Details

analyze346.0ms (12.3%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
43.7%	43.7%	12.6%	7
53.1%	34.3%	12.6%	8
57.8%	23.4%	18.8%	9
63.2%	18%	18.8%	10
66%	12.1%	22%	11
68.9%	9.2%	22%	12
70.3%	6.1%	23.5%	13
71.9%	4.6%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample29.0ms (1%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

13×	`fma-def_binary64`
7×	`associate-r_binary64`
7×	`associate-l_binary64`
5×	`*-commutative_binary64`
4×	`*-lft-identity_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	8
2	24	8
3	47	8
4	43	8
5	45	8
6	43	8

prune2.0ms (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

5.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.8b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.5b	(*.f64 x (fma.f64 y y 1))

series11.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

11.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

3.0ms

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

simplify80.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

746×	`unswap-sqr_binary64`
561×	`distribute-rgt-in_binary64`
550×	`fma-def_binary64`
534×	`distribute-lft-in_binary64`
336×	`distribute-rgt-out_binary64`

Counts

46 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	447
1	81	404
2	264	404
3	597	404
4	1918	404
5	2078	404
6	2869	404
7	4919	404
8	4929	404

prune27.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	34	6	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	6	41

Error

3.4b

Counts

41 → 6

Alt Table

Status	Error	Program
	6.9b	(.f64 (.f64 (cbrt.f64 (.f64 x (fma.f64 y y 1))) (cbrt.f64 (.f64 x (fma.f64 y y 1)))) (cbrt.f64 (*.f64 x (fma.f64 y y 1))))
▶	5.8b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	23.0b	x
	5.9b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
	7.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
	36.6b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))

Compiler

Compiled 583 to 341 computations (41.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	11.4b	(*.f64 (pow.f64 y 2) x)

series9.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

8.0ms

(*.f64 (pow.f64 y 2) x)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`associate-l_binary64`
6×	`add-exp-log_binary64`
4×	`unswap-sqr_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 29

Calls

1 calls:

5.0ms

(*.f64 (pow.f64 y 2) x)

simplify59.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
362×	`distribute-rgt-in_binary64`
350×	`*-commutative_binary64`
325×	`distribute-lft-in_binary64`
281×	`associate-/l*_binary64`

Counts

29 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	331
1	98	253
2	260	253
3	784	253
4	1194	253
5	2034	253
6	4662	253
7	4851	253

prune36.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	45	6	51

Error

0.0b

Counts

51 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
✓	5.8b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	1.9b	(+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 2) (*.f64 (pow.f64 (cbrt.f64 y) 2) x)) x)
	38.7b	(+.f64 (.f64 (.f64 (pow.f64 y 2) (sqrt.f64 x)) (sqrt.f64 x)) x)
	6.1b	(+.f64 (.f64 (.f64 (pow.f64 y 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) x)
	7.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))

Compiler

Compiled 712 to 385 computations (45.9% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 y (.f64 y x))

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(*.f64 y (*.f64 y x))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 y (*.f64 y x))

simplify67.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

758×	`associate-/l/_binary64`
649×	`fma-def_binary64`
350×	`distribute-rgt-in_binary64`
328×	`unswap-sqr_binary64`
315×	`distribute-lft-in_binary64`

Counts

44 → 29

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	387
1	86	342
2	244	342
3	436	340
4	682	340
5	1331	340
6	2344	340
7	4866	340
8	4903	340

prune24.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	27	2	29
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	28	7	35

Error

0.0b

Counts

35 → 7

Alt Table

Status	Error	Program
✓	5.8b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
▶	0.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 y x))) (cbrt.f64 (.f64 y (.f64 y x)))) (cbrt.f64 (.f64 y (.f64 y x)))) x)
✓	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
	34.5b	(+.f64 (.f64 (sqrt.f64 y) (.f64 x (pow.f64 y 3/2))) x)
	1.9b	(+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 2) (*.f64 (pow.f64 (cbrt.f64 y) 2) x)) x)
	6.1b	(+.f64 (.f64 (.f64 (pow.f64 y 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) x)
	7.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))

