Details

analyze205.0ms (5.8%)

Algorithm

1×

Search

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

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify88.0ms (2.5%)

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 → 0

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

1 alts after pruning (1 fresh and 0 done)

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

Error

62.0b

Counts

1 → 1

Alt Table

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

Compiler

Compiled 20 to 12 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

62.0b

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

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

62.0b

Rules

15×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`
6×	`div-sub_binary64`
6×	`add-exp-log_binary64`
5×	`flip3--_binary64`

Counts

1 → 54

Calls

1 calls:

15.0ms

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

Compiler

Compiled 810 to 177 computations (78.1% saved)

series22.0ms (0.6%)

Error

51.8b

Counts

1 → 10

Calls

1 calls:

13.0ms

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

Compiler

Compiled 304 to 187 computations (38.5% saved)

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
776×	`times-frac_binary64`
385×	`associate-/l*_binary64`
275×	`associate-/r*_binary64`
231×	`associate-*l/_binary64`

Counts

64 → 23

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	873
1	281	822
2	953	810
3	4779	810
4	5440	810

prune11.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	2	24

Error

51.8b

Counts

24 → 2

Alt Table

Status	Error	Program
	52.1b	(/.f64 (fma.f64 -1 x lo) lo)
▶	52.0b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (/.f64 (-.f64 x lo) hi))

Compiler

Compiled 350 to 127 computations (63.7% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(fma.f64 (/.f64 x hi) (/.f64 lo hi) (/.f64 (-.f64 x lo) hi))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

51.8b

Rules

5×	`add-cube-cbrt_binary64`
5×	`fma-udef_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

1 → 33

Calls

1 calls:

10.0ms

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

Compiler

Compiled 590 to 73 computations (87.6% saved)

series92.0ms (2.6%)

Error

51.8b

Counts

1 → 13

Calls

1 calls:

87.0ms

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

Compiler

Compiled 414 to 259 computations (37.4% saved)

simplify69.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-def_binary64`
752×	`distribute-rgt-in_binary64`
450×	`fma-neg_binary64`
209×	`cancel-sign-sub-inv_binary64`
183×	`associate-*l/_binary64`

Counts

46 → 28

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	789
1	164	734
2	471	719
3	1822	713
4	4613	713
5	5018	713

prune27.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	17	11	28
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	18	12	30

Error

51.8b

Counts

30 → 12

Alt Table

Status	Error	Program
	52.1b	(/.f64 (fma.f64 -1 x lo) lo)
	52.0b	(cbrt.f64 (pow.f64 (fma.f64 lo (/.f64 x (*.f64 hi hi)) (/.f64 (-.f64 x lo) hi)) 3))
	52.0b	(/.f64 (.f64 (fma.f64 lo (/.f64 x (.f64 hi hi)) (/.f64 (-.f64 x lo) hi)) (fma.f64 lo (/.f64 x (.f64 hi hi)) (/.f64 (-.f64 lo x) hi))) (fma.f64 lo (/.f64 x (.f64 hi hi)) (/.f64 (-.f64 lo x) hi)))
	52.0b	(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 lo hi) (/.f64 x hi)) 3) (pow.f64 (/.f64 (-.f64 x lo) hi) 3)) (fma.f64 (/.f64 x hi) (.f64 (/.f64 lo hi) (fma.f64 lo (/.f64 x (.f64 hi hi)) (/.f64 (-.f64 lo x) hi))) (.f64 (/.f64 (-.f64 x lo) hi) (/.f64 (-.f64 x lo) hi))))
	52.0b	(.f64 (sqrt.f64 (fma.f64 lo (/.f64 x (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))) (sqrt.f64 (fma.f64 lo (/.f64 x (*.f64 hi hi)) (/.f64 (-.f64 x lo) hi))))
	52.0b	(.f64 (cbrt.f64 (.f64 (fma.f64 lo (/.f64 x (.f64 hi hi)) (/.f64 (-.f64 x lo) hi)) (fma.f64 lo (/.f64 x (.f64 hi hi)) (/.f64 (-.f64 x lo) hi)))) (cbrt.f64 (fma.f64 lo (/.f64 x (*.f64 hi hi)) (/.f64 (-.f64 x lo) hi))))
	52.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 lo (/.f64 x (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))) (cbrt.f64 (fma.f64 lo (/.f64 x (.f64 hi hi)) (/.f64 (-.f64 x lo) hi)))) (cbrt.f64 (fma.f64 lo (/.f64 x (*.f64 hi hi)) (/.f64 (-.f64 x lo) hi))))
	52.0b	(log.f64 (exp.f64 (fma.f64 lo (/.f64 x (*.f64 hi hi)) (/.f64 (-.f64 x lo) hi))))
	52.0b	(-.f64 (exp.f64 (log1p.f64 (fma.f64 lo (/.f64 x (*.f64 hi hi)) (/.f64 (-.f64 x lo) hi)))) 1)
	52.0b	(log1p.f64 (expm1.f64 (fma.f64 lo (/.f64 x (*.f64 hi hi)) (/.f64 (-.f64 x lo) hi))))
	52.0b	(expm1.f64 (log1p.f64 (fma.f64 lo (/.f64 x (*.f64 hi hi)) (/.f64 (-.f64 x lo) hi))))
▶	52.0b	(*.f64 (/.f64 lo hi) (+.f64 (/.f64 x hi) -1))

