Details

analyze1.1s (3.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.8s (4.7%)

Results

1.1s	8256×	body	128	valid
449.0ms	3126×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify62.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	72	17
3	227	17
4	512	17
5	1044	17
6	1436	17
7	1492	17
8	1573	17
9	1615	17
10	1631	17
11	1631	17
12	1550	17

prune3.0ms (0%)

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

4.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize8.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series43.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

43.0ms

(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

rewrite102.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

26× egg-rr

Counts

1 → 26

Calls

2 calls:

102.0ms	((fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	232	17
2	2678	17
3	4790	17
4	4815	17
5	4945	17
0	0	0
1	0	0

simplify188.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

708×	`distribute-rgt-neg-in_binary64`
678×	`cube-prod_binary64`
657×	`fma-def_binary64`
600×	`fma-neg_binary64`
547×	`sqr-pow_binary64`

Counts

74 → 41

Iterations

Useful iterations: 11 (0.0ms)

Iter	Nodes	Cost
0	27	940
1	81	794
2	192	722
3	465	722
4	1047	722
5	1855	722
6	2608	722
7	3162	722
8	3174	722
9	3372	722
10	3536	722
11	3721	644
12	3351	644
13	3922	644
14	4612	644
15	4874	644

prune30.0ms (0.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	36	5	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	6	42

Error

4.0b

Counts

42 → 6

Alt Table

Status	Error	Program
✓	4.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
▶	5.7b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 3)
	43.7b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
	37.2b	(.f64 4 (.f64 y t))
	34.4b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 4 (-.f64 t (*.f64 z z)))))) 2)
	40.6b	(pow.f64 x 2)

Compiler

Compiled 788 to 394 computations (50% saved)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 3)
✓	2.5b	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))
	4.3b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series30.8s (82%)

Counts

2 → 96

Calls

2 calls:

30.6s	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 3)
181.0ms	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))

rewrite115.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

70× egg-rr

Counts

2 → 70

Calls

2 calls:

113.0ms	((cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) 3))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	278	36
2	3060	36
3	4894	36
4	4876	36
5	4855	36
0	0	0
1	0	0

simplify170.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-def_binary64`
451×	`times-frac_binary64`
372×	`associate-/l*_binary64`
348×	`associate-/r*_binary64`
181×	`*-commutative_binary64`

Counts

166 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	476	7898
1	1685	7571
2	4942	7553
3	5252	7553

prune250.0ms (0.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	216	9	225
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	217	14	231

Error

2.2b

Counts

231 → 14

Alt Table

Status	Error	Program
	59.1b	(pow.f64 (pow.f64 (exp.f64 1/3) (-.f64 (log.f64 (.f64 y -4)) (.f64 2 (log.f64 (/.f64 -1 z))))) 3)
	43.7b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
	37.2b	(.f64 4 (.f64 y t))
	34.5b	(pow.f64 (pow.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) 1/3) 3)
	33.9b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (.f64 x x))
	41.0b	(pow.f64 (cbrt.f64 (*.f64 x x)) 3)
✓	4.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
✓	5.7b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 3)
	59.1b	(pow.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (.f64 4 y))) (*.f64 2 (log.f64 (/.f64 -1 z)))))) 3)
	59.1b	(pow.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (.f64 y -4)) (.f64 (log.f64 z) 2))) 3)
	59.1b	(pow.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (.f64 4 y))) (*.f64 2 (log.f64 (/.f64 1 z)))))) 3)
	37.7b	(pow.f64 (cbrt.f64 (.f64 4 (.f64 y t))) 3)
▶	5.4b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (.f64 x x))
	34.4b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 4 (-.f64 t (*.f64 z z)))))) 2)

Compiler

Compiled 10372 to 6917 computations (33.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 y) 2)
✓	0.6b	(cbrt.f64 y)
✓	0.8b	(.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (*.f64 z z))))
✓	4.0b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (.f64 x x))

series757.0ms (2%)

Counts

4 → 108

Calls

4 calls:

470.0ms	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (.f64 x x))
175.0ms	(.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (*.f64 z z))))
68.0ms	(cbrt.f64 y)
43.0ms	(pow.f64 (cbrt.f64 y) 2)

rewrite72.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

83× egg-rr

Counts

4 → 83

Calls

2 calls:

70.0ms	((fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (.f64 x x)) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (*.f64 z z)))) (cbrt.f64 y) (pow.f64 (cbrt.f64 y) 2))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	51
1	311	41
2	3423	41
3	5131	41
0	0	0
1	0	0

simplify86.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

513×	`fma-neg_binary64`
438×	`unswap-sqr_binary64`
425×	`*-commutative_binary64`
369×	`distribute-rgt-in_binary64`
332×	`neg-mul-1_binary64`

Counts

191 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	1691
1	124	1530
2	325	1452
3	1065	1452
4	2251	1452
5	4570	1452
6	5005	1452

prune117.0ms (0.3%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	10	11
Picked	0	1	1
Done	0	2	2
Total	136	15	151

