Details

analyze945.0ms (10.7%)

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
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	35.7%	19.8%	13
45.5%	34.4%	20.1%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample212.0ms (2.4%)

Algorithm

1×

intervals

Results

62.0ms	93×	body	1024	valid
54.0ms	45×	body	2048	valid
14.0ms	41×	body	512	valid
4.0ms	55×	body	128	valid
4.0ms	21×	body	256	valid
3.0ms	8×	body	512	invalid
3.0ms	1×	body	4096	valid
2.0ms	14×	body	128	invalid
1.0ms	1×	body	2048	invalid
1.0ms	1×	body	1024	invalid
0.0ms	9×	body	128	nan
0.0ms	2×	body	256	invalid

Compiler

Compiled 37 to 25 computations (32.4% saved)

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-def_binary64`
563×	`associate-/r/_binary64`
484×	`associate-/r*_binary64`
474×	`associate-*l/_binary64`
421×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	29	22
2	67	20
3	164	20
4	463	20
5	1761	20
6	4847	20
7	5013	20

prune4.0ms (0%)

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

47.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	47.2b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
	47.4b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))

Compiler

Compiled 97 to 63 computations (35.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 i n))
✓	0.0b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
✓	1.2b	(fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)
✓	6.1b	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series232.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

130.0ms	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
62.0ms	(fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)
34.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
4.0ms	(+.f64 1 (/.f64 i n))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
5.0ms	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
4.0ms	(+.f64 1 (/.f64 i n))
0.0ms	(fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)

simplify131.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary64`
431×	`associate-/l*_binary64`
333×	`times-frac_binary64`
260×	`*-commutative_binary64`
214×	`+-commutative_binary64`

Counts

177 → 211

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	771	7696
1	2467	7382
2	5194	7382

prune232.0ms (2.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	198	13	211
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	199	14	213

Error

3.7b

Counts

213 → 14

Alt Table

Status	Error	Program
	42.8b	(.f64 n (/.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) i))
	47.3b	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (*.f64 (cbrt.f64 n) (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i)))
	55.2b	(.f64 n (/.f64 (.f64 n (*.f64 100 (-.f64 (log.f64 i) (log.f64 n)))) i))
	47.2b	(/.f64 (*.f64 n (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)) i)
	34.6b	(-.f64 (fma.f64 n 100 (fma.f64 (/.f64 (pow.f64 i 3) n) 275/6 (fma.f64 50 (.f64 i n) (fma.f64 25/6 (.f64 n (pow.f64 i 3)) (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50/3 (.f64 (.f64 i i) n))))))) (fma.f64 (pow.f64 i 3) 25 (fma.f64 50 (+.f64 i (.f64 i i)) (.f64 (/.f64 (pow.f64 i 3) (*.f64 n n)) 25))))
	32.0b	(fma.f64 n 100 (.f64 i (-.f64 (.f64 50 n) 50)))
✓	47.2b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
▶	31.4b	(*.f64 100 n)
	43.0b	(/.f64 (fma.f64 (exp.f64 i) 100 -100) (/.f64 i n))
	42.8b	(/.f64 (.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) n) i)
	55.9b	(.f64 (/.f64 (.f64 n n) i) (*.f64 100 (-.f64 (log.f64 i) (log.f64 n))))
	55.8b	(/.f64 (.f64 (pow.f64 n 2) (-.f64 (.f64 100 (log.f64 i)) (*.f64 100 (log.f64 n)))) i)
	55.2b	(.f64 n (/.f64 (.f64 n (-.f64 (.f64 100 (log.f64 i)) (.f64 100 (log.f64 n)))) i))
	56.9b	(-.f64 (+.f64 (.f64 100 (/.f64 (.f64 (pow.f64 n 3) (exp.f64 (.f64 (-.f64 (log.f64 (neg.f64 (/.f64 1 n))) (log.f64 (/.f64 -1 i))) n))) (pow.f64 i 2))) (.f64 100 (/.f64 (.f64 n (exp.f64 (.f64 (-.f64 (log.f64 (neg.f64 (/.f64 1 n))) (log.f64 (/.f64 -1 i))) n))) i))) (*.f64 100 (/.f64 n i)))

