Details

analyze359.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample2.3s (42.4%)

Alt Table

Status	Error	Program
▶	54.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Results

1.0s	3937×	body	256	valid
595.0ms	1534×	body	512	valid
422.0ms	2785×	body	128	valid
131.0ms	874×	body	128	invalid

Compiler

Compiled 146 to 104 computations (28.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	0.3b	(.f64 (.f64 3 a) c)
✓	27.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

series154.0ms (2.9%)

Counts

4 → 100

Calls

4 calls:

86.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
54.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(.f64 (.f64 3 a) c)

rewrite113.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

725×	`fma-def_binary64`
366×	`fma-neg_binary64`
285×	`egg-rr`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`

Counts

4 → 285

Calls

4 calls:

105.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
105.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
105.0ms	(.f64 (.f64 3 a) c)
105.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	66
1	297	56
2	3769	56
3	5480	56
0	0	0
1	0	0

prune225.0ms (4.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	380	5	385
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	381	5	386

Error

0.1b

Counts

386 → 5

Alt Table

Status	Error	Program
	54.3b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (*.f64 3 a))
	54.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	54.7b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
▶	1.0b	(neg.f64 (+.f64 (.f64 9/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 135/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (.f64 3/8 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b 3))) (*.f64 1/2 (/.f64 c b))))))
	1.4b	(/.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 3 a))

Compiler

Compiled 10948 to 6053 computations (44.7% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (pow.f64 c 4) (pow.f64 a 3))
✓	0.3b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))

series296.0ms (5.5%)

Counts

4 → 0

Calls

4 calls:

109.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
95.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))
72.0ms	(/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3))
20.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 3))

rewrite70.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

382×	`log1p-udef_binary64`
225×	`log1p-expm1-u_binary64`
225×	`expm1-log1p-u_binary64`
224×	`add-sqr-sqrt_binary64`
216×	`add-cbrt-cube_binary64`

Counts

4 → 72

Calls

4 calls:

68.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 3))
68.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))
68.0ms	(/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3))
68.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	506	55
2	4516	55
3	5298	55
0	0	0
1	0	0

prune117.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	72	5	77

Error

0.1b

Counts

77 → 5

Alt Table

Status	Error	Program
	54.3b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (*.f64 3 a))
	54.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	54.7b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
✓	1.0b	(neg.f64 (+.f64 (.f64 9/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 135/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (.f64 3/8 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b 3))) (*.f64 1/2 (/.f64 c b))))))
▶	1.4b	(/.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 3 a))

Compiler

Compiled 3865 to 2790 computations (27.8% saved)

localize33.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
✓	0.4b	(*.f64 (pow.f64 c 2) (pow.f64 a 2))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
✓	0.4b	(/.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 3 a))

series310.0ms (5.7%)

Counts

4 → 36

Calls

4 calls:

109.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
102.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
86.0ms	(/.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 3 a))
13.0ms	(*.f64 (pow.f64 c 2) (pow.f64 a 2))

rewrite74.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

422×	`log1p-expm1-u_binary64`
422×	`expm1-log1p-u_binary64`
398×	`add-log-exp_binary64`
386×	`pow1_binary64`
133×	`unpow-prod-down_binary64`

Counts

4 → 67

Calls

4 calls:

72.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
72.0ms	(*.f64 (pow.f64 c 2) (pow.f64 a 2))
72.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
72.0ms	(/.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 3 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	99
1	922	99
2	4985	99
3	4930	99
0	0	0
1	0	0

prune137.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	101	7	108

Error

0.1b

Counts

108 → 7

Alt Table

Status	Error	Program
	1.7b	(cbrt.f64 (pow.f64 (/.f64 (neg.f64 (fma.f64 3/2 (/.f64 (.f64 c a) b) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)) (.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5))))))) (.f64 a 3)) 3))
	54.3b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (*.f64 3 a))
	54.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	54.7b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
▶	1.5b	(.f64 (neg.f64 (fma.f64 3/2 (/.f64 (.f64 c a) b) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)) (.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5))))))) (/.f64 1 (*.f64 a 3)))
✓	1.0b	(neg.f64 (+.f64 (.f64 9/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 135/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (.f64 3/8 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b 3))) (*.f64 1/2 (/.f64 c b))))))
✓	1.4b	(/.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 3 a))

