Details

analyze181.0ms (6.8%)

Algorithm

1×

Search

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

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample26.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	256×	pre	128	true
6.0ms	256×	body	128	valid

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify76.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

530×	`div-sub_binary64`
326×	`times-frac_binary64`
174×	`associate-/l/_binary64`
166×	`sub-neg_binary64`
160×	`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	35	10
4	59	10
5	105	10
6	198	10
7	371	10
8	664	10
9	998	10
10	1100	10
11	1117	10
12	1088	10
13	1095	10
14	1097	10
15	1105	10
16	1105	10
17	1003	10

prune2.0ms (0.1%)

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 (0.2%)

Local error

Found 1 expressions with local error:

62.0b

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

rewrite36.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

62.0b

Rules

37×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
25×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/l_binary64` `associate-/r_binary64`

Counts

1 → 52

Calls

1 calls:

8.0ms

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

Compiler

Compiled 683 to 156 computations (77.2% saved)

series30.0ms (1.1%)

Error

51.8b

Counts

1 → 10

Calls

1 calls:

19.0ms

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

Compiler

Compiled 304 to 187 computations (38.5% saved)

simplify82.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

661×	`unsub-neg_binary64`
431×	`times-frac_binary64`
413×	`associate-/l*_binary64`
381×	`distribute-rgt-in_binary64`
358×	`distribute-lft-in_binary64`

Counts

62 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	1103
1	262	1061
2	600	1055
3	1461	1055
4	4206	1055
5	5117	1055

prune14.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	2	25

Error

51.9b

Counts

25 → 2

Alt Table

Status	Error	Program
▶	52.0b	(-.f64 1 (/.f64 x lo))
	58.0b	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))

Compiler

Compiled 269 to 99 computations (63.2% saved)

localize4.0ms (0.1%)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

51.9b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 51.9b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune2.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

51.9b

Counts

2 → 2

Alt Table

Status	Error	Program
✓	52.0b	(-.f64 1 (/.f64 x lo))
▶	58.0b	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))

Compiler

Compiled 40 to 24 computations (40% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))
0.0b	(/.f64 (-.f64 x lo) hi)
32.0b	(/.f64 (.f64 lo x) (.f64 hi hi))

rewrite68.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

51.8b

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 73

Calls

3 calls:

14.0ms	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))
5.0ms	(/.f64 (-.f64 x lo) hi)
5.0ms	(/.f64 (.f64 lo x) (.f64 hi hi))

Compiler

Compiled 1450 to 276 computations (81% saved)

series110.0ms (4.1%)

Error

51.8b

Counts

3 → 34

Calls

3 calls:

42.0ms	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))
35.0ms	(/.f64 (.f64 lo x) (.f64 hi hi))
23.0ms	(/.f64 (-.f64 x lo) hi)

Compiler

Compiled 1134 to 658 computations (42% saved)

simplify65.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

836×	`associate-/l*_binary64`
590×	`associate-*l/_binary64`
381×	`associate-/r*_binary64`
351×	`distribute-rgt-in_binary64`
319×	`distribute-lft-in_binary64`

Counts

107 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	1545
1	394	1483
2	1335	1480
3	5264	1480

prune37.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	57	9	66
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	58	10	68

Error

51.8b

Counts

68 → 10

Alt Table

Status	Error	Program
	58.0b	(.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 x lo) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))) (sqrt.f64 (+.f64 (/.f64 (.f64 x lo) (*.f64 hi hi)) (/.f64 (-.f64 x lo) hi))))
	58.0b	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (.f64 (.f64 (cbrt.f64 (-.f64 x lo)) (cbrt.f64 (-.f64 x lo))) (/.f64 (cbrt.f64 (-.f64 x lo)) hi)))
	58.0b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 (.f64 x lo) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))) (cbrt.f64 (+.f64 (/.f64 (.f64 x lo) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi)))) (cbrt.f64 (+.f64 (/.f64 (.f64 x lo) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))))
	58.0b	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (cbrt.f64 (pow.f64 (/.f64 (-.f64 x lo) hi) 3)))
	58.0b	(log.f64 (exp.f64 (+.f64 (/.f64 (.f64 x lo) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))))
▶	52.0b	(+.f64 (/.f64 lo (/.f64 hi (/.f64 x hi))) (/.f64 (-.f64 x lo) hi))
	58.0b	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (*.f64 (sqrt.f64 (-.f64 x lo)) (/.f64 (sqrt.f64 (-.f64 x lo)) hi)))
✓	52.0b	(-.f64 1 (/.f64 x lo))
	52.0b	(*.f64 (/.f64 lo hi) (+.f64 -1 (/.f64 x hi)))
	58.0b	(/.f64 (+.f64 (.f64 (/.f64 (.f64 x lo) (pow.f64 hi 4)) (.f64 x lo)) (/.f64 (/.f64 (-.f64 lo x) hi) (/.f64 hi (-.f64 x lo)))) (+.f64 (/.f64 (.f64 x lo) (*.f64 hi hi)) (/.f64 (-.f64 lo x) hi)))

Compiler

Compiled 1119 to 360 computations (67.8% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 lo (/.f64 hi (/.f64 x hi))) (/.f64 (-.f64 x lo) hi))
0.0b	(/.f64 (-.f64 x lo) hi)
30.9b	(/.f64 lo (/.f64 hi (/.f64 x hi)))

rewrite299.0ms (11.1%)