Error

2.2b

Counts

151 → 15

Alt Table

Status	Error	Program
	59.1b	(pow.f64 (pow.f64 (exp.f64 1/3) (-.f64 (log.f64 (.f64 y -4)) (.f64 2 (log.f64 (/.f64 -1 z))))) 3)
	43.7b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
	34.5b	(pow.f64 (pow.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) 1/3) 3)
▶	10.9b	(fma.f64 (sqrt.f64 (.f64 y (cbrt.f64 y))) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (*.f64 x x))
	33.9b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (.f64 x x))
	41.0b	(pow.f64 (cbrt.f64 (*.f64 x x)) 3)
✓	4.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
✓	5.7b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 3)
	59.1b	(pow.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (.f64 4 y))) (*.f64 2 (log.f64 (/.f64 -1 z)))))) 3)
	59.1b	(pow.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (.f64 y -4)) (.f64 (log.f64 z) 2))) 3)
	59.1b	(pow.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (.f64 4 y))) (*.f64 2 (log.f64 (/.f64 1 z)))))) 3)
	37.7b	(pow.f64 (cbrt.f64 (.f64 4 (.f64 y t))) 3)
	41.0b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 4 (.f64 (pow.f64 y 1/3) t)) (*.f64 x x))
✓	5.4b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (.f64 x x))
	34.4b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 4 (-.f64 t (*.f64 z z)))))) 2)

Compiler

Compiled 3218 to 1546 computations (52% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 y)
	0.8b	(.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (*.f64 z z))))
✓	4.0b	(fma.f64 (sqrt.f64 (.f64 y (cbrt.f64 y))) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (*.f64 x x))
✓	12.9b	(sqrt.f64 (*.f64 y (cbrt.f64 y)))

series602.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

549.0ms	(fma.f64 (sqrt.f64 (.f64 y (cbrt.f64 y))) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (*.f64 x x))
53.0ms	(sqrt.f64 (*.f64 y (cbrt.f64 y)))

rewrite63.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

51× egg-rr

Counts

2 → 51

Calls

2 calls:

62.0ms	((sqrt.f64 (.f64 y (cbrt.f64 y))) (fma.f64 (sqrt.f64 (.f64 y (cbrt.f64 y))) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (.f64 x x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	311	23
2	3537	23
3	4917	23
0	0	0
1	0	0

simplify106.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-neg_binary64`
687×	`distribute-rgt-neg-in_binary64`
627×	`distribute-lft-neg-in_binary64`
498×	`*-commutative_binary64`
492×	`fma-def_binary64`

Counts

111 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	1298
1	122	1145
2	336	955
3	1189	955
4	2841	955
5	4763	955
6	4981	955
7	4997	955
8	4958	955

prune107.0ms (0.3%)

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	11	11
Picked	0	1	1
Done	0	3	3
Total	148	16	164

Error

2.2b

Counts

164 → 16

Alt Table

Status	Error	Program
✓	4.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	43.2b	(fma.f64 (sqrt.f64 (.f64 y (cbrt.f64 y))) (.f64 4 (.f64 (pow.f64 y 1/3) t)) (.f64 x x))
	59.1b	(pow.f64 (pow.f64 (exp.f64 1/3) (-.f64 (log.f64 (.f64 y -4)) (.f64 2 (log.f64 (/.f64 -1 z))))) 3)
	43.7b	(cbrt.f64 (pow.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
	34.5b	(pow.f64 (pow.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) 1/3) 3)
✓	10.9b	(fma.f64 (sqrt.f64 (.f64 y (cbrt.f64 y))) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (*.f64 x x))
	33.9b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (.f64 x x))
	41.0b	(pow.f64 (cbrt.f64 (*.f64 x x)) 3)
✓	5.7b	(pow.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 3)
	59.1b	(pow.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (.f64 4 y))) (*.f64 2 (log.f64 (/.f64 -1 z)))))) 3)
	59.1b	(pow.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (.f64 y -4)) (.f64 (log.f64 z) 2))) 3)
	59.1b	(pow.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (.f64 4 y))) (*.f64 2 (log.f64 (/.f64 1 z)))))) 3)
	37.7b	(pow.f64 (cbrt.f64 (.f64 4 (.f64 y t))) 3)
	41.0b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 4 (.f64 (pow.f64 y 1/3) t)) (*.f64 x x))
✓	5.4b	(fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (.f64 4 (-.f64 t (.f64 z z)))) (.f64 x x))
	34.4b	(pow.f64 (hypot.f64 x (sqrt.f64 (.f64 y (.f64 4 (-.f64 t (*.f64 z z)))))) 2)

Compiler

Compiled 3385 to 1450 computations (57.2% saved)

regimes681.0ms (1.8%)

Accuracy

Total 1.8b remaining (39.5%)

Threshold costs 0b (0%)

Counts

50 → 2

Compiler

Compiled 9595 to 6845 computations (28.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
14×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`distribute-rgt-neg-in_binary64`
12×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	66
1	56	66
2	83	66
3	104	66
4	124	66
5	136	66
6	139	66
7	141	66
8	142	66
9	136	66

end224.0ms (0.6%)

Compiler: Compiled 391 to 285 computations (27.1% saved)

Details

analyze1.1s (3.1%)

sample1.8s (4.7%)

simplify62.0ms (0.2%)

prune3.0ms (0%)

localize8.0ms (0%)

series43.0ms (0.1%)

rewrite102.0ms (0.3%)

simplify188.0ms (0.5%)

prune30.0ms (0.1%)

localize10.0ms (0%)

series30.8s (82%)

rewrite115.0ms (0.3%)

simplify170.0ms (0.5%)

prune250.0ms (0.7%)

localize21.0ms (0.1%)

series757.0ms (2%)

rewrite72.0ms (0.2%)

simplify86.0ms (0.2%)

prune117.0ms (0.3%)

localize12.0ms (0%)

series602.0ms (1.6%)

rewrite63.0ms (0.2%)

simplify106.0ms (0.3%)

prune107.0ms (0.3%)

regimes681.0ms (1.8%)

bsearch1.0ms (0%)

simplify6.0ms (0%)

end224.0ms (0.6%)

Profiling