Details

analyze455.0ms (8.6%)

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
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.0s (18.9%)

Results

925.0ms	8255×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify133.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

prune6.0ms (0.1%)

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

1.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 56 to 29 computations (48.2% saved)

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series128.0ms (2.4%)

Counts

2 → 96

Calls

2 calls:

87.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
41.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite29.0ms (0.5%)

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:

19.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
1.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

simplify109.0ms (2%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
685×	`times-frac_binary64`
505×	`cancel-sign-sub-inv_binary64`
356×	`sub-neg_binary64`
161×	`+-commutative_binary64`

Counts

160 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	4135
1	699	4064
2	2396	3758
3	5075	3758

prune101.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	5	136

Error

0.0b

Counts

136 → 5

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	28.2b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	38.6b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x) 3))
	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))

Compiler

Compiled 3360 to 1095 computations (67.4% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series98.0ms (1.8%)

Counts

3 → 132

Calls

3 calls:

46.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
30.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
21.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))

rewrite88.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 214

Calls

3 calls:

21.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
13.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
1.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

simplify263.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

709×	`cancel-sign-sub-inv_binary64`
528×	`sub-neg_binary64`
232×	`fma-neg_binary64`
224×	`associate--l+_binary64`
221×	`+-commutative_binary64`

Counts

346 → 336

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	8765
1	1010	8314
2	3667	8134
3	5378	8134

prune342.0ms (6.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	336	5	341

Error

0.0b

Counts

341 → 5

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	28.2b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	38.6b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x) 3))
▶	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))

Compiler

Compiled 8580 to 2755 computations (67.9% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 z a))
✓	0.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	3.5b	(fma.f64 (/.f64 y (-.f64 z a)) z x)
✓	5.3b	(/.f64 (*.f64 y t) (-.f64 z a))

series129.0ms (2.4%)

Counts

4 → 156

Calls

4 calls:

50.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
38.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
23.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)
18.0ms	(/.f64 y (-.f64 z a))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
33×	`prod-diff_binary64`

Counts

4 → 141

Calls

4 calls:

8.0ms	(/.f64 y (-.f64 z a))
8.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
8.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
1.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)

simplify239.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

540×	`cancel-sign-sub-inv_binary64`
307×	`fma-neg_binary64`
252×	`sub-neg_binary64`
206×	`associate-/l*_binary64`
189×	`times-frac_binary64`

Counts

297 → 265

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	7851
1	956	7082
2	3439	6648
3	4776	6648
4	4997	6648
5	4858	6648

prune169.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	263	2	265
Fresh	2	0	2
Picked	0	1	1
Done	1	1	2
Total	266	4	270

Error

Counts

270 → 4

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	3.4b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 1 (/.f64 (-.f64 z a) (*.f64 y t))))
✓	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))

Compiler

Compiled 8512 to 1739 computations (79.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
✓	0.0b	(/.f64 (-.f64 z a) t)
	3.5b	(fma.f64 (/.f64 y (-.f64 z a)) z x)
✓	6.7b	(/.f64 y (/.f64 (-.f64 z a) t))

series93.0ms (1.8%)

Counts

3 → 136

Calls

3 calls:

53.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
29.0ms	(/.f64 y (/.f64 (-.f64 z a) t))
11.0ms	(/.f64 (-.f64 z a) t)

rewrite143.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

543×	`times-frac_binary64`
433×	`add-sqr-sqrt_binary64`
426×	`*-un-lft-identity_binary64`
320×	`add-cube-cbrt_binary64`
186×	`prod-diff_binary64`

Counts

3 → 405

Calls

3 calls:

23.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
6.0ms	(/.f64 y (/.f64 (-.f64 z a) t))
5.0ms	(/.f64 (-.f64 z a) t)

simplify545.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

390×	`associate-/r/_binary64`
330×	`associate-/l*_binary64`
217×	`distribute-neg-frac_binary64`
210×	`sub-neg_binary64`
203×	`associate-/l/_binary64`

Counts

541 → 563

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	807	31264
1	2248	21128
2	5047	21128

prune429.0ms (8.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	599	0	599
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	599	4	603

Error

Counts

603 → 4

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	3.4b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 1 (/.f64 (-.f64 z a) (*.f64 y t))))
✓	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))

Compiler

Compiled 26699 to 3897 computations (85.4% saved)

regimes610.0ms (11.5%)

Accuracy

Total 1.9b remaining (98.9%)

Threshold costs 0b (0%)

Counts

61 → 3

Compiler

Compiled 8360 to 5010 computations (40.1% saved)

bsearch18.0ms (0.3%)

Steps

Iters	Range		Point
1	3.8870268415844465e-172	1.0310584224805833e-170	1.9393432326971347e-171
7	-7.842934900007009e-206	-3.0679908620774666e-207	-1.6518303730418872e-206

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	54
1	36	54
2	48	54
3	54	54
4	57	54
5	55	54

end79.0ms (1.5%)

Compiler: Compiled 164 to 90 computations (45.1% saved)

Details

analyze455.0ms (8.6%)

sample1.0s (18.9%)

simplify133.0ms (2.5%)

prune6.0ms (0.1%)

localize15.0ms (0.3%)

series128.0ms (2.4%)

rewrite29.0ms (0.5%)

simplify109.0ms (2%)

prune101.0ms (1.9%)

localize11.0ms (0.2%)

series98.0ms (1.8%)

rewrite88.0ms (1.6%)

simplify263.0ms (4.9%)

prune342.0ms (6.4%)

localize21.0ms (0.4%)

series129.0ms (2.4%)

rewrite37.0ms (0.7%)

simplify239.0ms (4.5%)

prune169.0ms (3.2%)

localize13.0ms (0.2%)

series93.0ms (1.8%)

rewrite143.0ms (2.7%)

simplify545.0ms (10.3%)

prune429.0ms (8.1%)

regimes610.0ms (11.5%)

bsearch18.0ms (0.3%)

simplify5.0ms (0.1%)

end79.0ms (1.5%)

Profiling