Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample774.0ms (14.7%)

Infinites

20.4% of outputs are infinite.

Results

576.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify43.0ms (0.8%)

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

2.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.0b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 y z 1) z)
✓	2.0b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series14.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

10.0ms	(*.f64 x (-.f64 (fma.f64 y z 1) z))
4.0ms	(-.f64 (fma.f64 y z 1) z)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
27×	`prod-diff_binary64`
26×	`add-cube-cbrt_binary64`
14×	`distribute-lft-in_binary64`

Counts

2 → 83

Calls

2 calls:

5.0ms	(*.f64 x (-.f64 (fma.f64 y z 1) z))
4.0ms	(-.f64 (fma.f64 y z 1) z)

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

486×	`fma-def_binary64`
425×	`distribute-rgt-in_binary64`
399×	`distribute-lft-in_binary64`
324×	`exp-prod_binary64`
249×	`fma-neg_binary64`

Counts

143 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	1823
1	251	1705
2	904	1620
3	2834	1535
4	4552	1535
5	5143	1535

prune227.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	5	120

Error

0.0b

Counts

120 → 5

Alt Table

Status	Error	Program
	20.3b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
	28.3b	(.f64 x (/.f64 (-.f64 (pow.f64 (fma.f64 y z 1) 3) (pow.f64 z 3)) (fma.f64 z z (.f64 (fma.f64 y z 1) (+.f64 z (fma.f64 y z 1))))))
	6.3b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
▶	2.1b	(.f64 x (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 z)))
✓	2.0b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 2343 to 1109 computations (52.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 z))
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1)))
✓	2.0b	(.f64 x (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 z)))
✓	7.8b	(cbrt.f64 (fma.f64 y z 1))

series2.8s (52.6%)

Counts

4 → 108

Calls

4 calls:

1.8s	(.f64 x (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 z)))
884.0ms	(fma.f64 (*.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 z))
60.0ms	(cbrt.f64 (fma.f64 y z 1))
25.0ms	(*.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1)))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`pow1_binary64`

Counts

4 → 87

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1)))
3.0ms	(.f64 x (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 z)))
1.0ms	(cbrt.f64 (fma.f64 y z 1))
0.0ms	(fma.f64 (*.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 z))

simplify134.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

626×	`associate-/l*_binary64`
300×	`distribute-lft-in_binary64`
293×	`distribute-rgt-in_binary64`
234×	`cancel-sign-sub-inv_binary64`
217×	`fma-neg_binary64`

Counts

195 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	297	6320
1	844	5511
2	2439	4949
3	5276	4949

prune349.0ms (6.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	335	0	335
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	335	5	340

Error

0.0b

Counts

340 → 5

Alt Table

Status	Error	Program
	20.3b	(.f64 (.f64 x (sqrt.f64 (-.f64 (fma.f64 y z 1) z))) (sqrt.f64 (-.f64 (fma.f64 y z 1) z)))
	28.3b	(.f64 x (/.f64 (-.f64 (pow.f64 (fma.f64 y z 1) 3) (pow.f64 z 3)) (fma.f64 z z (.f64 (fma.f64 y z 1) (+.f64 z (fma.f64 y z 1))))))
▶	6.3b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	2.1b	(.f64 x (fma.f64 (.f64 (cbrt.f64 (fma.f64 y z 1)) (cbrt.f64 (fma.f64 y z 1))) (cbrt.f64 (fma.f64 y z 1)) (neg.f64 z)))
✓	2.0b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 12332 to 7617 computations (38.2% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (.f64 z x)) x)
✓	3.2b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	5.3b	(.f64 y (.f64 z x))

series28.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

12.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
8.0ms	(.f64 y (.f64 z x))
8.0ms	(+.f64 (.f64 y (.f64 z x)) x)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 56

Calls

3 calls:

6.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
4.0ms	(+.f64 (.f64 y (.f64 z x)) x)
3.0ms	(.f64 y (.f64 z x))

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-neg_binary64`
502×	`fma-def_binary64`
318×	`cancel-sign-sub-inv_binary64`
279×	`distribute-rgt-in_binary64`
247×	`distribute-lft-in_binary64`

