Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
99.7%	0%	0.3%	1

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample2.0s (45.3%)

Results

1.9s	8250×	body	128	valid
2.0ms	4×	body	512	valid
1.0ms	2×	body	256	valid

Compiler

Compiled 83 to 59 computations (28.9% saved)

simplify83.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

494×	`fma-neg_binary64`
474×	`distribute-neg-in_binary64`
463×	`associate--l-_binary64`
362×	`associate--r-_binary64`
354×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	49	27
2	141	25
3	466	25
4	1615	25
5	3794	25
6	4547	25
7	4966	25

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

2.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.5b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

Compiler

Compiled 93 to 60 computations (35.5% saved)

localize24.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (-.f64 1 t) x)
✓	0.5b	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))
✓	2.0b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))

series100.0ms (2.3%)

Counts

3 → 168

Calls

3 calls:

56.0ms	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
31.0ms	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))
12.0ms	(fma.f64 a (-.f64 1 t) x)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 30

Calls

3 calls:

1.0ms	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
1.0ms	(fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x))
1.0ms	(fma.f64 a (-.f64 1 t) x)

simplify226.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-neg_binary64`
482×	`associate--l+_binary64`
437×	`sub-neg_binary64`
413×	`associate-+l+_binary64`
409×	`associate-l_binary64`

Counts

198 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	3636
1	288	3535
2	856	3328
3	3026	3326
4	4873	3326
5	5376	3326

prune83.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Error

Counts

88 → 3

Alt Table

Status	Error	Program
	20.6b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))
✓	2.5b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
▶	15.0b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

Compiler

Compiled 1761 to 872 computations (50.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (-.f64 b z) (*.f64 b -2))
✓	0.0b	(+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2)))
✓	0.0b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

series49.0ms (1.1%)

Counts

3 → 144

Calls

3 calls:

24.0ms	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
16.0ms	(+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2)))
9.0ms	(fma.f64 y (-.f64 b z) (*.f64 b -2))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
17×	`add-log-exp_binary64`
10×	`distribute-lft-out_binary64`
9×	`sum-log_binary64`
7×	`fma-def_binary64`

Counts

3 → 54

Calls

3 calls:

7.0ms	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))
5.0ms	(+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2)))
1.0ms	(fma.f64 y (-.f64 b z) (*.f64 b -2))

simplify100.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-neg_binary64`
497×	`sub-neg_binary64`
416×	`fma-def_binary64`
379×	`associate-+l+_binary64`
290×	`associate-+r+_binary64`

Counts

198 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	3321
1	341	3106
2	1030	2860
3	3480	2860
4	4883	2860

prune112.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	109	3	112

Error

Counts

112 → 3

Alt Table

Status	Error	Program
▶	20.6b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))
✓	2.5b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
✓	15.0b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

Compiler

Compiled 2100 to 868 computations (58.7% saved)

localize14.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 t (-.f64 b a) (*.f64 b -2))
✓	0.0b	(+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2)))

series26.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

14.0ms	(+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2)))
12.0ms	(fma.f64 t (-.f64 b a) (*.f64 b -2))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
7×	`add-log-exp_binary64`
4×	`distribute-lft-out_binary64`
4×	`fma-def_binary64`
3×	`sum-log_binary64`

Counts

2 → 32

Calls

2 calls:

5.0ms	(+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2)))
0.0ms	(fma.f64 t (-.f64 b a) (*.f64 b -2))

simplify139.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-neg_binary64`
445×	`distribute-rgt-in_binary64`
418×	`distribute-lft-in_binary64`
285×	`cancel-sign-sub-inv_binary64`
245×	`exp-sum_binary64`

Counts

116 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1759
1	219	1600
2	589	1492
3	2928	1492
4	4292	1492
5	5069	1492

prune109.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	70	3	73

Error

Counts

73 → 3

Alt Table

Status	Error	Program
✓	20.6b	(+.f64 x (+.f64 (+.f64 a z) (fma.f64 t (-.f64 b a) (*.f64 b -2))))
✓	2.5b	(fma.f64 (-.f64 (+.f64 y t) 2) b (fma.f64 z (-.f64 1 y) (fma.f64 a (-.f64 1 t) x)))
✓	15.0b	(+.f64 a (+.f64 (+.f64 z x) (fma.f64 y (-.f64 b z) (*.f64 b -2))))

Compiler

Compiled 1287 to 551 computations (57.2% saved)

regimes1.2s (26.4%)

Accuracy

Total 1.4b remaining (99.7%)

Threshold costs 0b (0%)

Counts

99 → 2

Compiler

Compiled 11541 to 8034 computations (30.4% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 27 to 19 computations (29.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`+-commutative_binary64`
16×	`sub-neg_binary64`
12×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	81
1	68	81
2	96	81
3	112	81
4	121	81
5	122	81
6	118	81

end115.0ms (2.6%)

Compiler: Compiled 188 to 118 computations (37.2% saved)

Details

analyze6.0ms (0.1%)

sample2.0s (45.3%)

simplify83.0ms (1.9%)

prune7.0ms (0.2%)

localize24.0ms (0.6%)

series100.0ms (2.3%)

rewrite4.0ms (0.1%)

simplify226.0ms (5.1%)

prune83.0ms (1.9%)

localize9.0ms (0.2%)

series49.0ms (1.1%)

rewrite17.0ms (0.4%)

simplify100.0ms (2.3%)

prune112.0ms (2.6%)

localize14.0ms (0.3%)

series26.0ms (0.6%)

rewrite7.0ms (0.2%)

simplify139.0ms (3.2%)

prune109.0ms (2.5%)

regimes1.2s (26.4%)

bsearch3.0ms (0.1%)

simplify5.0ms (0.1%)

end115.0ms (2.6%)

Profiling