Details

analyze181.0ms (3.8%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.2s (24.7%)

Results

1.1s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 64 to 40 computations (37.5% saved)

preprocess34.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

421×	`fma-neg_binary64`
351×	`associate--l+_binary64`
326×	`associate-+l+_binary64`
312×	`unsub-neg_binary64`
293×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	78
1	101	74
2	350	74
3	1237	74
4	3107	66
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 31 to 19 computations (38.7% saved)

simplify34.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
320×	`+-commutative_binary64`
277×	`sub-neg_binary64`
265×	`associate-l_binary64`
250×	`unsub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	198	37
3	696	37
4	2292	33
5	4251	33

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)

▶

0.0b

(fma.f64 4 (-.f64 (fma.f64 b (*.f64 b (+.f64 a 3)) (*.f64 a a)) (pow.f64 a 3)) (+.f64 (pow.f64 (hypot.f64 a b) 4) -1))

Compiler

Compiled 166 to 105 computations (36.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 b (+.f64 a 3))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3))
✓	0.1b	(fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a))

series50.0ms (1.1%)

Counts

4 → 96

Calls

24 calls:

6.0ms	(pow.f64 (hypot.f64 a b) 4)	b	inf
4.0ms	(pow.f64 (hypot.f64 a b) 4)	b	-inf
4.0ms	(pow.f64 (hypot.f64 a b) 4)	a	-inf
4.0ms	(pow.f64 (hypot.f64 a b) 4)	a	inf
4.0ms	(-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3))	b	-inf

rewrite72.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

442×	`fma-def_binary64`
243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`
242×	`fma-neg_binary64`
169×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	295	48
2	3807	48

Stop Event

1×	node limit

Counts

4 → 169

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

550×	`unswap-sqr_binary64`
532×	`fma-def_binary64`
400×	`fma-neg_binary64`
395×	`associate-l_binary64`
347×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	1279
1	84	1205
2	241	1173
3	735	1173
4	2652	1173

Stop Event

1×	node limit

Counts

265 → 202

prune281.0ms (6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	201	3	204

Error

0.0b

Counts

204 → 3

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
	14.1b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) -1))

Compiler

Compiled 6328 to 3751 computations (40.7% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 b (+.f64 a 3))
	0.0b	(-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3))
	0.1b	(fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a))
✓	0.6b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series13.0ms (0.3%)

Counts

1 → 0

Calls

6 calls:

4.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	a	-inf
2.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	a	0
2.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	b	-inf
2.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	a	inf
2.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	b	inf

rewrite32.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

528×	`log1p-expm1-u_binary64`
528×	`expm1-log1p-u_binary64`
399×	`unpow-prod-down_binary64`
296×	`log-prod_binary64`
161×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	144	7
2	1607	7

Stop Event

1×	node limit

Counts

1 → 18

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

18 → 18

prune291.0ms (6.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	196	3	199

Error

0.0b

Counts

199 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) -1))
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
	14.1b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) -1))

Compiler

Compiled 8418 to 5720 computations (32.1% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
✓	0.1b	(.f64 (.f64 a a) (-.f64 1 a))
✓	0.2b	(.f64 (.f64 b b) (+.f64 3 a))
✓	0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series44.0ms (0.9%)

Counts

4 → 84

Calls

21 calls:

8.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))	b	0
5.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))	b	inf
4.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))	b	-inf
3.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))	a	0
2.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)	a	0

rewrite43.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

200×	`log1p-expm1-u_binary64`
200×	`expm1-log1p-u_binary64`
198×	`add-sqr-sqrt_binary64`
196×	`add-cbrt-cube_binary64`
189×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	67
1	420	63

Stop Event

1×	node limit

Counts

4 → 85

simplify47.0ms (1%)

Algorithm

1×	egg-herbie

Rules

709×	`associate-l_binary64`
571×	`fma-def_binary64`
392×	`cancel-sign-sub-inv_binary64`
359×	`associate-+l+_binary64`
312×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	1546
1	171	1502
2	585	1319
3	2712	1305

Stop Event

1×	node limit

Counts

169 → 128

prune167.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	127	4	131

Error

Counts

131 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) -1))
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	11.1b	(-.f64 (*.f64 (pow.f64 a 3) (+.f64 a -4)) 1)
	14.1b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) -1))

Compiler

Compiled 4582 to 2811 computations (38.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 (pow.f64 a 3) (+.f64 a -4)) 1)
✓	0.1b	(*.f64 (pow.f64 a 3) (+.f64 a -4))

series6.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))	a	inf
1.0ms	(-.f64 (*.f64 (pow.f64 a 3) (+.f64 a -4)) 1)	a	inf
1.0ms	(-.f64 (*.f64 (pow.f64 a 3) (+.f64 a -4)) 1)	a	-inf
1.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))	a	0
1.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))	a	-inf

rewrite57.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

518×	`prod-diff_binary64`
397×	`log-prod_binary64`
293×	`fma-def_binary64`
229×	`fma-neg_binary64`
163×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	206	21
2	2583	21

Stop Event

1×	node limit

Counts

2 → 119

simplify30.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-neg_binary64`
609×	`cancel-sign-sub-inv_binary64`
507×	`associate-l_binary64`
330×	`unswap-sqr_binary64`
319×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	261
1	42	261
2	106	237
3	333	220
4	935	208
5	3004	208

Stop Event

1×	node limit

Counts

143 → 128

prune147.0ms (3.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	128	4	132

Error

Counts

132 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) -1))
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
✓	11.1b	(-.f64 (*.f64 (pow.f64 a 3) (+.f64 a -4)) 1)
	14.1b	(fma.f64 4 (-.f64 (fma.f64 b (.f64 b (+.f64 a 3)) (.f64 a a)) (pow.f64 a 3)) (+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) -1))

Compiler

Compiled 2014 to 1549 computations (23.1% saved)

regimes1.8s (37.9%)

Accuracy

Total 0.0b remaining (62.8%)

Threshold costs 0.0b (62.8%)

Counts

285 → 1

Compiler

Compiled 37396 to 26946 computations (27.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	31	48
2	35	48
3	37	48
4	38	48

Stop Event

1×

saturated

end113.0ms (2.4%)

Stop Event

1×

fuel

Compiler

Compiled 177 to 125 computations (29.4% saved)

Details

analyze181.0ms (3.8%)

sample1.2s (24.7%)

preprocess34.0ms (0.7%)

simplify34.0ms (0.7%)

prune5.0ms (0.1%)

localize16.0ms (0.3%)

series50.0ms (1.1%)

rewrite72.0ms (1.5%)

simplify51.0ms (1.1%)

prune281.0ms (6%)

localize22.0ms (0.5%)

series13.0ms (0.3%)

rewrite32.0ms (0.7%)

simplify6.0ms (0.1%)

prune291.0ms (6.2%)

localize18.0ms (0.4%)

series44.0ms (0.9%)

rewrite43.0ms (0.9%)

simplify47.0ms (1%)

prune167.0ms (3.5%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite57.0ms (1.2%)

simplify30.0ms (0.6%)

prune147.0ms (3.1%)

regimes1.8s (37.9%)

simplify3.0ms (0.1%)

end113.0ms (2.4%)

Profiling