Compiler

Compiled 1065 to 332 computations (68.8% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 (/.f64 lo hi) (+.f64 (/.f64 x hi) -1))

rewrite43.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

51.8b

Rules

11×	`pow1_binary64`
9×	`flip3-+_binary64`
8×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`frac-times_binary64`

Counts

1 → 53

Calls

1 calls:

17.0ms

(*.f64 (/.f64 lo hi) (+.f64 (/.f64 x hi) -1))

Compiler

Compiled 916 to 408 computations (55.5% saved)

series30.0ms (0.9%)

Error

51.8b

Counts

1 → 12

Calls

1 calls:

29.0ms

(*.f64 (/.f64 lo hi) (+.f64 (/.f64 x hi) -1))

Compiler

Compiled 287 to 187 computations (34.8% saved)

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-*l/_binary64`
480×	`associate-*r/_binary64`
352×	`fma-neg_binary64`
300×	`distribute-rgt-in_binary64`
251×	`distribute-lft-in_binary64`

Counts

65 → 46

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	1050
1	310	948
2	1091	916
3	4899	916
4	5149	916

prune32.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	36	10	46
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	47	11	58

Error

51.8b

Counts

58 → 11

Alt Table

Status	Error	Program
	52.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))) 1)
	52.1b	(/.f64 (fma.f64 -1 x lo) lo)
	52.0b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi) 3))
	52.0b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))))
	52.0b	(expm1.f64 (log1p.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(.f64 (.f64 lo (+.f64 (pow.f64 (/.f64 x hi) 3) (pow.f64 -1 3))) (/.f64 1 (+.f64 hi (.f64 (.f64 (/.f64 x hi) (+.f64 (/.f64 x hi) 1)) hi))))
	52.0b	(/.f64 1 (.f64 (/.f64 hi (.f64 lo (+.f64 -1 (pow.f64 (/.f64 x hi) 3)))) (+.f64 1 (*.f64 (/.f64 x hi) (+.f64 (/.f64 x hi) 1)))))
	52.0b	(/.f64 (.f64 (pow.f64 (/.f64 lo hi) 3) (+.f64 -1 (pow.f64 (/.f64 x hi) 3))) (.f64 (pow.f64 (/.f64 lo hi) 2) (+.f64 1 (*.f64 (/.f64 x hi) (+.f64 (/.f64 x hi) 1)))))
	52.0b	(.f64 (sqrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi)) (sqrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 lo hi) 2) (pow.f64 (-.f64 (/.f64 x hi) 1) 2))) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
▶	52.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi)) (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi))) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))

Compiler

Compiled 1023 to 591 computations (42.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))
0.5b	(cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))
0.5b	(cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))
0.5b	(.f64 (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi)) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))

rewrite152.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

51.8b

Rules

31×	`cbrt-div_binary64`
28×	`add-cube-cbrt_binary64`
27×	`pow1/3_binary64`
17×	`add-sqr-sqrt_binary64`
12×	`add-exp-log_binary64`

Counts

4 → 156

Calls

4 calls:

15.0ms	(.f64 (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi)) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
12.0ms	(cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))
10.0ms	(cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))
10.0ms	(cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))

Compiler

Compiled 4406 to 2449 computations (44.4% saved)

series371.0ms (10.4%)

Error

51.8b

Counts

4 → 36

Calls

4 calls:

