Details

analyze109.0ms (5.6%)

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)

sample14.0ms (0.7%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify7.0ms (0.4%)

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

prune6.0ms (0.3%)

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

3.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.8b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.6b	(*.f64 x (fma.f64 y y 1))

series9.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite3.0ms (0.2%)

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))

simplify84.0ms (4.3%)

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

prune29.0ms (1.5%)

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

1.8b

Counts

41 → 6

Alt Table

Status	Error	Program
	5.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
	30.9b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))
	39.7b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 y y 1) x) 3))
▶	3.8b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	20.5b	x
	3.9b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))

Compiler

Compiled 555 to 325 computations (41.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.4b	(*.f64 (pow.f64 y 2) x)

series9.0ms (0.5%)

Counts

1 → 0

Calls

1 calls:

9.0ms

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

rewrite5.0ms (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:

4.0ms

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

simplify65.0ms (3.4%)

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

prune35.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	44	7	51

Error

0.0b

Counts

51 → 7

Alt Table

Status	Error	Program
	31.2b	(+.f64 (.f64 (.f64 y (*.f64 y (sqrt.f64 x))) (sqrt.f64 x)) x)
	5.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
▶	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
	32.7b	(+.f64 (.f64 (pow.f64 (sqrt.f64 y) 2) (.f64 y x)) x)
	2.1b	(+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 2) (*.f64 (pow.f64 (cbrt.f64 y) 2) x)) x)
	39.7b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 y y 1) x) 3))
✓	3.8b	(+.f64 (*.f64 (pow.f64 y 2) x) x)

Compiler

Compiled 726 to 397 computations (45.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.5%)

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))

simplify66.0ms (3.4%)

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

prune22.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	27	2	29
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	29	7	36

Error

0.0b

Counts

36 → 7

Alt Table

Status	Error	Program
	31.2b	(+.f64 (.f64 (.f64 y (*.f64 y (sqrt.f64 x))) (sqrt.f64 x)) x)
	5.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
	32.7b	(+.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 y x))) x)
✓	3.8b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
✓	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
	39.7b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 y y 1) x) 3))
▶	0.5b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x))) x)

Compiler

Compiled 499 to 197 computations (60.5% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x)))
✓	0.3b	(.f64 (cbrt.f64 y) (.f64 y x))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)

series447.0ms (23%)

Counts

4 → 72

Calls

4 calls:

345.0ms	(.f64 (cbrt.f64 y) (.f64 y x))
38.0ms	(cbrt.f64 y)
37.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
27.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x)))

rewrite27.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 108

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x)))
4.0ms	(.f64 (cbrt.f64 y) (.f64 y x))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify129.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

436×	`log-prod_binary64`
431×	`*-commutative_binary64`
363×	`sqr-pow_binary64`
298×	`associate-+l+_binary64`
294×	`exp-prod_binary64`

Counts

180 → 146

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	1693
1	247	1441
2	910	1400
3	1677	1330
4	3646	1230
5	4554	1230
6	4809	1230
7	4836	1230

prune123.0ms (6.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	181	8	189

Error

0.0b

Counts

189 → 8

Alt Table

Status	Error	Program
	31.2b	(+.f64 (.f64 (.f64 y (*.f64 y (sqrt.f64 x))) (sqrt.f64 x)) x)
	5.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
	12.7b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (pow.f64 (pow.f64 y 4) 1/3) x)) x)
	39.7b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 y y 1) x) 3))
	32.7b	(+.f64 (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 y x))) x)
✓	3.8b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
✓	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
✓	0.5b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x))) x)

Compiler

Compiled 3407 to 925 computations (72.9% saved)

regimes130.0ms (6.7%)

Accuracy

Total 0.1b remaining (74.8%)

Threshold costs 0.1b (74.8%)

Counts

30 → 1

Compiler

Compiled 2119 to 1287 computations (39.3% saved)

simplify2.0ms (0.1%)

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)

sample584.0ms (30.1%)

Algorithm

1×

intervals

Results

215.0ms	8000×	body	128	valid
4.0ms	165×	body	128	invalid

Compiler

Compiled 124 to 74 computations (40.3% saved)

Details

analyze109.0ms (5.6%)

sample14.0ms (0.7%)

simplify7.0ms (0.4%)

prune6.0ms (0.3%)

localize4.0ms (0.2%)

series9.0ms (0.5%)

rewrite3.0ms (0.2%)

simplify84.0ms (4.3%)

prune29.0ms (1.5%)

localize4.0ms (0.2%)

series9.0ms (0.5%)

rewrite5.0ms (0.2%)

simplify65.0ms (3.4%)

prune35.0ms (1.8%)

localize4.0ms (0.2%)

series9.0ms (0.5%)

rewrite4.0ms (0.2%)

simplify66.0ms (3.4%)

prune22.0ms (1.1%)

localize10.0ms (0.5%)

series447.0ms (23%)

rewrite27.0ms (1.4%)

simplify129.0ms (6.6%)

prune123.0ms (6.4%)

regimes130.0ms (6.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample584.0ms (30.1%)

Profiling