Details

analyze4.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.8%	0.1%	0.1%	12
99.8%	0%	0.1%	13
99.8%	0%	0.2%	14

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample31.0ms (2.1%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 22 to 20 computations (9.1% saved)

simplify6.0ms (0.4%)

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

prune3.0ms (0.2%)

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

0.1b

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)

localize2.0ms (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)

simplify110.0ms (7.4%)

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

prune15.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	13	4	17

Error

0.1b

Counts

17 → 4

Alt Table

Status	Error	Program
	17.5b	(*.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) (sqrt.f64 (fma.f64 841/108 x 4/29)))
	1.8b	(.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)))
▶	0.1b	(+.f64 4/29 (*.f64 841/108 x))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 182 to 150 computations (17.6% 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))
✓	0.2b	(*.f64 841/108 x)

series3.0ms (0.2%)

Counts

2 → 3

Calls

2 calls:

2.0ms	(+.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))

simplify109.0ms (7.3%)

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

prune33.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	48	4	52

Error

0.0b

Counts

52 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 4/29 (*.f64 x 841/108))
	0.3b	(+.f64 4/29 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 (cbrt.f64 841/108) x)))
	0.7b	(+.f64 4/29 (.f64 (.f64 841/108 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 534 to 439 computations (17.8% saved)

localize3.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series4.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

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

simplify92.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-def_binary64`
432×	`fma-neg_binary64`
394×	`distribute-rgt-in_binary64`
364×	`*-commutative_binary64`
346×	`distribute-lft-in_binary64`

Counts

60 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	410
1	134	349
2	343	344
3	817	342
4	1690	342
5	2273	342
6	2619	342
7	3845	342
8	4864	342
9	4769	342

prune34.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	58	4	62

Error

0.0b

Counts

62 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 4/29 (*.f64 x 841/108))
▶	0.3b	(+.f64 4/29 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 (cbrt.f64 841/108) x)))
	0.7b	(+.f64 4/29 (.f64 (.f64 841/108 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 608 to 491 computations (19.2% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4/29 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 (cbrt.f64 841/108) x)))
✓	0.1b	(*.f64 (cbrt.f64 841/108) x)
✓	0.4b	(.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 (cbrt.f64 841/108) x))
✓	1.0b	(*.f64 (cbrt.f64 841/108) (cbrt.f64 841/108))

series27.0ms (1.8%)

Counts

4 → 24

Calls

4 calls:

14.0ms	(.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 (cbrt.f64 841/108) x))
9.0ms	(+.f64 4/29 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 (cbrt.f64 841/108) x)))
4.0ms	(*.f64 (cbrt.f64 841/108) x)
0.0ms	(*.f64 (cbrt.f64 841/108) (cbrt.f64 841/108))

rewrite23.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
20×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 106

Calls

4 calls:

6.0ms	(.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 (cbrt.f64 841/108) x))
5.0ms	(+.f64 4/29 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 (cbrt.f64 841/108) x)))
4.0ms	(*.f64 (cbrt.f64 841/108) (cbrt.f64 841/108))
3.0ms	(*.f64 (cbrt.f64 841/108) x)

simplify108.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

543×	`unswap-sqr_binary64`
417×	`fma-neg_binary64`
336×	`*-commutative_binary64`
295×	`cancel-sign-sub-inv_binary64`
281×	`sqr-pow_binary64`

Counts

130 → 143

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1114
1	233	1000
2	774	992
3	1847	978
4	3582	902
5	4288	902
6	4763	902
7	4829	902

prune103.0ms (7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	143	4	147

Error

0.0b

Counts

147 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 4/29 (*.f64 x 841/108))
✓	0.3b	(+.f64 4/29 (.f64 (.f64 (cbrt.f64 841/108) (cbrt.f64 841/108)) (*.f64 (cbrt.f64 841/108) x)))
	0.7b	(+.f64 4/29 (.f64 (.f64 841/108 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 2382 to 2170 computations (8.9% saved)

regimes100.0ms (6.8%)

Accuracy

Total 0.1b remaining (86.6%)

Threshold costs 0.1b (86.6%)

Counts

28 → 1

Compiler

Compiled 977 to 815 computations (16.6% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

sample639.0ms (43.2%)

Algorithm

1×

intervals

Results

391.0ms	7994×	body	128	valid
0.0ms	3×	body	1024	valid
0.0ms	3×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 54 to 44 computations (18.5% saved)

Details

analyze4.0ms (0.3%)

sample31.0ms (2.1%)

simplify6.0ms (0.4%)

prune3.0ms (0.2%)

localize2.0ms (0.2%)

series2.0ms (0.1%)

rewrite1.0ms (0%)

simplify110.0ms (7.4%)

prune15.0ms (1%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite6.0ms (0.4%)

simplify109.0ms (7.3%)

prune33.0ms (2.2%)

localize3.0ms (0.2%)

series4.0ms (0.3%)

rewrite6.0ms (0.4%)

simplify92.0ms (6.2%)

prune34.0ms (2.3%)

localize6.0ms (0.4%)

series27.0ms (1.8%)

rewrite23.0ms (1.6%)

simplify108.0ms (7.3%)

prune103.0ms (7%)

regimes100.0ms (6.8%)

simplify5.0ms (0.3%)

end0.0ms (0%)

sample639.0ms (43.2%)

Profiling