Details

analyze353.0ms (7.6%)

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)

sample1.5s (31.7%)

Alt Table

Status	Error	Program
▶	29.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Results

1.2s	7947×	body	128	valid
120.0ms	850×	body	128	invalid
82.0ms	309×	body	256	valid

Compiler

Compiled 146 to 104 computations (28.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	28.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series186.0ms (4%)

Counts

4 → 96

Calls

4 calls:

82.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
52.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
42.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite118.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

278×	`expm1-udef_binary64`
278×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`

Counts

4 → 156

Calls

4 calls:

112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
112.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
112.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
112.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	337	62
2	4158	62
3	4987	62
4	4850	62
0	0	0
1	0	0

prune153.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	245	7	252
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	245	8	253

Error

0.7b

Counts

253 → 8

Alt Table

Status	Error	Program
	29.1b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (/.f64 1 (.f64 a -2)))
	29.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (fma.f64 (.f64 a -4) c (.f64 (.f64 4 a) c))))) (.f64 2 a))
	28.3b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
▶	5.0b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
✓	29.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	5.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	6.8b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (*.f64 2 a))
	10.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))))) (*.f64 2 a))

Compiler

Compiled 6578 to 3980 computations (39.5% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series288.0ms (6.2%)

Counts

4 → 0

Calls

4 calls:

106.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
93.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))
70.0ms	(/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3))
19.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 3))

rewrite65.0ms (1.4%)

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:

63.0ms	(/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3))
63.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))
63.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))
63.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 3))

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

prune172.0ms (3.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Error

0.7b

Counts

80 → 8

Alt Table

Status	Error	Program
	29.1b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (/.f64 1 (.f64 a -2)))
	29.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (fma.f64 (.f64 a -4) c (.f64 (.f64 4 a) c))))) (.f64 2 a))
	28.3b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
✓	5.0b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
✓	29.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
▶	5.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	6.8b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (*.f64 2 a))
	10.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))))) (*.f64 2 a))

Compiler

Compiled 3751 to 2636 computations (29.7% saved)

localize31.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
✓	0.3b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
✓	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))

series230.0ms (5%)

Counts

4 → 0

Calls

4 calls:

177.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
21.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
20.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
11.0ms	(*.f64 (pow.f64 c 2) (pow.f64 a 2))

rewrite100.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

282×	`expm1-udef_binary64`
282×	`log1p-udef_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`
172×	`add-sqr-sqrt_binary64`

Counts

4 → 92

Calls

4 calls:

98.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
98.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
98.0ms	(*.f64 (pow.f64 c 2) (pow.f64 a 2))
98.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	34
1	408	34
2	3951	34
3	4989	34
4	4814	34
0	0	0
1	0	0

prune163.0ms (3.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	92	8	100

Error

0.7b

Counts

100 → 8

Alt Table

Status	Error	Program
	29.1b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (/.f64 1 (.f64 a -2)))
	29.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (fma.f64 (.f64 a -4) c (.f64 (.f64 4 a) c))))) (.f64 2 a))
	28.3b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
✓	5.0b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
✓	29.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	5.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
▶	6.8b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (*.f64 2 a))
	10.7b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))))) (*.f64 2 a))

Compiler

Compiled 5563 to 3935 computations (29.3% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series144.0ms (3.1%)

Counts

4 → 0

Calls

4 calls:

101.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
19.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
13.0ms	(*.f64 (pow.f64 c 2) (pow.f64 a 2))
11.0ms	(/.f64 (*.f64 c a) b)

rewrite77.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

276×	`expm1-udef_binary64`
276×	`log1p-udef_binary64`
166×	`log1p-expm1-u_binary64`
166×	`expm1-log1p-u_binary64`
163×	`add-sqr-sqrt_binary64`

Counts

4 → 116

Calls

4 calls:

74.0ms	(/.f64 (*.f64 c a) b)
74.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
74.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
74.0ms	(*.f64 (pow.f64 c 2) (pow.f64 a 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	34
1	372	34
2	4080	34
3	4955	34
0	0	0
1	0	0

prune204.0ms (4.4%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	1	3	4
Picked	0	1	1
Done	0	3	3
Total	113	11	124

Error

0.7b

Counts

124 → 11

Alt Table

Status	Error	Program
	29.1b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c))))) (/.f64 1 (.f64 a -2)))
	29.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (fma.f64 (.f64 a -4) c (.f64 (.f64 4 a) c))))) (.f64 2 a))
	28.3b	(/.f64 (/.f64 (-.f64 (fma.f64 b b (.f64 -4 (.f64 a c))) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
✓	5.0b	(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
✓	29.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	6.9b	(/.f64 (neg.f64 (+.f64 (.f64 2 (.f64 c (/.f64 1 (/.f64 b a)))) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (*.f64 2 a))
✓	5.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
✓	6.8b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (*.f64 2 a))
	7.1b	(/.f64 (neg.f64 (+.f64 (.f64 2 (cbrt.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 3)))) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (*.f64 2 a))
	6.9b	(/.f64 (neg.f64 (+.f64 (.f64 2 (pow.f64 (/.f64 b (.f64 c a)) -1)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (*.f64 2 a))
	7.0b	(/.f64 (neg.f64 (+.f64 (.f64 2 (pow.f64 (sqrt.f64 (/.f64 (.f64 c a) b)) 2)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))) (*.f64 2 a))

Compiler

Compiled 5404 to 3745 computations (30.7% saved)

regimes525.0ms (11.4%)

Accuracy

Total 5.0b remaining (86.1%)

Threshold costs 0b (0%)

Counts

89 → 1

Compiler

Compiled 12764 to 9438 computations (26.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
22×	`+-commutative_binary64`
19×	`sub-neg_binary64`
19×	`neg-sub0_binary64`
19×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	63
1	45	61
2	64	61
3	91	61
4	121	61
5	154	61
6	176	61
7	189	61
8	193	61
9	191	61

end281.0ms (6.1%)

Compiler: Compiled 518 to 387 computations (25.3% saved)

Details

analyze353.0ms (7.6%)

sample1.5s (31.7%)

localize12.0ms (0.3%)

series186.0ms (4%)

rewrite118.0ms (2.6%)

prune153.0ms (3.3%)

localize25.0ms (0.5%)

series288.0ms (6.2%)

rewrite65.0ms (1.4%)

prune172.0ms (3.7%)

localize31.0ms (0.7%)

series230.0ms (5%)

rewrite100.0ms (2.2%)

prune163.0ms (3.5%)

localize23.0ms (0.5%)

series144.0ms (3.1%)

rewrite77.0ms (1.7%)

prune204.0ms (4.4%)

regimes525.0ms (11.4%)

simplify5.0ms (0.1%)

end281.0ms (6.1%)

Profiling