Details

analyze429.0ms (18.3%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
37.4%	49.9%	12.6%	10
43.7%	43.7%	12.6%	11
49.1%	38.2%	12.6%	12
54.6%	26.5%	18.9%	13
58.5%	22.6%	18.9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample860.0ms (36.7%)

Results

760.0ms	8256×	body	128	valid
69.0ms	676×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	8
2	16	8
3	17	8

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

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
	7.1b	(fma.f64 y (*.f64 z z) x)
▶	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y z) z))
✓	0.2b	(.f64 (.f64 y z) z)

series21.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

11.0ms	(.f64 (.f64 y z) z)
9.0ms	(+.f64 x (.f64 (.f64 y z) z))

rewrite41.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

929×	`prod-diff_binary64`
762×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`
73×	`log1p-expm1-u_binary64`
72×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	149	15
2	2051	15

Stop Event

1×	node limit

Counts

2 → 51

Calls

2 calls:

40.0ms	(+.f64 x (.f64 (.f64 y z) z))
40.0ms	(.f64 (.f64 y z) z)

simplify75.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
449×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	423
1	16	423
2	28	423
3	52	423
4	118	423
5	329	423
6	1249	423
7	2149	423
8	2313	423
9	2497	423
10	2705	423
11	2999	423
12	3390	423
13	3870	423
14	4431	423

Stop Event

1×	node limit

Counts

111 → 55

prune27.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Error

0.0b

Counts

57 → 4

Alt Table

Status	Error	Program
	20.3b	(+.f64 x (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)))
	29.6b	(+.f64 x (pow.f64 (*.f64 (sqrt.f64 y) z) 2))
▶	7.1b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 768 to 256 computations (66.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.7b	(fma.f64 y (*.f64 z z) x)

series10.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

9.0ms

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

rewrite31.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

496×	`log1p-expm1-u_binary64`
496×	`expm1-log1p-u_binary64`
311×	`unpow-prod-down_binary64`
265×	`log-prod_binary64`
154×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	118	8
2	1393	8

Stop Event

1×	node limit

Counts

1 → 36

Calls

1 calls:

30.0ms

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

simplify64.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

606×	`sqr-pow_binary64`
441×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
270×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	255
1	16	255
2	28	255
3	52	255
4	115	255
5	338	255
6	1253	255
7	2150	255
8	2314	255
9	2498	255
10	2706	255
11	2998	255
12	3389	255
13	3867	255
14	4430	255

Stop Event

1×	node limit

Counts

72 → 41

prune16.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	41	4	45

Error

0.0b

Counts

45 → 4

Alt Table

Status	Error	Program
▶	20.3b	(+.f64 x (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)))
	29.6b	(+.f64 x (pow.f64 (*.f64 (sqrt.f64 y) z) 2))
✓	7.1b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 570 to 197 computations (65.4% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)))
✓	0.2b	(pow.f64 (.f64 y (.f64 z z)) 3)
✓	10.5b	(.f64 y (.f64 z z))
✓	29.2b	(cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3))

series86.0ms (3.7%)

Counts

4 → 108

Calls

4 calls:

27.0ms	(cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3))
26.0ms	(+.f64 x (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)))
20.0ms	(pow.f64 (.f64 y (.f64 z z)) 3)
12.0ms	(.f64 y (.f64 z z))

rewrite53.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

913×	`log1p-expm1-u_binary64`
913×	`expm1-log1p-u_binary64`
117×	`egg-rr`
94×	`add-sqr-sqrt_binary64`
92×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	212	32
2	2548	32

Stop Event

1×	node limit

Counts

4 → 117

Calls

4 calls:

51.0ms	(+.f64 x (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)))
51.0ms	(pow.f64 (.f64 y (.f64 z z)) 3)
51.0ms	(.f64 y (.f64 z z))
51.0ms	(cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3))

simplify59.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

711×	`unswap-sqr_binary64`
507×	`fma-def_binary64`
463×	`associate-l_binary64`
363×	`associate-r_binary64`
177×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	887
1	50	887
2	130	887
3	425	887
4	1894	887
5	3648	887
6	4551	887