Compiler

Compiled 10400 to 6429 computations (38.2% saved)

localize2.0ms (0%)

prune15.0ms (0.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	12	12
Picked	1	1
Done	1	1
Total	14	14

Error

3.7b

Counts

14 → 14

Alt Table

Status	Error	Program
	42.8b	(.f64 n (/.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) i))
	47.3b	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (*.f64 (cbrt.f64 n) (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i)))
	55.2b	(.f64 n (/.f64 (.f64 n (*.f64 100 (-.f64 (log.f64 i) (log.f64 n)))) i))
	47.2b	(/.f64 (*.f64 n (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)) i)
	34.6b	(-.f64 (fma.f64 n 100 (fma.f64 (/.f64 (pow.f64 i 3) n) 275/6 (fma.f64 50 (.f64 i n) (fma.f64 25/6 (.f64 n (pow.f64 i 3)) (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50/3 (.f64 (.f64 i i) n))))))) (fma.f64 (pow.f64 i 3) 25 (fma.f64 50 (+.f64 i (.f64 i i)) (.f64 (/.f64 (pow.f64 i 3) (*.f64 n n)) 25))))
▶	32.0b	(fma.f64 n 100 (.f64 i (-.f64 (.f64 50 n) 50)))
✓	47.2b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
✓	31.4b	(*.f64 100 n)
	43.0b	(/.f64 (fma.f64 (exp.f64 i) 100 -100) (/.f64 i n))
	42.8b	(/.f64 (.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) n) i)
	55.9b	(.f64 (/.f64 (.f64 n n) i) (*.f64 100 (-.f64 (log.f64 i) (log.f64 n))))
	55.8b	(/.f64 (.f64 (pow.f64 n 2) (-.f64 (.f64 100 (log.f64 i)) (*.f64 100 (log.f64 n)))) i)
	55.2b	(.f64 n (/.f64 (.f64 n (-.f64 (.f64 100 (log.f64 i)) (.f64 100 (log.f64 n)))) i))
	56.9b	(-.f64 (+.f64 (.f64 100 (/.f64 (.f64 (pow.f64 n 3) (exp.f64 (.f64 (-.f64 (log.f64 (neg.f64 (/.f64 1 n))) (log.f64 (/.f64 -1 i))) n))) (pow.f64 i 2))) (.f64 100 (/.f64 (.f64 n (exp.f64 (.f64 (-.f64 (log.f64 (neg.f64 (/.f64 1 n))) (log.f64 (/.f64 -1 i))) n))) i))) (*.f64 100 (/.f64 n i)))

Compiler

Compiled 543 to 379 computations (30.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 n 100 (.f64 i (-.f64 (.f64 50 n) 50)))
✓	0.1b	(.f64 i (-.f64 (.f64 50 n) 50))

series14.0ms (0.2%)

Counts

2 → 36

Calls

2 calls:

8.0ms	(.f64 i (-.f64 (.f64 50 n) 50))
6.0ms	(fma.f64 n 100 (.f64 i (-.f64 (.f64 50 n) 50)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`distribute-lft-in_binary64`
7×	`distribute-rgt-in_binary64`

Counts

2 → 46

Calls

2 calls:

6.0ms	(.f64 i (-.f64 (.f64 50 n) 50))
0.0ms	(fma.f64 n 100 (.f64 i (-.f64 (.f64 50 n) 50)))

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-def_binary64`
373×	`distribute-neg-out_binary64`
350×	`*-commutative_binary64`
309×	`associate-l_binary64`
293×	`unsub-neg_binary64`

Counts

82 → 82

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	115	1066
1	204	871
2	551	871
3	1465	871
4	2762	871
5	4971	871
6	4908	871