Compiler

Compiled 533 to 209 computations (60.8% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 y (.f64 y x))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 y x))) (cbrt.f64 (.f64 y (.f64 y x)))) (cbrt.f64 (.f64 y (.f64 y x))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 y (.f64 y x))) (cbrt.f64 (.f64 y (*.f64 y x))))
✓	16.2b	(cbrt.f64 (.f64 y (.f64 y x)))

series994.0ms (35.5%)

Counts

3 → 72

Calls

3 calls:

533.0ms

(*.f64 (cbrt.f64 (*.f64 y (*.f64 y x))) (cbrt.f64 (*.f64 y (*.f64 y x))))

441.0ms

(cbrt.f64 (*.f64 y (*.f64 y x)))

21.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 y (*.f64 y x))) (cbrt.f64 (*.f64 y (*.f64 y x)))) (cbrt.f64 (*.f64 y (*.f64 y x))))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (*.f64 y (*.f64 y x))) (cbrt.f64 (*.f64 y (*.f64 y x))))

7.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 y (*.f64 y x))) (cbrt.f64 (*.f64 y (*.f64 y x)))) (cbrt.f64 (*.f64 y (*.f64 y x))))

2.0ms

(cbrt.f64 (*.f64 y (*.f64 y x)))

simplify126.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

649×	`unswap-sqr_binary64`
407×	`fma-neg_binary64`
356×	`fma-def_binary64`
202×	`exp-prod_binary64`
202×	`log-prod_binary64`

Counts

151 → 130

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	2309
1	275	1989
2	684	1631
3	1474	1451
4	4525	1427
5	4951	1427
6	4968	1427

prune226.0ms (8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	272	8	280

Error

0.0b

Counts

280 → 8

Alt Table

Status	Error	Program
✓	5.8b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
✓	0.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 y x))) (cbrt.f64 (.f64 y (.f64 y x)))) (cbrt.f64 (.f64 y (.f64 y x)))) x)
✓	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
	34.5b	(+.f64 (.f64 (sqrt.f64 y) (.f64 x (pow.f64 y 3/2))) x)
	1.9b	(+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 2) (*.f64 (pow.f64 (cbrt.f64 y) 2) x)) x)
	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 y x))) (.f64 (cbrt.f64 y) (cbrt.f64 (.f64 y x)))) (cbrt.f64 (.f64 y (.f64 y x)))) x)
	6.1b	(+.f64 (.f64 (.f64 (pow.f64 y 2) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) x)
	7.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))

Compiler

Compiled 7070 to 1586 computations (77.6% saved)

regimes156.0ms (5.6%)

Accuracy

Total 0.1b remaining (73.7%)

Threshold costs 0.1b (73.7%)

Counts

34 → 1

Compiler

Compiled 2560 to 1489 computations (41.8% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	9	10

end0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

sample538.0ms (19.2%)

Algorithm

1×

intervals

Results

220.0ms	8000×	body	128	valid
4.0ms	166×	body	128	invalid

Compiler

Compiled 149 to 80 computations (46.3% saved)

Details

analyze346.0ms (12.3%)

sample29.0ms (1%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series11.0ms (0.4%)

rewrite3.0ms (0.1%)

simplify80.0ms (2.8%)

prune27.0ms (0.9%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite6.0ms (0.2%)

simplify59.0ms (2.1%)

prune36.0ms (1.3%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite4.0ms (0.2%)

simplify67.0ms (2.4%)

prune24.0ms (0.9%)

localize7.0ms (0.3%)

series994.0ms (35.5%)

rewrite22.0ms (0.8%)

simplify126.0ms (4.5%)

prune226.0ms (8%)

regimes156.0ms (5.6%)

simplify5.0ms (0.2%)

end0.0ms (0%)

sample538.0ms (19.2%)

Profiling