Details

analyze197.0ms (7.9%)

Algorithm

1×

Search

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

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample22.0ms (0.9%)

Algorithm

1×

intervals

Results

5.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify82.0ms (3.3%)

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))

rewrite45.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

62.0b

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 → 52

Calls

1 calls:

9.0ms

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

Compiler

Compiled 683 to 156 computations (77.2% saved)

series32.0ms (1.3%)

Error

51.8b

Counts

1 → 10

Calls

1 calls:

20.0ms

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

Compiler

Compiled 304 to 187 computations (38.5% saved)

simplify108.0ms (4.3%)

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	1457	1055
4	4197	1055
5	5103	1055

prune15.0ms (0.6%)

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))
	57.4b	(+.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)

simplify8.0ms (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))
▶	57.4b	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))

Compiler

Compiled 40 to 24 computations (40% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))
0.3b	(/.f64 (-.f64 x lo) hi)
29.8b	(/.f64 (.f64 lo x) (.f64 hi hi))

rewrite81.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

51.8b

Rules

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

Counts

3 → 73

Calls

3 calls:

16.0ms	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))
8.0ms	(/.f64 (.f64 lo x) (.f64 hi hi))
6.0ms	(/.f64 (-.f64 x lo) hi)

Compiler

Compiled 1450 to 276 computations (81% saved)

series108.0ms (4.3%)

Error

51.8b

Counts

3 → 34

Calls

3 calls:

40.0ms	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (/.f64 (-.f64 x lo) hi))
33.0ms	(/.f64 (.f64 lo x) (.f64 hi hi))
25.0ms	(/.f64 (-.f64 x lo) hi)

Compiler

Compiled 1134 to 658 computations (42% saved)

simplify74.0ms (2.9%)

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	5262	1480

prune44.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	56	10	66
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	57	11	68

Error

51.8b

Counts

68 → 11

Alt Table

Status	Error	Program
	57.4b	(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))
	57.4b	(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 x lo) (.f64 hi hi)) 3) (pow.f64 (/.f64 (-.f64 x lo) hi) 3)) (+.f64 (.f64 (/.f64 (.f64 x lo) (pow.f64 hi 4)) (.f64 x lo)) (.f64 (/.f64 (-.f64 x lo) hi) (-.f64 (/.f64 (-.f64 x lo) hi) (/.f64 (.f64 x lo) (.f64 hi hi))))))
	57.4b	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (*.f64 (sqrt.f64 (-.f64 x lo)) (/.f64 (sqrt.f64 (-.f64 x lo)) hi)))
	61.7b	(.f64 x (+.f64 (/.f64 1 hi) (/.f64 lo (.f64 hi hi))))
	57.4b	(.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))))
	57.4b	(+.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)))
	57.4b	(.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))))
	57.4b	(+.f64 (/.f64 (.f64 lo x) (.f64 hi hi)) (cbrt.f64 (pow.f64 (/.f64 (-.f64 x lo) hi) 3)))
▶	52.0b	(*.f64 (/.f64 lo hi) (+.f64 -1 (/.f64 x hi)))
✓	52.0b	(-.f64 1 (/.f64 x lo))

Compiler

Compiled 1171 to 384 computations (67.2% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

rewrite67.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

51.8b

Rules

15×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-l_binary64`
10×	`times-frac_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 51

Calls

2 calls:

13.0ms	(*.f64 (/.f64 lo hi) (+.f64 -1 (/.f64 x hi)))
6.0ms	(+.f64 -1 (/.f64 x hi))

Compiler

Compiled 848 to 371 computations (56.3% saved)

series56.0ms (2.2%)

Error

51.8b

Counts

2 → 21

Calls

2 calls:

37.0ms	(*.f64 (/.f64 lo hi) (+.f64 -1 (/.f64 x hi)))
15.0ms	(+.f64 -1 (/.f64 x hi))