Algorithm

1×	rewrite-expression-head

Error

51.8b

Rules

415×	`times-frac_binary64`
217×	`*-un-lft-identity_binary64`
206×	`add-sqr-sqrt_binary64`
198×	`add-cube-cbrt_binary64`
47×	`associate-/r*_binary64`

Counts

3 → 250

Calls

3 calls:

119.0ms	(+.f64 (/.f64 lo (/.f64 hi (/.f64 x hi))) (/.f64 (-.f64 x lo) hi))
12.0ms	(/.f64 lo (/.f64 hi (/.f64 x hi)))
6.0ms	(/.f64 (-.f64 x lo) hi)

Compiler

Compiled 6265 to 1369 computations (78.1% saved)

series107.0ms (4%)

Error

51.8b

Counts

3 → 34

Calls

3 calls:

42.0ms	(+.f64 (/.f64 lo (/.f64 hi (/.f64 x hi))) (/.f64 (-.f64 x lo) hi))
34.0ms	(/.f64 lo (/.f64 hi (/.f64 x hi)))
24.0ms	(/.f64 (-.f64 x lo) hi)

Compiler

Compiled 1134 to 645 computations (43.1% saved)

simplify269.0ms (10%)

Algorithm

1×	egg-herbie

Rules

576×	`associate-/r/_binary64`
414×	`associate-/l/_binary64`
364×	`associate-*r/_binary64`
342×	`associate-*l/_binary64`
323×	`*-commutative_binary64`

Counts

284 → 225

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	514	6441
1	1156	6094
2	3962	5941
3	4748	5893
4	4991	5893
5	4988	5893

prune84.0ms (3.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	220	5	225
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	225	10	235

Error

51.8b

Counts

235 → 10

Alt Table

Status	Error	Program
	52.0b	(+.f64 (/.f64 lo (/.f64 hi (/.f64 x hi))) (.f64 (-.f64 x lo) (/.f64 1 (.f64 (sqrt.f64 hi) (sqrt.f64 hi)))))
	52.0b	(.f64 lo (-.f64 (/.f64 x (.f64 hi hi)) (/.f64 1 hi)))
	58.0b	(.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 (.f64 x lo) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))) (cbrt.f64 (+.f64 (/.f64 (.f64 x lo) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi)))) (cbrt.f64 (+.f64 (/.f64 (.f64 x lo) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))))
	52.0b	(+.f64 (/.f64 lo (/.f64 hi (/.f64 x hi))) (*.f64 (sqrt.f64 (-.f64 x lo)) (/.f64 (sqrt.f64 (-.f64 x lo)) hi)))
	52.0b	(+.f64 (/.f64 lo (/.f64 hi (/.f64 x hi))) (/.f64 (-.f64 x lo) hi))
	52.0b	(+.f64 (/.f64 lo (/.f64 hi (/.f64 x hi))) (.f64 (.f64 (cbrt.f64 (-.f64 x lo)) (cbrt.f64 (-.f64 x lo))) (/.f64 (cbrt.f64 (-.f64 x lo)) hi)))
	52.0b	(+.f64 (/.f64 lo (/.f64 hi (/.f64 x hi))) (cbrt.f64 (pow.f64 (/.f64 (-.f64 x lo) hi) 3)))
	52.0b	(-.f64 1 (/.f64 x lo))
	52.0b	(*.f64 (/.f64 lo hi) (+.f64 -1 (/.f64 x hi)))
	58.0b	(/.f64 (+.f64 (.f64 (/.f64 (.f64 x lo) (pow.f64 hi 4)) (.f64 x lo)) (/.f64 (/.f64 (-.f64 lo x) hi) (/.f64 hi (-.f64 x lo)))) (+.f64 (/.f64 (.f64 x lo) (*.f64 hi hi)) (/.f64 (-.f64 lo x) hi)))

Compiler

Compiled 3850 to 783 computations (79.7% saved)

regimes337.0ms (12.5%)

Accuracy

Total 0.2b remaining (0.3%)

Threshold costs 0.2b (0.3%)

Compiler

Compiled 5918 to 3088 computations (47.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	18	25
2	26	25
3	30	25
4	32	25
5	32	25

end1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

sample825.0ms (30.7%)

Algorithm

1×

intervals

Results

181.0ms	8000×	body	128	valid
151.0ms	8000×	pre	128	true

Compiler

Compiled 266 to 136 computations (48.9% saved)

Details

analyze181.0ms (6.8%)

sample26.0ms (1%)

simplify76.0ms (2.8%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite36.0ms (1.3%)

series30.0ms (1.1%)

simplify82.0ms (3.1%)

prune14.0ms (0.5%)

localize4.0ms (0.1%)

rewrite1.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.3%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

rewrite68.0ms (2.5%)

series110.0ms (4.1%)

simplify65.0ms (2.4%)

prune37.0ms (1.4%)

localize8.0ms (0.3%)

rewrite299.0ms (11.1%)

series107.0ms (4%)

simplify269.0ms (10%)

prune84.0ms (3.1%)

regimes337.0ms (12.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample825.0ms (30.7%)

Profiling