Details

analyze472.0ms (3.1%)

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
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
34.3%	62.4%	3.3%	9
42.1%	49.9%	7.9%	10
53.8%	37.8%	8.3%	11
56.2%	33%	10.9%	12
60.3%	25.6%	14.1%	13
66.4%	19.4%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.2s (8%)

Results

918.0ms	8256×	body	128	valid
99.0ms	698×	body	128	invalid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
210×	`distribute-rgt-in_binary64`
164×	`distribute-lft-in_binary64`
139×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	47	11
3	132	11
4	334	11
5	640	11
6	965	11
7	1254	11
8	1262	11
9	1262	11
10	1191	11

prune3.0ms (0%)

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

4.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.8b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.5b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series10.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

10.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

rewrite56.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

804×	`log1p-expm1-u_binary64`
804×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
83×	`add-sqr-sqrt_binary64`
76×	`add-cbrt-cube_binary64`

Counts

1 → 22

Calls

1 calls:

55.0ms

(*.f64 x (-.f64 (fma.f64 y z 1) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	163	11
2	2007	11
3	5600	11
0	0	0
1	0	0

simplify59.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-neg_binary64`
383×	`fma-def_binary64`
129×	`cancel-sign-sub-inv_binary64`
112×	`distribute-rgt-in_binary64`
97×	`unsub-neg_binary64`

Counts

58 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	432
1	59	372
2	153	372
3	277	372
4	569	372
5	925	372
6	1071	372
7	1230	372
8	1242	372
9	1242	372
10	1171	372

prune26.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Error

0.0b

Counts

33 → 5

Alt Table

Status	Error	Program
▶	2.3b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	34.5b	(pow.f64 (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))) 2)
	5.9b	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))) 3)
	17.6b	(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y z 1) 2) (.f64 z z)) x) (+.f64 z (fma.f64 y z 1)))
✓	4.8b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 507 to 301 computations (40.6% saved)

localize87.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (.f64 z x)) x)
✓	0.0b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	4.1b	(.f64 y (.f64 z x))

series34.0ms (0.2%)

Counts

3 → 60

Calls

3 calls:

17.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
9.0ms	(.f64 y (.f64 z x))
8.0ms	(+.f64 (.f64 y (.f64 z x)) x)

rewrite85.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

680×	`fma-def_binary64`
532×	`log-prod_binary64`
321×	`fma-neg_binary64`
256×	`egg-rr`
178×	`expm1-udef_binary64`

Counts

3 → 256

Calls

3 calls:

79.0ms	(+.f64 (.f64 y (.f64 z x)) x)
79.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
79.0ms	(.f64 y (.f64 z x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	187	29
2	2642	29
3	5635	29
0	0	0
1	0	0

simplify74.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-def_binary64`
459×	`fma-neg_binary64`
147×	`distribute-rgt-in_binary64`
135×	`unsub-neg_binary64`
110×	`distribute-lft-in_binary64`

Counts

316 → 270

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	696
1	71	528
2	173	528
3	388	528
4	809	528
5	1155	528
6	1272	528
7	1292	528
8	1292	528
9	1221	528

prune188.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	268	7	275

Error

0.0b

Counts

275 → 7

Alt Table

Status	Error	Program
✓	2.3b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
▶	3.6b	(fma.f64 z (.f64 x y) (-.f64 x (.f64 z x)))
	34.5b	(pow.f64 (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))) 2)
	5.9b	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))) 3)
	28.5b	(-.f64 (/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 y (.f64 z x)) 2)) (-.f64 x (.f64 y (.f64 z x)))) (.f64 z x))
	31.6b	(fma.f64 (.f64 (.f64 y z) (sqrt.f64 x)) (sqrt.f64 x) (-.f64 x (*.f64 z x)))
✓	4.8b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 5032 to 1201 computations (76.1% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 z x))
✓	3.4b	(fma.f64 z (.f64 x y) (-.f64 x (.f64 z x)))

series18.0ms (0.1%)

Counts

2 → 51

Calls

2 calls:

14.0ms	(fma.f64 z (.f64 x y) (-.f64 x (.f64 z x)))
4.0ms	(-.f64 x (*.f64 z x))

rewrite83.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

890×	`expm1-log1p-u_binary64`
757×	`prod-diff_binary64`
125×	`egg-rr`
91×	`add-sqr-sqrt_binary64`
86×	`log1p-expm1-u_binary64`

Counts

2 → 125

Calls

2 calls:

80.0ms	(-.f64 x (*.f64 z x))
80.0ms	(fma.f64 z (.f64 x y) (-.f64 x (.f64 z x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	173	21
2	2241	21
3	5312	21
0	0	0
1	0	0