163.0ms	(.f64 (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi)) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
85.0ms	(cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))
49.0ms	(cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))
47.0ms	(cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))

Compiler

Compiled 4340 to 2966 computations (31.7% saved)

simplify172.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

383×	`fma-neg_binary64`
376×	`associate-l_binary64`
358×	`exp-prod_binary64`
300×	`associate-r_binary64`
244×	`log-prod_binary64`

Counts

192 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	3441
1	413	2926
2	929	2801
3	3576	2739
4	4955	2739
5	4981	2739
6	4942	2739

prune134.0ms (3.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	103	11	114
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	108	17	125

Error

51.8b

Counts

125 → 17

Alt Table

Status	Error	Program
	52.0b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi) 3))
	52.0b	(.f64 (.f64 (expm1.f64 (log1p.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi))))) (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi))) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(.f64 (.f64 (.f64 (cbrt.f64 lo) (cbrt.f64 (/.f64 -1 hi))) (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi))) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi))) 1)
	52.1b	(/.f64 (fma.f64 -1 x lo) lo)
	52.0b	(.f64 (.f64 lo (+.f64 (pow.f64 (/.f64 x hi) 3) (pow.f64 -1 3))) (/.f64 1 (+.f64 hi (.f64 (.f64 (/.f64 x hi) (+.f64 (/.f64 x hi) 1)) hi))))
	52.0b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi)) (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi))) (expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi))))))
	52.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi)))) 5) (cbrt.f64 (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (.f64 lo (-.f64 (/.f64 x hi) 1))) (/.f64 (cbrt.f64 (.f64 lo (-.f64 (/.f64 x hi) 1))) (cbrt.f64 hi))) (cbrt.f64 hi)) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(.f64 (/.f64 (cbrt.f64 (.f64 lo (-.f64 (/.f64 x hi) 1))) (/.f64 (cbrt.f64 hi) (/.f64 (cbrt.f64 (.f64 lo (-.f64 (/.f64 x hi) 1))) (cbrt.f64 hi)))) (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi)))) 4) (.f64 (cbrt.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi)))) (cbrt.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi)))))) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi)) 2/3)) (cbrt.f64 (pow.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi)) 2/3))) (cbrt.f64 (pow.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi)) 2/3))) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(.f64 (cbrt.f64 (pow.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi)) 2)) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(expm1.f64 (log1p.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(/.f64 1 (.f64 (/.f64 hi (.f64 lo (+.f64 -1 (pow.f64 (/.f64 x hi) 3)))) (+.f64 1 (*.f64 (/.f64 x hi) (+.f64 (/.f64 x hi) 1)))))
	52.0b	(.f64 (.f64 (log.f64 (exp.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi))))) (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi))) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (cbrt.f64 (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo hi))))) 1) (cbrt.f64 (/.f64 (.f64 lo (-.f64 (/.f64 x hi) 1)) hi))) (cbrt.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))

Compiler

Compiled 3213 to 1787 computations (44.4% saved)

regimes741.0ms (20.9%)

Accuracy

Total 0.2b remaining (0.3%)

Threshold costs 0.2b (0.3%)

Compiler

Compiled 18982 to 11308 computations (40.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	53
1	25	53
2	26	53
3	24	53

end1.0ms (0%)

Compiler: Compiled 37 to 23 computations (37.8% saved)

sample1.1s (31.1%)

Algorithm

1×

intervals

Results

252.0ms	8000×	pre	128	true
245.0ms	8000×	body	128	valid

Compiler

Compiled 593 to 375 computations (36.8% saved)

Details

analyze205.0ms (5.8%)

sample24.0ms (0.7%)

simplify88.0ms (2.5%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite35.0ms (1%)

series22.0ms (0.6%)

simplify65.0ms (1.8%)

prune11.0ms (0.3%)

localize8.0ms (0.2%)

rewrite23.0ms (0.7%)

series92.0ms (2.6%)

simplify69.0ms (1.9%)

prune27.0ms (0.7%)

localize6.0ms (0.2%)

rewrite43.0ms (1.2%)

series30.0ms (0.9%)

simplify75.0ms (2.1%)

prune32.0ms (0.9%)

localize11.0ms (0.3%)

rewrite152.0ms (4.3%)

series371.0ms (10.4%)

simplify172.0ms (4.8%)

prune134.0ms (3.8%)

regimes741.0ms (20.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (31.1%)

Profiling