Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample979.0ms (31.9%)

Results

771.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 28 computations (36.4% saved)

simplify84.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

649×	`fma-neg_binary64`
504×	`div-sub_binary64`
481×	`fma-def_binary64`
326×	`times-frac_binary64`
174×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	21	10
3	37	10
4	64	10
5	113	10
6	216	10
7	415	10
8	754	10
9	1183	10
10	1537	10
11	1612	10
12	1657	10
13	1684	10
14	1694	10
15	1702	10
16	1702	10
17	1600	10

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

62.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	62.0b	(/.f64 (-.f64 x lo) (-.f64 hi lo))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	62.0b	(/.f64 (-.f64 x lo) (-.f64 hi lo))

series19.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

19.0ms

(/.f64 (-.f64 x lo) (-.f64 hi lo))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

1 → 54

Calls

1 calls:

7.0ms

(/.f64 (-.f64 x lo) (-.f64 hi lo))

simplify78.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-neg_binary64`
418×	`fma-def_binary64`
402×	`associate--l+_binary64`
279×	`cancel-sign-sub-inv_binary64`
264×	`times-frac_binary64`

Counts

90 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	2093
1	436	2033
2	1358	1879
3	4643	1879
4	5346	1879

prune41.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	80	4	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	4	85

Error

51.3b

Counts

85 → 4

Alt Table

Status	Error	Program
▶	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	57.3b	(-.f64 (+.f64 1 (+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))

Compiler

Compiled 1901 to 683 computations (64.1% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))
✓	0.7b	(pow.f64 (/.f64 lo hi) 3)
✓	1.8b	(+.f64 (/.f64 lo hi) 1)
✓	1.8b	(-.f64 -1 (/.f64 lo hi))

series42.0ms (1.4%)

Counts

4 → 96

Calls

4 calls:

17.0ms	(*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))
15.0ms	(pow.f64 (/.f64 lo hi) 3)
6.0ms	(-.f64 -1 (/.f64 lo hi))
4.0ms	(+.f64 (/.f64 lo hi) 1)

rewrite58.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

173×	`add-sqr-sqrt_binary64`
164×	`*-un-lft-identity_binary64`
158×	`add-cube-cbrt_binary64`
147×	`times-frac_binary64`
117×	`prod-diff_binary64`

Counts

4 → 293

Calls

4 calls:

14.0ms	(*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))
6.0ms	(-.f64 -1 (/.f64 lo hi))
5.0ms	(+.f64 (/.f64 lo hi) 1)
3.0ms	(pow.f64 (/.f64 lo hi) 3)

simplify181.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
480×	`associate-l_binary64`
444×	`associate-r_binary64`
380×	`log-prod_binary64`
293×	`*-commutative_binary64`

Counts

389 → 340

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	410	7239
1	1125	5197
2	3283	4476
3	4278	4476
4	4846	4476

prune225.0ms (7.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	332	8	340
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	333	11	344

Error

50.7b

Counts

344 → 11

Alt Table

Status	Error	Program
	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (sqrt.f64 hi)) 3) (pow.f64 (/.f64 (cbrt.f64 lo) (sqrt.f64 hi)) 3))))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (.f64 (.f64 (cbrt.f64 (-.f64 -1 (/.f64 lo hi))) (cbrt.f64 (-.f64 -1 (/.f64 lo hi)))) (cbrt.f64 (-.f64 -1 (/.f64 lo hi)))))) (pow.f64 (/.f64 lo hi) 3)))
	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (.f64 lo (/.f64 (-.f64 -1 (/.f64 lo hi)) hi))) (pow.f64 (/.f64 lo hi) 3)))
▶	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
	52.1b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (/.f64 (.f64 lo (-.f64 1 (pow.f64 (/.f64 lo hi) 2))) (*.f64 hi (+.f64 -1 (/.f64 lo hi))))) (pow.f64 (/.f64 lo hi) 3)))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (*.f64 (cbrt.f64 hi) (cbrt.f64 hi))) 3) (pow.f64 (/.f64 (cbrt.f64 lo) (cbrt.f64 hi)) 3))))
	57.3b	(-.f64 (+.f64 1 (+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	57.3b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (neg.f64 (pow.f64 (/.f64 lo hi) 2))) (pow.f64 (/.f64 lo hi) 3)))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (+.f64 -1 (.f64 (neg.f64 (/.f64 1 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)))) (/.f64 lo (cbrt.f64 hi)))))) (pow.f64 (/.f64 lo hi) 3)))

Compiler

Compiled 17859 to 6122 computations (65.7% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))
✓	0.5b	(*.f64 (/.f64 lo hi) (/.f64 lo hi))
	0.7b	(pow.f64 (/.f64 lo hi) 3)
	1.8b	(-.f64 -1 (/.f64 lo hi))

series30.0ms (1%)

Counts

1 → 24

Calls

1 calls:

30.0ms

(*.f64 (/.f64 lo hi) (/.f64 lo hi))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
29×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

1 → 69

Calls

1 calls:

8.0ms

(*.f64 (/.f64 lo hi) (/.f64 lo hi))

simplify86.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

726×	`associate-/l*_binary64`
529×	`associate-*l/_binary64`
408×	`times-frac_binary64`
392×	`associate-*r/_binary64`
392×	`unswap-sqr_binary64`

Counts

93 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	1390
1	310	1161
2	972	975
3	3558	909
4	4638	909
5	5010	909

prune228.0ms (7.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	401	7	408
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	409	10	419