prune71.0ms (0.8%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	81	15	96

Error

3.7b

Counts

96 → 15

Alt Table

Status	Error	Program
	42.8b	(.f64 n (/.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) i))
	47.3b	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (*.f64 (cbrt.f64 n) (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i)))
	55.2b	(.f64 n (/.f64 (.f64 n (*.f64 100 (-.f64 (log.f64 i) (log.f64 n)))) i))
	49.8b	(fma.f64 n 100 (exp.f64 (log.f64 (*.f64 i (fma.f64 50 n -50)))))
	47.2b	(/.f64 (*.f64 n (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)) i)
▶	34.6b	(-.f64 (fma.f64 n 100 (fma.f64 (/.f64 (pow.f64 i 3) n) 275/6 (fma.f64 50 (.f64 i n) (fma.f64 25/6 (.f64 n (pow.f64 i 3)) (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50/3 (.f64 (.f64 i i) n))))))) (fma.f64 (pow.f64 i 3) 25 (fma.f64 50 (+.f64 i (.f64 i i)) (.f64 (/.f64 (pow.f64 i 3) (*.f64 n n)) 25))))
✓	32.0b	(fma.f64 n 100 (.f64 i (-.f64 (.f64 50 n) 50)))
✓	47.2b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
✓	31.4b	(*.f64 100 n)
	43.0b	(/.f64 (fma.f64 (exp.f64 i) 100 -100) (/.f64 i n))
	42.8b	(/.f64 (.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) n) i)
	55.9b	(.f64 (/.f64 (.f64 n n) i) (*.f64 100 (-.f64 (log.f64 i) (log.f64 n))))
	55.8b	(/.f64 (.f64 (pow.f64 n 2) (-.f64 (.f64 100 (log.f64 i)) (*.f64 100 (log.f64 n)))) i)
	55.2b	(.f64 n (/.f64 (.f64 n (-.f64 (.f64 100 (log.f64 i)) (.f64 100 (log.f64 n)))) i))
	56.9b	(-.f64 (+.f64 (.f64 100 (/.f64 (.f64 (pow.f64 n 3) (exp.f64 (.f64 (-.f64 (log.f64 (neg.f64 (/.f64 1 n))) (log.f64 (/.f64 -1 i))) n))) (pow.f64 i 2))) (.f64 100 (/.f64 (.f64 n (exp.f64 (.f64 (-.f64 (log.f64 (neg.f64 (/.f64 1 n))) (log.f64 (/.f64 -1 i))) n))) i))) (*.f64 100 (/.f64 n i)))

Compiler

Compiled 1886 to 1379 computations (26.9% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.8b	(.f64 (.f64 i i) n)
✓	7.7b	(/.f64 (*.f64 i i) n)
✓	9.8b	(fma.f64 25/6 (.f64 n (pow.f64 i 3)) (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50/3 (.f64 (*.f64 i i) n))))
✓	15.3b	(/.f64 (pow.f64 i 3) (*.f64 n n))

series83.0ms (0.9%)

Counts

4 → 96

Calls

4 calls:

35.0ms	(/.f64 (pow.f64 i 3) (*.f64 n n))
28.0ms	(fma.f64 25/6 (.f64 n (pow.f64 i 3)) (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50/3 (.f64 (*.f64 i i) n))))
11.0ms	(/.f64 (*.f64 i i) n)
8.0ms	(.f64 (.f64 i i) n)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64`
19×	`add-cbrt-cube_binary64`
15×	`times-frac_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`associate-/l*_binary64`

Counts

4 → 99

Calls

4 calls:

5.0ms	(/.f64 (*.f64 i i) n)
5.0ms	(/.f64 (pow.f64 i 3) (*.f64 n n))
4.0ms	(.f64 (.f64 i i) n)
0.0ms	(fma.f64 25/6 (.f64 n (pow.f64 i 3)) (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50/3 (.f64 (*.f64 i i) n))))

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/r/_binary64`
581×	`associate-/l/_binary64`
490×	`unswap-sqr_binary64`
201×	`associate-l_binary64`
174×	`associate-r_binary64`

Counts

195 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	2669
1	330	2436
2	1660	2276
3	5047	2276

prune181.0ms (2%)

Pruning

15 alts after pruning (11 fresh and 4 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	11	11
Picked	0	1	1
Done	0	3	3
Total	138	15	153