Compiler

Compiled 470 to 301 computations (36% saved)

simplify128.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

507×	`associate-l_binary64`
481×	`times-frac_binary64`
427×	`associate-*l/_binary64`
424×	`associate-r_binary64`
363×	`associate-*r/_binary64`

Counts

72 → 54

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	103	1046
1	345	947
2	931	947
3	4190	947
4	4937	947
5	4997	947
6	4968	947

prune42.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	44	10	54
Fresh	7	2	9
Picked	1	0	1
Done	0	1	1
Total	52	13	65

Error

51.8b

Counts

65 → 13

Alt Table

Status	Error	Program
	52.0b	(+.f64 (/.f64 lo (/.f64 hi (/.f64 x hi))) (/.f64 (-.f64 x lo) hi))
	61.7b	(.f64 x (+.f64 (/.f64 1 hi) (/.f64 lo (.f64 hi hi))))
	52.0b	(.f64 (/.f64 (.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (sqrt.f64 hi)) (*.f64 (-.f64 (/.f64 x hi) 1) (/.f64 (cbrt.f64 lo) (sqrt.f64 hi))))
	52.0b	(.f64 (/.f64 1 (sqrt.f64 hi)) (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo (sqrt.f64 hi))))
	52.0b	(.f64 (/.f64 (.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (.f64 (cbrt.f64 hi) (cbrt.f64 hi))) (.f64 (-.f64 (/.f64 x hi) 1) (/.f64 (cbrt.f64 lo) (cbrt.f64 hi))))
	52.0b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi) 3))
	52.0b	(-.f64 1 (/.f64 x lo))
	52.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 hi) (cbrt.f64 hi))) (*.f64 (-.f64 (/.f64 x hi) 1) (/.f64 lo (cbrt.f64 hi))))
	52.0b	(.f64 (.f64 (cbrt.f64 (/.f64 lo hi)) (cbrt.f64 (/.f64 lo hi))) (*.f64 (-.f64 (/.f64 x hi) 1) (cbrt.f64 (/.f64 lo hi))))
	52.0b	(log.f64 (exp.f64 (/.f64 (*.f64 lo (-.f64 (/.f64 x hi) 1)) hi)))
	52.0b	(*.f64 lo (/.f64 (-.f64 (/.f64 x hi) 1) hi))
	52.0b	(.f64 (/.f64 (.f64 (cbrt.f64 lo) (cbrt.f64 lo)) 1) (*.f64 (-.f64 (/.f64 x hi) 1) (/.f64 (cbrt.f64 lo) hi)))
	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)))

Compiler

Compiled 898 to 435 computations (51.6% saved)

regimes465.0ms (18.5%)

Accuracy

Total 0.2b remaining (0.3%)

Threshold costs 0.2b (0.3%)

Compiler

Compiled 6854 to 3924 computations (42.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
1×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	8	6
2	12	6
3	15	6
4	18	6
5	19	6
6	19	6

end1.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample899.0ms (35.9%)

Algorithm

1×

intervals

Results

193.0ms	8000×	body	128	valid
160.0ms	8000×	pre	128	true

Compiler

Compiled 262 to 163 computations (37.8% saved)

Details

analyze197.0ms (7.9%)

sample22.0ms (0.9%)

simplify82.0ms (3.3%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite45.0ms (1.8%)

series32.0ms (1.3%)

simplify108.0ms (4.3%)

prune15.0ms (0.6%)

localize4.0ms (0.1%)

rewrite1.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize9.0ms (0.4%)

rewrite81.0ms (3.2%)

series108.0ms (4.3%)

simplify74.0ms (2.9%)

prune44.0ms (1.7%)

localize9.0ms (0.4%)

rewrite67.0ms (2.7%)

series56.0ms (2.2%)

simplify128.0ms (5.1%)

prune42.0ms (1.7%)

regimes465.0ms (18.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample899.0ms (35.9%)

Profiling