Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample545.0ms (37.9%)

Results

511.0ms	8252×	body	128	valid
1.0ms	3×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 32 to 29 computations (9.4% saved)

simplify7.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	16	5
3	14	5

prune5.0ms (0.4%)

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
	0.1b	(+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))
▶	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 44 to 38 computations (13.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)

series2.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(fma.f64 841/108 x 4/29)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 841/108 x 4/29)

simplify125.0ms (8.7%)

Algorithm

1×	egg-herbie

Rules

639×	`associate-*r/_binary64`
493×	`distribute-rgt-in_binary64`
446×	`distribute-lft-out_binary64`
406×	`distribute-rgt-out_binary64`
402×	`associate-l_binary64`

Counts

22 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	142
1	19	131
2	42	131
3	104	131
4	284	131
5	900	131
6	1555	131
7	2510	131
8	2614	131
9	3104	131
10	4503	131
11	4867	131
12	4989	131
13	4799	131

prune13.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	11	4	15
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	12	5	17

Error

0.0b

Counts

17 → 5

Alt Table

Status	Error	Program
	15.6b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	1.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (cbrt.f64 (fma.f64 841/108 x 4/29))) (cbrt.f64 (fma.f64 841/108 x 4/29)))
	15.4b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))
▶	0.1b	(+.f64 4/29 (*.f64 841/108 x))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 198 to 164 computations (17.2% saved)

localize3.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4/29 (*.f64 841/108 x))
✓	0.1b	(*.f64 841/108 x)

series7.0ms (0.5%)

Counts

2 → 3

Calls

2 calls:

5.0ms	(+.f64 4/29 (*.f64 841/108 x))
2.0ms	(*.f64 841/108 x)

rewrite6.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 36

Calls

2 calls:

3.0ms	(*.f64 841/108 x)
2.0ms	(+.f64 4/29 (*.f64 841/108 x))

simplify110.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

479×	`distribute-rgt-in_binary64`
447×	`fma-def_binary64`
374×	`distribute-rgt-out_binary64`
359×	`fma-neg_binary64`
344×	`associate-l_binary64`

Counts

39 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	60	299
1	135	256
2	291	249
3	660	249
4	1346	249
5	2177	249
6	3278	249
7	4259	249
8	4921	249
9	4994	249
10	4830	249

prune31.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	49	4	53

Error

0.0b

Counts

53 → 4

Alt Table

Status	Error	Program
	33.9b	(+.f64 4/29 (.f64 (.f64 (sqrt.f64 841/108) (sqrt.f64 x)) (*.f64 (sqrt.f64 841/108) (sqrt.f64 x))))
✓	0.1b	(+.f64 4/29 (*.f64 841/108 x))
▶	0.2b	(+.f64 4/29 (.f64 (sqrt.f64 841/108) (.f64 (sqrt.f64 841/108) x)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 524 to 434 computations (17.2% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4/29 (.f64 (sqrt.f64 841/108) (.f64 (sqrt.f64 841/108) x)))
✓	0.2b	(*.f64 (sqrt.f64 841/108) x)
✓	0.3b	(.f64 (sqrt.f64 841/108) (.f64 (sqrt.f64 841/108) x))

series18.0ms (1.3%)

Counts

3 → 24

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 841/108) (.f64 (sqrt.f64 841/108) x))
6.0ms	(+.f64 4/29 (.f64 (sqrt.f64 841/108) (.f64 (sqrt.f64 841/108) x)))
3.0ms	(*.f64 (sqrt.f64 841/108) x)

rewrite17.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`

Counts

3 → 63

Calls

3 calls:

9.0ms	(.f64 (sqrt.f64 841/108) (.f64 (sqrt.f64 841/108) x))
4.0ms	(*.f64 (sqrt.f64 841/108) x)
2.0ms	(+.f64 4/29 (.f64 (sqrt.f64 841/108) (.f64 (sqrt.f64 841/108) x)))

simplify86.0ms (6%)

Algorithm

1×	egg-herbie

Rules

771×	`fma-def_binary64`
548×	`fma-neg_binary64`
467×	`unswap-sqr_binary64`
379×	`distribute-rgt-in_binary64`
342×	`*-commutative_binary64`

Counts

87 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	623
1	196	593
2	591	589
3	1262	579
4	2633	579
5	3534	579
6	4840	579
7	4796	579

prune80.0ms (5.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	88	3	91

Error

Counts

91 → 3

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 4/29 (*.f64 (pow.f64 (sqrt.f64 841/108) 2) x))
✓	0.1b	(+.f64 4/29 (*.f64 841/108 x))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 1202 to 1063 computations (11.6% saved)

localize5.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4/29 (*.f64 (pow.f64 (sqrt.f64 841/108) 2) x))
✓	0.1b	(*.f64 (pow.f64 (sqrt.f64 841/108) 2) x)
✓	1.0b	(pow.f64 (sqrt.f64 841/108) 2)

series15.0ms (1%)

Counts

3 → 12

Calls

3 calls:

8.0ms	(*.f64 (pow.f64 (sqrt.f64 841/108) 2) x)
6.0ms	(+.f64 4/29 (*.f64 (pow.f64 (sqrt.f64 841/108) 2) x))
0.0ms	(pow.f64 (sqrt.f64 841/108) 2)

rewrite16.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
14×	`unpow-prod-down_binary64`
11×	`associate-l_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

3 → 75

Calls

3 calls:

6.0ms	(pow.f64 (sqrt.f64 841/108) 2)
5.0ms	(*.f64 (pow.f64 (sqrt.f64 841/108) 2) x)
2.0ms	(+.f64 4/29 (*.f64 (pow.f64 (sqrt.f64 841/108) 2) x))

simplify97.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
539×	`distribute-rgt-in_binary64`
384×	`*-commutative_binary64`
290×	`unswap-sqr_binary64`
276×	`associate-l_binary64`

Counts

87 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	993
1	209	535
2	520	524
3	1452	524
4	3301	524
5	4584	524
6	4874	524
7	4819	524

prune127.0ms (8.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	111	3	114

Error

Counts

114 → 3

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 4/29 (*.f64 (pow.f64 (sqrt.f64 841/108) 2) x))
✓	0.1b	(+.f64 4/29 (*.f64 841/108 x))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 1395 to 1227 computations (12% saved)

regimes64.0ms (4.5%)

Accuracy

Total 0.1b remaining (96.1%)

Threshold costs 0.1b (96.1%)

Counts

16 → 1

Compiler

Compiled 590 to 500 computations (15.3% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end45.0ms (3.1%)

Compiler: Compiled 30 to 25 computations (16.7% saved)

Details

analyze1.0ms (0.1%)

sample545.0ms (37.9%)

simplify7.0ms (0.5%)

prune5.0ms (0.4%)

localize3.0ms (0.2%)

series2.0ms (0.1%)

rewrite1.0ms (0%)

simplify125.0ms (8.7%)

prune13.0ms (0.9%)

localize3.0ms (0.2%)

series7.0ms (0.5%)

rewrite6.0ms (0.4%)

simplify110.0ms (7.7%)

prune31.0ms (2.1%)

localize5.0ms (0.3%)

series18.0ms (1.3%)

rewrite17.0ms (1.2%)

simplify86.0ms (6%)

prune80.0ms (5.6%)

localize5.0ms (0.4%)

series15.0ms (1%)

rewrite16.0ms (1.1%)

simplify97.0ms (6.8%)

prune127.0ms (8.9%)

regimes64.0ms (4.5%)

simplify2.0ms (0.2%)

end45.0ms (3.1%)

Profiling