

Counts

3 → 132

Calls

3 calls:

49.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
36.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
18.0ms	(/.f64 y (-.f64 a t))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
31×	`times-frac_binary64`

Counts

3 → 155

Calls

3 calls:

10.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
6.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
4.0ms	(/.f64 y (-.f64 a t))

simplify210.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

422×	`sub-neg_binary64`
404×	`fma-neg_binary64`
222×	`associate--l+_binary64`
218×	`+-commutative_binary64`
182×	`associate-l_binary64`

Counts

287 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	443	6869
1	1078	6148
2	3977	6052
3	4707	6051
4	4994	6051
5	4942	6051

prune183.0ms (3.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	309	4	313

Error

Counts

313 → 4

Alt Table

Status	Error	Program
	30.4b	(+.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 z t))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	10.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	1.8b	(+.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) x)
▶	2.8b	(fma.f64 (-.f64 z t) (/.f64 y (-.f64 a t)) x)

Compiler

Compiled 8010 to 2055 computations (74.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (-.f64 a t))
✓	2.6b	(fma.f64 (-.f64 z t) (/.f64 y (-.f64 a t)) x)

series39.0ms (0.8%)

Counts

1 → 60

Calls

1 calls:

39.0ms

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

rewrite1.0ms (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 z t) (/.f64 y (-.f64 a t)) x)

simplify85.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

533×	`fma-def_binary64`
505×	`times-frac_binary64`
502×	`cancel-sign-sub-inv_binary64`
451×	`associate-/l*_binary64`
405×	`fma-neg_binary64`

Counts

70 → 51

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	2041
1	361	2012
2	1295	1445
3	4449	1445
4	4963	1445
5	5075	1445

prune66.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	116	4	120

Error

Counts

120 → 4

Alt Table

Status	Error	Program
	30.4b	(+.f64 (.f64 (.f64 y (sqrt.f64 (-.f64 z t))) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	10.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	1.8b	(+.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) x)
✓	2.8b	(fma.f64 (-.f64 z t) (/.f64 y (-.f64 a t)) x)

Compiler

Compiled 2561 to 783 computations (69.4% saved)

regimes602.0ms (12.2%)

Accuracy

Total 0.8b remaining (98.2%)

Threshold costs 0.8b (98.2%)

Counts

63 → 3

Compiler

Compiled 7324 to 4426 computations (39.6% saved)

bsearch22.0ms (0.4%)

Steps

Iters	Range		Point
3	2.8223299479526395e-123	4.405377189292774e-122	3.208986056831293e-122
4	-1.3027587407642273e+65	-8.065825821754518e+64	-8.181875273801221e+64

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	44
1	28	44
2	34	44
3	36	44
4	37	44
5	37	44

end78.0ms (1.6%)

Compiler: Compiled 139 to 79 computations (43.2% saved)

Details

analyze1.3s (25.7%)

sample1.4s (28.8%)

simplify116.0ms (2.3%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series67.0ms (1.4%)

rewrite11.0ms (0.2%)

simplify118.0ms (2.4%)

prune95.0ms (1.9%)

localize7.0ms (0.2%)

series80.0ms (1.6%)

rewrite24.0ms (0.5%)

simplify100.0ms (2%)

prune176.0ms (3.6%)

localize8.0ms (0.2%)

series103.0ms (2.1%)

rewrite33.0ms (0.7%)

simplify210.0ms (4.2%)

prune183.0ms (3.7%)

localize9.0ms (0.2%)

series39.0ms (0.8%)

rewrite1.0ms (0%)

simplify85.0ms (1.7%)

prune66.0ms (1.3%)

regimes602.0ms (12.2%)

bsearch22.0ms (0.4%)

simplify4.0ms (0.1%)

end78.0ms (1.6%)

Profiling