Details

analyze127.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
0%	50%	50%	5
6.2%	31.2%	62.5%	6
9.4%	28.1%	62.5%	7
14%	17.2%	68.8%	8
14.8%	16.4%	68.8%	9
17.6%	9.8%	72.7%	10
18.1%	8.8%	73.1%	11
19.6%	5.2%	75.2%	12
20%	4.5%	75.5%	13
20.7%	2.7%	76.6%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.2s (40.5%)

Results

1.1s	8256×	body	128	valid
66.0ms	520×	body	128	invalid

Compiler

Compiled 46 to 40 computations (13% saved)

preprocess49.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

692×	`fma-def_binary64`
438×	`fma-neg_binary64`
227×	`sub-neg_binary64`
210×	`distribute-rgt-neg-in_binary64`
204×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	52	42
2	141	38
3	395	38
4	1005	38
5	1898	38
6	2873	38
7	4197	38
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 22 to 19 computations (13.6% saved)

simplify71.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1035×	`fma-def_binary64`
742×	`fma-neg_binary64`
189×	`distribute-rgt-in_binary64`
177×	`cancel-sign-sub-inv_binary64`
156×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	32	21
2	82	19
3	199	19
4	510	19
5	969	19
6	1470	19
7	2421	19
8	3626	19
9	4073	19
10	4231	19
11	4272	19
12	4275	19
13	4828	19
14	4828	19

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (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
▶	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 109 to 91 computations (16.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
✓	0.2b	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
✓	0.4b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

series62.0ms (2.1%)

Counts

4 → 41

Calls

18 calls:

6.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)	a	-inf
5.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))	a	inf
5.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))	a	-inf
5.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)	a	inf
4.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))	a	inf

rewrite67.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`prod-diff_binary64`
142×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`
138×	`expm1-log1p-u_binary64`
137×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	308	49
2	3888	49

Stop Event

1×	node limit

Counts

4 → 126

simplify39.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

549×	`fma-def_binary64`
374×	`associate-/l*_binary64`
332×	`times-frac_binary64`
239×	`associate-r_binary64`
236×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1029
1	397	973
2	1459	905

Stop Event

1×	node limit

Counts

167 → 165

prune161.0ms (5.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	161	4	165
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	4	167

Error

Counts

167 → 4

Alt Table

Status	Error	Program
	8.6b	(+.f64 a (+.f64 -1/3 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3)))))
	0.1b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
▶	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (+.f64 (*.f64 a 9) -3) -1/2) rand)))
	0.1b	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))

Compiler

Compiled 4033 to 3286 computations (18.5% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 a 9) -3)
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (+.f64 (*.f64 a 9) -3) -1/2) rand)))
✓	0.2b	(.f64 (pow.f64 (+.f64 (.f64 a 9) -3) -1/2) rand)
✓	0.4b	(pow.f64 (+.f64 (*.f64 a 9) -3) -1/2)

series51.0ms (1.7%)

Counts

4 → 58

Calls

18 calls:

5.0ms	(.f64 (pow.f64 (+.f64 (.f64 a 9) -3) -1/2) rand)	rand	0
4.0ms	(.f64 (pow.f64 (+.f64 (.f64 a 9) -3) -1/2) rand)	rand	-inf
4.0ms	(.f64 (pow.f64 (+.f64 (.f64 a 9) -3) -1/2) rand)	a	-inf
4.0ms	(.f64 (pow.f64 (+.f64 (.f64 a 9) -3) -1/2) rand)	rand	inf
4.0ms	(.f64 (pow.f64 (+.f64 (.f64 a 9) -3) -1/2) rand)	a	inf

rewrite71.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

679×	`prod-diff_binary64`
167×	`add-sqr-sqrt_binary64`
164×	`log1p-expm1-u_binary64`
164×	`expm1-log1p-u_binary64`
162×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	358	42
2	4356	42

Stop Event

1×	node limit

Counts

4 → 108

simplify42.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

536×	`fma-def_binary64`
398×	`associate-+l+_binary64`
283×	`times-frac_binary64`
274×	`associate-/l*_binary64`
234×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	1464
1	400	1396
2	1340	1176

Stop Event

1×	node limit

Counts

166 → 159

prune164.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	159	4	163

Error

Counts

163 → 4

Alt Table

Status	Error	Program
	8.6b	(+.f64 a (+.f64 -1/3 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3)))))
▶	0.1b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (+.f64 (*.f64 a 9) -3) -1/2) rand)))
	0.1b	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))

