Details

analyze1.0s (8.6%)

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%	55.8%	11.8%	9
36.3%	50.9%	12.8%	10
40.7%	41.5%	17.9%	11
42.6%	38.6%	18.8%	12
44.5%	33.5%	22%	13
45.5%	32%	22.5%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample6.7s (55.5%)

Results

2.8s	1751×	body	2048	valid
2.2s	2732×	body	1024	valid
541.0ms	1199×	body	512	valid
322.0ms	1938×	body	128	valid
173.0ms	191×	body	1024	invalid
167.0ms	601×	body	256	valid
140.0ms	246×	body	512	invalid
86.0ms	35×	body	4096	valid
77.0ms	499×	body	128	invalid
63.0ms	157×	body	256	invalid
29.0ms	22×	body	2048	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify44.0ms (0.4%)

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

47.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	47.6b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
	47.6b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))

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 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
✓	2.6b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
✓	7.1b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
✓	8.9b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

series317.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

117.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
110.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
59.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
29.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

rewrite151.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64`
502×	`add-sqr-sqrt_binary64`
391×	`*-un-lft-identity_binary64`
241×	`add-cube-cbrt_binary64`
174×	`associate-r_binary64`

Counts

4 → 494

Calls

4 calls:

38.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
16.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
11.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify404.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-def_binary64`
386×	`times-frac_binary64`
336×	`*-commutative_binary64`
275×	`+-commutative_binary64`
222×	`associate-*r/_binary64`

Counts

590 → 793

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1123	23638
1	3503	23269
2	4974	23269

prune689.0ms (5.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	784	9	793
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	785	10	795

Error

0.2b

Counts

795 → 10

Alt Table

Status	Error	Program
	44.7b	(.f64 100 (/.f64 (expm1.f64 (.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
	56.0b	(.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (.f64 n n))))
▶	20.4b	(.f64 100 (/.f64 (.f64 n (expm1.f64 i)) i))
	30.4b	(-.f64 (+.f64 (.f64 100 n) (+.f64 (.f64 275/6 (/.f64 (pow.f64 i 3) n)) (+.f64 (.f64 50 (.f64 n i)) (+.f64 (.f64 25/6 (.f64 n (pow.f64 i 3))) (+.f64 (.f64 50/3 (.f64 n (pow.f64 i 2))) (.f64 100/3 (/.f64 (pow.f64 i 2) n))))))) (+.f64 (.f64 25 (pow.f64 i 3)) (+.f64 (.f64 50 i) (+.f64 (.f64 50 (pow.f64 i 2)) (*.f64 25 (/.f64 (pow.f64 i 3) (pow.f64 n 2)))))))
	28.3b	(-.f64 (fma.f64 n 100 (.f64 (.f64 n i) 50)) (*.f64 i 50))
	47.6b	(.f64 (sqrt.f64 100) (.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) -1) (/.f64 i n)) 10))
	57.3b	(-.f64 (+.f64 (.f64 50 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 3)) i)) (+.f64 (.f64 100 (/.f64 (.f64 (pow.f64 n 2) (log.f64 i)) i)) (+.f64 (.f64 100 (/.f64 (pow.f64 n 3) (pow.f64 i 2))) (.f64 50 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i))))) (+.f64 (.f64 100 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 3) (log.f64 n))) i)) (.f64 100 (/.f64 (.f64 (pow.f64 n 2) (log.f64 n)) i))))
	47.6b	(/.f64 (*.f64 100 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)) (/.f64 i n))
	47.6b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
	47.6b	(.f64 100 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) i) n))

Compiler

Compiled 31752 to 18088 computations (43% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 n (expm1.f64 i))
✓	0.1b	(.f64 100 (/.f64 (.f64 n (expm1.f64 i)) i))
✓	7.8b	(/.f64 (*.f64 n (expm1.f64 i)) i)

series32.0ms (0.3%)

Counts

3 → 72

Calls

3 calls:

13.0ms	(.f64 100 (/.f64 (.f64 n (expm1.f64 i)) i))
12.0ms	(/.f64 (*.f64 n (expm1.f64 i)) i)
6.0ms	(*.f64 n (expm1.f64 i))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`associate-r_binary64`
10×	`*-un-lft-identity_binary64`

Counts

3 → 72

Calls

3 calls:

