Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 10 to 7 computations (30% saved)

sample517.0ms (29.6%)

Infinites

25.1% of outputs are infinite.

Results

465.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 20 computations (31% 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

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

3.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.7b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.7b	(*.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))

simplify82.0ms (4.7%)

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

prune28.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	35	5	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	5	41

Error

2.1b

Counts

41 → 5

Alt Table

Status	Error	Program
▶	3.7b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	3.7b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
	3.9b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 y y 1)) (cbrt.f64 (fma.f64 y y 1)))) (cbrt.f64 (fma.f64 y y 1)))
	28.3b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))
	33.6b	(cbrt.f64 (.f64 (.f64 (.f64 x (fma.f64 y y 1)) (.f64 x (fma.f64 y y 1))) (*.f64 x (fma.f64 y y 1))))

Compiler

Compiled 585 to 345 computations (41% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	8.0b	(*.f64 (pow.f64 y 2) x)

series10.0ms (0.6%)

Counts

1 → 0

Calls

1 calls:

10.0ms

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

rewrite5.0ms (0.3%)

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)

simplify60.0ms (3.5%)

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

prune39.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	4	0	4
Picked	0	1	1
Done	0	0	0
Total	45	5	50

Error

0.0b

Counts

50 → 5

Alt Table

Status	Error	Program
✓	3.7b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
▶	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
	2.0b	(+.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) 2) (*.f64 (pow.f64 (cbrt.f64 y) 2) x)) x)
	28.1b	(+.f64 (.f64 (.f64 y (sqrt.f64 x)) (*.f64 y (sqrt.f64 x))) x)
	13.4b	(+.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 y y) x) 3)) x)

Compiler

Compiled 674 to 363 computations (46.1% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 y (.f64 y x))

series8.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(*.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:

3.0ms

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

simplify62.0ms (3.5%)

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

prune20.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	27	2	29
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	29	5	34

Error

0.0b

Counts

34 → 5

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x))) x)
✓	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
✓	3.7b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	35.9b	(+.f64 (.f64 (sqrt.f64 y) (.f64 x (pow.f64 y 3/2))) x)
	28.1b	(+.f64 (.f64 (.f64 y (sqrt.f64 x)) (*.f64 y (sqrt.f64 x))) x)

Compiler

Compiled 445 to 165 computations (62.9% saved)

localize8.0ms (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)

series414.0ms (23.7%)

Counts

4 → 72

Calls

4 calls:

318.0ms	(.f64 (cbrt.f64 y) (.f64 y x))
40.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
36.0ms	(cbrt.f64 y)
20.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x)))

rewrite25.0ms (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)))
7.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
4.0ms	(.f64 (cbrt.f64 y) (.f64 y x))
1.0ms	(cbrt.f64 y)

simplify131.0ms (7.5%)

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

prune110.0ms (6.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	181	6	187

Error

Counts

187 → 6

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 y x))) x)
✓	0.1b	(+.f64 (.f64 y (.f64 y x)) x)
✓	3.7b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	13.9b	(+.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 (.f64 y (.f64 (.f64 (.f64 y x) (.f64 y x)) (.f64 y x))))) x)
	35.9b	(+.f64 (.f64 (sqrt.f64 y) (.f64 x (pow.f64 y 3/2))) x)
	28.1b	(+.f64 (.f64 (.f64 y (sqrt.f64 x)) (*.f64 y (sqrt.f64 x))) x)

Compiler

Compiled 3387 to 909 computations (73.2% saved)

regimes121.0ms (6.9%)

Accuracy

Total 0.0b remaining (76.5%)

Threshold costs 0.0b (76.5%)

Counts

28 → 1

Compiler

Compiled 2031 to 1260 computations (38% 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

end62.0ms (3.6%)

Compiler: Compiled 101 to 54 computations (46.5% saved)

Details

analyze1.0ms (0.1%)

sample517.0ms (29.6%)

simplify7.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.3%)

series9.0ms (0.5%)

rewrite3.0ms (0.2%)

simplify82.0ms (4.7%)

prune28.0ms (1.6%)

localize4.0ms (0.3%)

series10.0ms (0.6%)

rewrite5.0ms (0.3%)

simplify60.0ms (3.5%)

prune39.0ms (2.3%)

localize4.0ms (0.2%)

series8.0ms (0.4%)

rewrite4.0ms (0.2%)

simplify62.0ms (3.5%)

prune20.0ms (1.1%)

localize8.0ms (0.5%)

series414.0ms (23.7%)

rewrite25.0ms (1.4%)

simplify131.0ms (7.5%)

prune110.0ms (6.3%)

regimes121.0ms (6.9%)

simplify2.0ms (0.1%)

end62.0ms (3.6%)

Profiling