Stop Event

1×	node limit

Counts

225 → 112

prune59.0ms (2.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	110	6	116

Error

0.0b

Counts

116 → 6

Alt Table

Status	Error	Program
✓	20.3b	(+.f64 x (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)))
	29.6b	(+.f64 x (pow.f64 (*.f64 (sqrt.f64 y) z) 2))
	31.3b	(+.f64 x (.f64 (.f64 (*.f64 y z) (sqrt.f64 z)) (sqrt.f64 z)))
▶	0.5b	(+.f64 x (.f64 (.f64 (*.f64 y z) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z)))
✓	7.1b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 1591 to 693 computations (56.4% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (*.f64 y z) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z))
✓	0.3b	(.f64 (.f64 y z) (pow.f64 (cbrt.f64 z) 2))
✓	0.5b	(pow.f64 (cbrt.f64 z) 2)
✓	0.6b	(cbrt.f64 z)

series119.0ms (5.1%)

Counts

4 → 36

Calls

4 calls:

59.0ms	(.f64 (.f64 y z) (pow.f64 (cbrt.f64 z) 2))
31.0ms	(.f64 (.f64 (*.f64 y z) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z))
20.0ms	(pow.f64 (cbrt.f64 z) 2)
9.0ms	(cbrt.f64 z)

rewrite42.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

729×	`log1p-expm1-u_binary64`
729×	`expm1-log1p-u_binary64`
149×	`expm1-udef_binary64`
149×	`log1p-udef_binary64`
91×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	182	28
2	2127	28

Stop Event

1×	node limit

Counts

4 → 71

Calls

4 calls:

41.0ms	(.f64 (.f64 (*.f64 y z) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z))
41.0ms	(.f64 (.f64 y z) (pow.f64 (cbrt.f64 z) 2))
41.0ms	(pow.f64 (cbrt.f64 z) 2)
41.0ms	(cbrt.f64 z)

simplify66.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

791×	`sqr-pow_binary64`
406×	`cube-prod_binary64`
357×	`pow-sqr_binary64`
266×	`fabs-mul_binary64`
256×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	276
1	27	276
2	52	276
3	101	276
4	240	276
5	719	276
6	1304	276
7	1487	276
8	1727	276
9	2028	276
10	2442	276
11	3041	276
12	3763	276
13	4656	276

Stop Event

1×	node limit

Counts

107 → 75

prune70.0ms (3%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	96	8	104

Error

0.0b

Counts

104 → 8

Alt Table

Status	Error	Program
	0.5b	(+.f64 x (.f64 (pow.f64 (.f64 z (*.f64 y (pow.f64 (cbrt.f64 z) 2))) 1) (cbrt.f64 z)))
✓	20.3b	(+.f64 x (cbrt.f64 (pow.f64 (.f64 y (.f64 z z)) 3)))
	29.6b	(+.f64 x (pow.f64 (*.f64 (sqrt.f64 y) z) 2))
	31.3b	(+.f64 x (.f64 (.f64 (*.f64 y z) (sqrt.f64 z)) (sqrt.f64 z)))
✓	0.5b	(+.f64 x (.f64 (.f64 (*.f64 y z) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z)))
✓	7.1b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(+.f64 x (.f64 (.f64 y z) z))
	0.5b	(+.f64 x (pow.f64 (cbrt.f64 (.f64 z (.f64 z y))) 3))

Compiler

Compiled 1601 to 760 computations (52.5% saved)

regimes78.0ms (3.3%)

Accuracy

Total 0.1b remaining (77.8%)

Threshold costs 0.1b (77.8%)

Counts

14 → 1

Compiler

Compiled 860 to 554 computations (35.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8

Stop Event

1×

saturated

end101.0ms (4.3%)

Compiler: Compiled 122 to 77 computations (36.9% saved)

Details

analyze429.0ms (18.3%)

sample860.0ms (36.7%)

simplify6.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series21.0ms (0.9%)

rewrite41.0ms (1.7%)

simplify75.0ms (3.2%)

prune27.0ms (1.1%)

localize4.0ms (0.2%)

series10.0ms (0.4%)

rewrite31.0ms (1.3%)

simplify64.0ms (2.7%)

prune16.0ms (0.7%)

localize9.0ms (0.4%)

series86.0ms (3.7%)

rewrite53.0ms (2.2%)

simplify59.0ms (2.5%)

prune59.0ms (2.5%)

localize10.0ms (0.4%)

series119.0ms (5.1%)

rewrite42.0ms (1.8%)

simplify66.0ms (2.8%)

prune70.0ms (3%)

regimes78.0ms (3.3%)

simplify2.0ms (0.1%)

end101.0ms (4.3%)

Profiling