Counts

116 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1397
1	285	1233
2	896	1196
3	2752	1195
4	4487	1195
5	4963	1195

prune54.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	2	0	2
Picked	0	1	1
Done	1	1	2
Total	105	3	108

Error

Counts

108 → 3

Alt Table

Status	Error	Program
▶	25.0b	(.f64 (-.f64 (.f64 y x) x) z)
✓	6.3b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	2.0b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 1769 to 453 computations (74.4% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 y x) x)
✓	2.1b	(.f64 (-.f64 (.f64 y x) x) z)

series16.0ms (0.3%)

Counts

2 → 39

Calls

2 calls:

12.0ms	(.f64 (-.f64 (.f64 y x) x) z)
4.0ms	(-.f64 (*.f64 y x) x)

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
4×	`associate-l_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 44

Calls

2 calls:

6.0ms	(.f64 (-.f64 (.f64 y x) x) z)
3.0ms	(-.f64 (*.f64 y x) x)

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

607×	`fma-neg_binary64`
302×	`exp-prod_binary64`
302×	`fma-def_binary64`
269×	`*-commutative_binary64`
185×	`distribute-rgt-out_binary64`

Counts

83 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	957
1	217	823
2	808	810
3	2189	806
4	4106	806
5	4992	806

prune44.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	86	3	89

Error

Counts

89 → 3

Alt Table

Status	Error	Program
✓	25.0b	(.f64 (-.f64 (.f64 y x) x) z)
✓	6.3b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	2.0b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

Compiler

Compiled 1121 to 423 computations (62.3% saved)

regimes415.0ms (7.9%)

Accuracy

Total 1.4b remaining (99.1%)

Threshold costs 0b (0%)

Counts

53 → 2

Compiler

Compiled 6042 to 3797 computations (37.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

46×	`distribute-rgt-neg-in_binary64`
36×	`cancel-sign-sub-inv_binary64`
29×	`distribute-lft-neg-in_binary64`
26×	`distribute-lft-neg-out_binary64`
26×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	31	35
2	49	35
3	65	35
4	80	35
5	92	35
6	108	35
7	123	35
8	136	35
9	154	35
10	181	35
11	207	35
12	223	35
13	227	35
14	223	35

end50.0ms (1%)

Compiler: Compiled 89 to 56 computations (37.1% saved)

Iter	Nodes	Cost
0	16	35
1	31	35
2	49	35
3	65	35
4	80	35
5	92	35
6	108	35
7	123	35
8	136	35
9	154	35
10	181	35
11	207	35
12	223	35
13	227	35
14	223	35

Iter	Nodes	Cost
0	16	35
1	31	35
2	49	35
3	65	35
4	80	35
5	92	35
6	108	35
7	123	35
8	136	35
9	154	35
10	181	35
11	207	35
12	223	35
13	227	35
14	223	35

Details

analyze2.0ms (0%)

sample774.0ms (14.7%)

simplify43.0ms (0.8%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series14.0ms (0.3%)

rewrite14.0ms (0.3%)

simplify92.0ms (1.7%)

prune227.0ms (4.3%)

localize9.0ms (0.2%)

series2.8s (52.6%)

rewrite12.0ms (0.2%)

simplify134.0ms (2.5%)

prune349.0ms (6.6%)

localize5.0ms (0.1%)

series28.0ms (0.5%)

rewrite16.0ms (0.3%)

simplify81.0ms (1.5%)

prune54.0ms (1%)

localize4.0ms (0.1%)

series16.0ms (0.3%)

rewrite10.0ms (0.2%)

simplify81.0ms (1.5%)

prune44.0ms (0.8%)

regimes415.0ms (7.9%)

bsearch1.0ms (0%)

simplify11.0ms (0.2%)

end50.0ms (1%)

Profiling

Iter	Nodes	Cost
0	16	35
1	31	35
2	49	35
3	65	35
4	80	35
5	92	35
6	108	35
7	123	35
8	136	35
9	154	35
10	181	35
11	207	35
12	223	35
13	227	35
14	223	35