Compiler

Compiled 5163 to 3583 computations (30.6% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (pow.f64 (*.f64 c a) 4) (pow.f64 b 7))
✓	0.5b	(pow.f64 (*.f64 c a) 2)
✓	0.7b	(pow.f64 (*.f64 c a) 3)
✓	0.9b	(pow.f64 (*.f64 c a) 4)

series149.0ms (2.8%)

Counts

4 → 108

Calls

4 calls:

111.0ms	(/.f64 (pow.f64 (*.f64 c a) 4) (pow.f64 b 7))
16.0ms	(pow.f64 (*.f64 c a) 4)
12.0ms	(pow.f64 (*.f64 c a) 3)
8.0ms	(pow.f64 (*.f64 c a) 2)

rewrite72.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

622×	`log-prod_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
208×	`log-pow_binary64`
138×	`log1p-expm1-u_binary64`

Counts

4 → 129

Calls

4 calls:

68.0ms	(/.f64 (pow.f64 (*.f64 c a) 4) (pow.f64 b 7))
68.0ms	(pow.f64 (*.f64 c a) 2)
68.0ms	(pow.f64 (*.f64 c a) 3)
68.0ms	(pow.f64 (*.f64 c a) 4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	307	34
2	3083	34
3	5095	34
0	0	0
1	0	0

prune406.0ms (7.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	237	7	244

Error

0.1b

Counts

244 → 7

Alt Table

Status	Error	Program
	1.7b	(cbrt.f64 (pow.f64 (/.f64 (neg.f64 (fma.f64 3/2 (/.f64 (.f64 c a) b) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)) (.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5))))))) (.f64 a 3)) 3))
	54.3b	(/.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (*.f64 3 a))
	54.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	54.7b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
✓	1.5b	(.f64 (neg.f64 (fma.f64 3/2 (/.f64 (.f64 c a) b) (fma.f64 9/8 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)) (fma.f64 405/128 (/.f64 (pow.f64 (.f64 c a) 4) (pow.f64 b 7)) (.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5))))))) (/.f64 1 (*.f64 a 3)))
✓	1.0b	(neg.f64 (+.f64 (.f64 9/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 135/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (.f64 3/8 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b 3))) (*.f64 1/2 (/.f64 c b))))))
✓	1.4b	(/.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 3 a))

Compiler

Compiled 12351 to 7856 computations (36.4% saved)

regimes316.0ms (5.8%)

Accuracy

Total 1.2b remaining (85.8%)

Threshold costs 0b (0%)

Counts

50 → 1

Compiler

Compiled 7407 to 5274 computations (28.8% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
24×	`+-commutative_binary64`
21×	`sub-neg_binary64`
21×	`neg-sub0_binary64`
21×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	69
1	53	67
2	72	67
3	99	67
4	139	67
5	170	67
6	198	67
7	215	67
8	223	67
9	225	67
10	221	67

end211.0ms (3.9%)

Compiler: Compiled 377 to 270 computations (28.4% saved)

Iter	Nodes	Cost
0	36	69
1	53	67
2	72	67
3	99	67
4	139	67
5	170	67
6	198	67
7	215	67
8	223	67
9	225	67
10	221	67

Iter	Nodes	Cost
0	36	69
1	53	67
2	72	67
3	99	67
4	139	67
5	170	67
6	198	67
7	215	67
8	223	67
9	225	67
10	221	67

Details

analyze359.0ms (6.6%)

sample2.3s (42.4%)

localize11.0ms (0.2%)

series154.0ms (2.9%)

rewrite113.0ms (2.1%)

prune225.0ms (4.2%)

localize27.0ms (0.5%)

series296.0ms (5.5%)

rewrite70.0ms (1.3%)

prune117.0ms (2.2%)

localize33.0ms (0.6%)

series310.0ms (5.7%)

rewrite74.0ms (1.4%)

prune137.0ms (2.5%)

localize24.0ms (0.4%)

series149.0ms (2.8%)

rewrite72.0ms (1.3%)

prune406.0ms (7.5%)

regimes316.0ms (5.8%)

simplify7.0ms (0.1%)

end211.0ms (3.9%)

Profiling

Iter	Nodes	Cost
0	36	69
1	53	67
2	72	67
3	99	67
4	139	67
5	170	67
6	198	67
7	215	67
8	223	67
9	225	67
10	221	67