Error

3.7b

Counts

153 → 15

Alt Table

Status	Error	Program
	42.8b	(.f64 n (/.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) i))
	47.3b	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (*.f64 (cbrt.f64 n) (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i)))
	55.2b	(.f64 n (/.f64 (.f64 n (*.f64 100 (-.f64 (log.f64 i) (log.f64 n)))) i))
	49.8b	(fma.f64 n 100 (exp.f64 (log.f64 (*.f64 i (fma.f64 50 n -50)))))
	47.2b	(/.f64 (*.f64 n (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)) i)
✓	34.6b	(-.f64 (fma.f64 n 100 (fma.f64 (/.f64 (pow.f64 i 3) n) 275/6 (fma.f64 50 (.f64 i n) (fma.f64 25/6 (.f64 n (pow.f64 i 3)) (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50/3 (.f64 (.f64 i i) n))))))) (fma.f64 (pow.f64 i 3) 25 (fma.f64 50 (+.f64 i (.f64 i i)) (.f64 (/.f64 (pow.f64 i 3) (*.f64 n n)) 25))))
✓	32.0b	(fma.f64 n 100 (.f64 i (-.f64 (.f64 50 n) 50)))
✓	47.2b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
✓	31.4b	(*.f64 100 n)
	43.0b	(/.f64 (fma.f64 (exp.f64 i) 100 -100) (/.f64 i n))
	42.8b	(/.f64 (.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) n) i)
	55.9b	(.f64 (/.f64 (.f64 n n) i) (*.f64 100 (-.f64 (log.f64 i) (log.f64 n))))
	55.8b	(/.f64 (.f64 (pow.f64 n 2) (-.f64 (.f64 100 (log.f64 i)) (*.f64 100 (log.f64 n)))) i)
	55.2b	(.f64 n (/.f64 (.f64 n (-.f64 (.f64 100 (log.f64 i)) (.f64 100 (log.f64 n)))) i))
	56.9b	(-.f64 (+.f64 (.f64 100 (/.f64 (.f64 (pow.f64 n 3) (exp.f64 (.f64 (-.f64 (log.f64 (neg.f64 (/.f64 1 n))) (log.f64 (/.f64 -1 i))) n))) (pow.f64 i 2))) (.f64 100 (/.f64 (.f64 n (exp.f64 (.f64 (-.f64 (log.f64 (neg.f64 (/.f64 1 n))) (log.f64 (/.f64 -1 i))) n))) i))) (*.f64 100 (/.f64 n i)))

Compiler

Compiled 8913 to 4793 computations (46.2% saved)

regimes671.0ms (7.6%)

Accuracy

Total 8.8b remaining (74.5%)

Threshold costs 0b (0%)

Counts

67 → 3

Compiler

Compiled 8176 to 5712 computations (30.1% saved)

bsearch129.0ms (1.5%)

Steps

Iters	Range		Point
6	1.058389826657086e-6	8.904937312693545e-6	8.722702919778021e-6
10	-182447.8088561704	-1.0810450025815593e-5	-0.0001322261859959142

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	91
1	59	91
2	73	91
3	85	91
4	99	91
5	105	91
6	107	91
7	105	91

end1.0ms (0%)

Compiler: Compiled 64 to 41 computations (35.9% saved)

sample5.7s (63.8%)

Algorithm

1×

intervals

Results

2.4s	1748×	body	2048	valid
1.7s	2562×	body	1024	valid
360.0ms	1181×	body	512	valid
149.0ms	1916×	body	128	valid
120.0ms	170×	body	1024	invalid
107.0ms	249×	body	512	invalid
94.0ms	560×	body	256	valid
71.0ms	33×	body	4096	valid
55.0ms	455×	body	128	invalid
32.0ms	120×	body	256	invalid
20.0ms	309×	body	128	nan
13.0ms	13×	body	2048	invalid

Compiler

Compiled 379 to 262 computations (30.9% saved)

Details

analyze945.0ms (10.7%)

sample212.0ms (2.4%)

simplify43.0ms (0.5%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series232.0ms (2.6%)

rewrite20.0ms (0.2%)

simplify131.0ms (1.5%)

prune232.0ms (2.6%)

localize2.0ms (0%)

prune15.0ms (0.2%)

localize6.0ms (0.1%)

series14.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify78.0ms (0.9%)

prune71.0ms (0.8%)

localize28.0ms (0.3%)

series83.0ms (0.9%)

rewrite18.0ms (0.2%)

simplify68.0ms (0.8%)

prune181.0ms (2%)

regimes671.0ms (7.6%)

bsearch129.0ms (1.5%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample5.7s (63.8%)

Profiling