Error

50.7b

Counts

419 → 10

Alt Table

Status	Error	Program
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (sqrt.f64 hi)) 3) (pow.f64 (/.f64 (cbrt.f64 lo) (sqrt.f64 hi)) 3))))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (.f64 (.f64 (cbrt.f64 (-.f64 -1 (/.f64 lo hi))) (cbrt.f64 (-.f64 -1 (/.f64 lo hi)))) (cbrt.f64 (-.f64 -1 (/.f64 lo hi)))))) (pow.f64 (/.f64 lo hi) 3)))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (/.f64 lo hi)) (.f64 lo (/.f64 (-.f64 -1 (/.f64 lo hi)) hi))) (pow.f64 (/.f64 lo hi) 3)))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (*.f64 (cbrt.f64 hi) (cbrt.f64 hi))) 3) (pow.f64 (/.f64 (cbrt.f64 lo) (cbrt.f64 hi)) 3))))
▶	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (+.f64 -1 (.f64 (neg.f64 (/.f64 1 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)))) (/.f64 lo (cbrt.f64 hi)))))) (pow.f64 (/.f64 lo hi) 3)))
	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	57.3b	(-.f64 (+.f64 1 (+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	57.3b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (/.f64 lo hi) (/.f64 lo hi)) (neg.f64 (pow.f64 (/.f64 lo hi) 2))) (pow.f64 (/.f64 lo hi) 3)))
	52.1b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (/.f64 lo hi)) (/.f64 (.f64 lo (-.f64 1 (pow.f64 (/.f64 lo hi) 2))) (*.f64 hi (+.f64 -1 (/.f64 lo hi))))) (pow.f64 (/.f64 lo hi) 3)))

Compiler

Compiled 19693 to 5839 computations (70.3% saved)

localize19.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (/.f64 lo hi) (/.f64 lo hi))
✓	0.6b	(*.f64 (cbrt.f64 hi) (cbrt.f64 hi))
	0.7b	(pow.f64 (/.f64 lo hi) 3)
✓	1.8b	(+.f64 -1 (.f64 (neg.f64 (/.f64 1 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)))) (/.f64 lo (cbrt.f64 hi))))

series61.0ms (2%)

Counts

2 → 36

Calls

2 calls:

41.0ms	(*.f64 (cbrt.f64 hi) (cbrt.f64 hi))
20.0ms	(+.f64 -1 (.f64 (neg.f64 (/.f64 1 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)))) (/.f64 lo (cbrt.f64 hi))))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 59

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 hi) (cbrt.f64 hi))
2.0ms	(+.f64 -1 (.f64 (neg.f64 (/.f64 1 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)))) (/.f64 lo (cbrt.f64 hi))))

simplify102.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-neg_binary64`
460×	`associate-l_binary64`
356×	`associate-r_binary64`
290×	`associate-*l/_binary64`
280×	`times-frac_binary64`

Counts

95 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1194
1	195	1006
2	613	764
3	3092	745
4	4879	745
5	5000	745
6	4951	745

prune135.0ms (4.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	243	7	250

Error

50.7b

Counts

250 → 7

Alt Table

Status	Error	Program
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (+.f64 -1 (.f64 (neg.f64 (/.f64 1 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 hi) (cbrt.f64 hi)))))) (/.f64 lo (cbrt.f64 hi)))))) (pow.f64 (/.f64 lo hi) 3)))
	57.3b	(-.f64 (+.f64 1 (+.f64 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
	51.9b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (/.f64 lo hi)) (.f64 (/.f64 lo hi) (+.f64 -1 (*.f64 (neg.f64 (/.f64 1 (pow.f64 hi 2/3))) (/.f64 lo (cbrt.f64 hi)))))) (pow.f64 (/.f64 lo hi) 3)))
	51.9b	(-.f64 (+.f64 1 (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 x lo)))
	57.3b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (/.f64 lo hi) (/.f64 lo hi)) (neg.f64 (pow.f64 (/.f64 lo hi) 2))) (pow.f64 (/.f64 lo hi) 3)))
	52.1b	(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (/.f64 lo hi)) (/.f64 (.f64 lo (-.f64 1 (pow.f64 (/.f64 lo hi) 2))) (*.f64 hi (+.f64 -1 (/.f64 lo hi))))) (pow.f64 (/.f64 lo hi) 3)))

Compiler

Compiled 11310 to 3764 computations (66.7% saved)

regimes495.0ms (16.1%)

Accuracy

Total 1.2b remaining (2.3%)

Threshold costs 0b (0%)

Counts

100 → 1

Compiler

Compiled 16646 to 7872 computations (52.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`*-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	37	55
2	48	55
3	58	55
4	64	55
5	67	55
6	68	55
7	66	55

end135.0ms (4.4%)

Compiler: Compiled 331 to 170 computations (48.6% saved)

Details

analyze2.0ms (0.1%)

sample979.0ms (31.9%)

simplify84.0ms (2.7%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series19.0ms (0.6%)

rewrite11.0ms (0.4%)

simplify78.0ms (2.5%)

prune41.0ms (1.4%)

localize14.0ms (0.5%)

series42.0ms (1.4%)

rewrite58.0ms (1.9%)

simplify181.0ms (5.9%)

prune225.0ms (7.3%)

localize12.0ms (0.4%)

series30.0ms (1%)

rewrite13.0ms (0.4%)

simplify86.0ms (2.8%)

prune228.0ms (7.4%)

localize19.0ms (0.6%)

series61.0ms (2%)

rewrite9.0ms (0.3%)

simplify102.0ms (3.3%)

prune135.0ms (4.4%)

regimes495.0ms (16.1%)

simplify4.0ms (0.1%)

end135.0ms (4.4%)

Profiling