Details

analyze1.4s (30.3%)

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)

sample1.2s (26.5%)

Results

1.0s	8256×	body	128	valid
100.0ms	771×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify114.0ms (2.5%)

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
▶	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	11.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series61.0ms (1.4%)

Counts

2 → 96

Calls

2 calls:

41.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
20.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite10.0ms (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)

simplify132.0ms (2.9%)

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

prune93.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	136	4	140

Error

0.0b

Counts

140 → 4

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	4.1b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	11.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	25.8b	(+.f64 (+.f64 x y) (*.f64 (/.f64 y t) (-.f64 a z)))

Compiler

Compiled 3311 to 1100 computations (66.8% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	12.1b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series53.0ms (1.2%)

Counts

2 → 72

Calls

2 calls:

35.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
17.0ms	(/.f64 y (-.f64 a t))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
31×	`times-frac_binary64`
21×	`associate-l_binary64`

Counts

2 → 113

Calls

2 calls:

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

simplify147.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

766×	`cancel-sign-sub-inv_binary64`
366×	`fma-neg_binary64`
238×	`sub-neg_binary64`
178×	`times-frac_binary64`
174×	`associate-/l*_binary64`

Counts

185 → 203

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	340	4235
1	810	4049
2	3050	3971
3	4777	3970
4	4973	3970
5	4980	3970

prune111.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	203	4	207

Error

0.0b

Counts

207 → 4

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	4.1b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
▶	11.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	25.8b	(+.f64 (+.f64 x y) (*.f64 (/.f64 y t) (-.f64 a z)))

Compiler

Compiled 5095 to 1460 computations (71.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z t))
✓	11.6b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

series41.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

33.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
7.0ms	(*.f64 y (-.f64 z t))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 81

Calls

2 calls:

7.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
6.0ms	(*.f64 y (-.f64 z t))

simplify119.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

784×	`cancel-sign-sub-inv_binary64`
329×	`fma-neg_binary64`
245×	`sub-neg_binary64`
232×	`associate-/l*_binary64`
200×	`times-frac_binary64`

Counts

165 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	264	2954
1	628	2771
2	2830	2693
3	4707	2690
4	4973	2690
5	4932	2690

prune94.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	150	4	154

Error

Counts

154 → 4

Alt Table

Status	Error	Program
▶	1.3b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	4.1b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	11.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 3596 to 1102 computations (69.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	1.8b	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))

series57.0ms (1.3%)

Counts

2 → 84

Calls

2 calls:

33.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))
23.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
194×	`*-un-lft-identity_binary64`
194×	`add-sqr-sqrt_binary64`
90×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

2 → 198

Calls

2 calls:

10.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
9.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))

simplify193.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

412×	`sub-neg_binary64`
269×	`associate-/r/_binary64`
265×	`fma-neg_binary64`
215×	`associate-/l/_binary64`
194×	`div-sub_binary64`

Counts

282 → 307

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	424	7629
1	1093	7431
2	4149	7365
3	4696	7360
4	5114	7360

prune162.0ms (3.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	307	0	307
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	307	4	311

Error

Counts

311 → 4

Alt Table

Status	Error	Program
✓	1.3b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	4.1b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	11.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 7865 to 1999 computations (74.6% saved)

regimes354.0ms (7.9%)

Accuracy

Total 0.4b remaining (97.3%)

Threshold costs 0.4b (97.3%)

Counts

42 → 3

Compiler

Compiled 4188 to 2760 computations (34.1% saved)

bsearch19.0ms (0.4%)

Steps

Iters	Range		Point
1	1.940838875180652e-20	1.6644190984218104e-19	5.3766154638147954e-20
7	-2.7435961110591997e-40	-7.836757707528564e-42	-4.292063565913367e-41

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-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	21	60
1	27	60
2	33	60
3	35	60
4	36	60
5	36	60

end64.0ms (1.4%)

Compiler: Compiled 155 to 77 computations (50.3% saved)

Details

analyze1.4s (30.3%)

sample1.2s (26.5%)

simplify114.0ms (2.5%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series61.0ms (1.4%)

rewrite10.0ms (0.2%)

simplify132.0ms (2.9%)

prune93.0ms (2.1%)

localize8.0ms (0.2%)

series53.0ms (1.2%)

rewrite23.0ms (0.5%)

simplify147.0ms (3.3%)

prune111.0ms (2.5%)

localize8.0ms (0.2%)

series41.0ms (0.9%)

rewrite18.0ms (0.4%)

simplify119.0ms (2.6%)

prune94.0ms (2.1%)

localize8.0ms (0.2%)

series57.0ms (1.3%)

rewrite40.0ms (0.9%)

simplify193.0ms (4.3%)

prune162.0ms (3.6%)

regimes354.0ms (7.9%)

bsearch19.0ms (0.4%)

simplify3.0ms (0.1%)

end64.0ms (1.4%)

Profiling