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-def_binary64`
489×	`fma-neg_binary64`
156×	`distribute-rgt-in_binary64`
138×	`unsub-neg_binary64`
125×	`distribute-lft-in_binary64`

Counts

176 → 141

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	559
1	88	469
2	198	469
3	398	469
4	886	469
5	1220	469
6	1260	469
7	1270	469
8	1270	469
9	1199	469

prune92.0ms (0.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	141	7	148

Error

0.0b

Counts

148 → 7

Alt Table

Status	Error	Program
✓	2.3b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	3.6b	(fma.f64 z (.f64 x y) (-.f64 x (.f64 z x)))
	34.5b	(pow.f64 (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))) 2)
▶	5.9b	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))) 3)
	28.5b	(-.f64 (/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 y (.f64 z x)) 2)) (-.f64 x (.f64 y (.f64 z x)))) (.f64 z x))
	31.6b	(fma.f64 (.f64 (.f64 y z) (sqrt.f64 x)) (sqrt.f64 x) (-.f64 x (*.f64 z x)))
✓	4.8b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 3344 to 682 computations (79.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))) 3)
	4.5b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series11.0s (73.2%)

Counts

2 → 72

Calls

2 calls:

10.6s	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))) 3)
380.0ms	(cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z)))

rewrite85.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

466×	`log-prod_binary64`
367×	`prod-diff_binary64`
233×	`fma-def_binary64`
178×	`expm1-udef_binary64`
178×	`log1p-udef_binary64`

Counts

2 → 74

Calls

2 calls:

83.0ms	(cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z)))
83.0ms	(pow.f64 (cbrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	211	24
2	2443	24
3	4967	24
4	4902	24
0	0	0
1	0	0

simplify159.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

929×	`times-frac_binary64`
220×	`fma-def_binary64`
219×	`sub-neg_binary64`
201×	`fma-neg_binary64`
156×	`associate-r_binary64`

Counts

146 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	254	3825
1	834	3634
2	2926	3514
3	4992	3514

prune173.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	0	3	3
Picked	1	0	1
Done	0	3	3
Total	185	7	192

Error

Counts

192 → 7

Alt Table

Status	Error	Program
✓	2.3b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	3.6b	(fma.f64 z (.f64 x y) (-.f64 x (.f64 z x)))
	34.5b	(pow.f64 (sqrt.f64 (*.f64 x (-.f64 (fma.f64 y z 1) z))) 2)
	5.4b	(.f64 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) 2) (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) x))
	28.5b	(-.f64 (/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 y (.f64 z x)) 2)) (-.f64 x (.f64 y (.f64 z x)))) (.f64 z x))
	31.6b	(fma.f64 (.f64 (.f64 y z) (sqrt.f64 x)) (sqrt.f64 x) (-.f64 x (*.f64 z x)))
✓	4.8b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 5411 to 3448 computations (36.3% saved)

regimes829.0ms (5.5%)

Accuracy

Total 0.1b remaining (93%)

Threshold costs 0.1b (93%)

Counts

61 → 3

Compiler

Compiled 6372 to 4126 computations (35.2% saved)

bsearch19.0ms (0.1%)

Steps

Iters	Range		Point
2	466341157737649.94	435511731531713540.0	75475486738441900.0
5	-6.8543458238062e+49	-7.2853865785928e+42	-5.3988853793724826e+48

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	54
1	33	54
2	42	54
3	47	54
4	49	54
5	49	54

end117.0ms (0.8%)

Compiler: Compiled 199 to 103 computations (48.2% saved)

Details

analyze472.0ms (3.1%)

sample1.2s (8%)

simplify44.0ms (0.3%)

prune3.0ms (0%)

localize5.0ms (0%)

series10.0ms (0.1%)

rewrite56.0ms (0.4%)

simplify59.0ms (0.4%)

prune26.0ms (0.2%)

localize87.0ms (0.6%)

series34.0ms (0.2%)

rewrite85.0ms (0.6%)

simplify74.0ms (0.5%)

prune188.0ms (1.3%)

localize6.0ms (0%)

series18.0ms (0.1%)

rewrite83.0ms (0.6%)

simplify68.0ms (0.5%)

prune92.0ms (0.6%)

localize11.0ms (0.1%)

series11.0s (73.2%)

rewrite85.0ms (0.6%)

simplify159.0ms (1.1%)

prune173.0ms (1.2%)

regimes829.0ms (5.5%)

bsearch19.0ms (0.1%)

simplify3.0ms (0%)

end117.0ms (0.8%)

Profiling