Compiler

Compiled 4088 to 3283 computations (19.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 a 1/3))
✓	0.0b	(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
✓	0.2b	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
✓	0.3b	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))

series46.0ms (1.5%)

Counts

4 → 21

Calls

21 calls:

4.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))	a	-inf
4.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))	a	inf
3.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))	a	inf
3.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))	rand	inf
3.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))	a	-inf

rewrite53.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

970×	`prod-diff_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
102×	`add-sqr-sqrt_binary64`
98×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	42
1	203	40
2	2742	40

Stop Event

1×	node limit

Counts

4 → 91

simplify32.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

598×	`associate-/r*_binary64`
397×	`fma-neg_binary64`
379×	`associate-/r/_binary64`
292×	`associate-/l/_binary64`
180×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	508
1	195	480
2	617	464
3	2447	441

Stop Event

1×	node limit

Counts

112 → 121

prune108.0ms (3.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	121	4	125

Error

Counts

125 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (fma.f64 (*.f64 1/3 rand) (sqrt.f64 (+.f64 a -1/3)) a) 1/3)
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (+.f64 (*.f64 a 9) -3) -1/2) rand)))
✓	0.1b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
	0.1b	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))

Compiler

Compiled 2452 to 1890 computations (22.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 a -1/3))
✓	0.1b	(fma.f64 (*.f64 1/3 rand) (sqrt.f64 (+.f64 a -1/3)) a)
✓	0.3b	(*.f64 1/3 rand)

series18.0ms (0.6%)

Counts

3 → 22

Calls

12 calls:

4.0ms	(sqrt.f64 (+.f64 a -1/3))	a	inf
2.0ms	(sqrt.f64 (+.f64 a -1/3))	a	-inf
2.0ms	(fma.f64 (*.f64 1/3 rand) (sqrt.f64 (+.f64 a -1/3)) a)	a	-inf
2.0ms	(fma.f64 (*.f64 1/3 rand) (sqrt.f64 (+.f64 a -1/3)) a)	a	inf
2.0ms	(fma.f64 (*.f64 1/3 rand) (sqrt.f64 (+.f64 a -1/3)) a)	a	0

rewrite46.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

849×	`log1p-expm1-u_binary64`
849×	`expm1-log1p-u_binary64`
146×	`prod-diff_binary64`
93×	`add-sqr-sqrt_binary64`
88×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	191	23
2	2261	23

Stop Event

1×	node limit

Counts

3 → 61

simplify25.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

564×	`associate-*l/_binary64`
525×	`associate-/r*_binary64`
524×	`cancel-sign-sub-inv_binary64`
299×	`associate-/r/_binary64`
218×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	395
1	154	361
2	480	355
3	1920	347

Stop Event

1×	node limit

Counts

83 → 81

prune65.0ms (2.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	81	4	85

Error

Counts

85 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (fma.f64 (*.f64 1/3 rand) (sqrt.f64 (+.f64 a -1/3)) a) 1/3)
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (+.f64 (*.f64 a 9) -3) -1/2) rand)))
✓	0.1b	(-.f64 (+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1/3)
	0.1b	(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (/.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))

Compiler

Compiled 1428 to 1115 computations (21.9% saved)

regimes327.0ms (11.1%)

Accuracy

Total 0.1b remaining (85.1%)

Threshold costs 0.1b (85.1%)

Counts

76 → 1

Compiler

Compiled 5226 to 4322 computations (17.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	20
1	24	20
2	25	20

Stop Event

1×

saturated

end91.0ms (3.1%)

Stop Event

1×

fuel

Compiler

Compiled 96 to 78 computations (18.8% saved)

Details

analyze127.0ms (4.3%)

sample1.2s (40.5%)

preprocess49.0ms (1.7%)

simplify71.0ms (2.4%)

prune4.0ms (0.1%)

localize10.0ms (0.3%)

series62.0ms (2.1%)

rewrite67.0ms (2.3%)

simplify39.0ms (1.3%)

prune161.0ms (5.4%)

localize13.0ms (0.4%)

series51.0ms (1.7%)

rewrite71.0ms (2.4%)

simplify42.0ms (1.4%)

prune164.0ms (5.6%)

localize9.0ms (0.3%)

series46.0ms (1.5%)

rewrite53.0ms (1.8%)

simplify32.0ms (1.1%)

prune108.0ms (3.7%)

localize7.0ms (0.2%)

series18.0ms (0.6%)

rewrite46.0ms (1.6%)

simplify25.0ms (0.9%)

prune65.0ms (2.2%)

regimes327.0ms (11.1%)

simplify2.0ms (0.1%)

end91.0ms (3.1%)

Profiling