5.0ms	(.f64 100 (/.f64 (.f64 n (expm1.f64 i)) i))
4.0ms	(*.f64 n (expm1.f64 i))
3.0ms	(/.f64 (*.f64 n (expm1.f64 i)) i)

simplify113.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

976×	`times-frac_binary64`
431×	`fma-def_binary64`
238×	`associate-/l/_binary64`
199×	`distribute-rgt-in_binary64`
194×	`distribute-lft-in_binary64`

Counts

144 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	1784
1	383	1599
2	1367	1579
3	4720	1579
4	4994	1579
5	4998	1579
6	4988	1579

prune92.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Error

0.1b

Counts

135 → 10

Alt Table

Status	Error	Program
▶	20.3b	(/.f64 (.f64 (expm1.f64 i) (.f64 n 100)) i)
	56.0b	(.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (.f64 n n))))
	44.7b	(.f64 100 (/.f64 (expm1.f64 (.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
	30.4b	(-.f64 (+.f64 (.f64 100 n) (+.f64 (.f64 275/6 (/.f64 (pow.f64 i 3) n)) (+.f64 (.f64 50 (.f64 n i)) (+.f64 (.f64 25/6 (.f64 n (pow.f64 i 3))) (+.f64 (.f64 50/3 (.f64 n (pow.f64 i 2))) (.f64 100/3 (/.f64 (pow.f64 i 2) n))))))) (+.f64 (.f64 25 (pow.f64 i 3)) (+.f64 (.f64 50 i) (+.f64 (.f64 50 (pow.f64 i 2)) (*.f64 25 (/.f64 (pow.f64 i 3) (pow.f64 n 2)))))))
	20.5b	(.f64 (sqrt.f64 100) (.f64 (/.f64 (*.f64 n (expm1.f64 i)) i) 10))
	28.3b	(-.f64 (fma.f64 n 100 (.f64 (.f64 n i) 50)) (*.f64 i 50))
	57.3b	(-.f64 (+.f64 (.f64 50 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 3)) i)) (+.f64 (.f64 100 (/.f64 (.f64 (pow.f64 n 2) (log.f64 i)) i)) (+.f64 (.f64 100 (/.f64 (pow.f64 n 3) (pow.f64 i 2))) (.f64 50 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i))))) (+.f64 (.f64 100 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 3) (log.f64 n))) i)) (.f64 100 (/.f64 (.f64 (pow.f64 n 2) (log.f64 n)) i))))
	47.6b	(/.f64 (*.f64 100 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)) (/.f64 i n))
	47.6b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
	47.6b	(.f64 100 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) i) n))

Compiler

Compiled 2216 to 1099 computations (50.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (expm1.f64 i) (.f64 n 100))
✓	7.7b	(/.f64 (.f64 (expm1.f64 i) (.f64 n 100)) i)

series26.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(/.f64 (.f64 (expm1.f64 i) (.f64 n 100)) i)
9.0ms	(.f64 (expm1.f64 i) (.f64 n 100))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`cbrt-unprod_binary64`
6×	`prod-exp_binary64`

Counts

2 → 45

Calls

2 calls:

5.0ms	(/.f64 (.f64 (expm1.f64 i) (.f64 n 100)) i)
4.0ms	(.f64 (expm1.f64 i) (.f64 n 100))

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

470×	`div-sub_binary64`
442×	`associate-*l/_binary64`
418×	`associate-/r*_binary64`
333×	`associate-*r/_binary64`
296×	`fma-def_binary64`

Counts

93 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	1363
1	319	1157
2	1315	1138
3	4627	1138
4	5821	1138

prune70.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Error

0.1b

Counts

103 → 10

Alt Table

Status	Error	Program
✓	20.3b	(/.f64 (.f64 (expm1.f64 i) (.f64 n 100)) i)
	56.0b	(.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (.f64 n n))))
	44.7b	(.f64 100 (/.f64 (expm1.f64 (.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
	30.4b	(-.f64 (+.f64 (.f64 100 n) (+.f64 (.f64 275/6 (/.f64 (pow.f64 i 3) n)) (+.f64 (.f64 50 (.f64 n i)) (+.f64 (.f64 25/6 (.f64 n (pow.f64 i 3))) (+.f64 (.f64 50/3 (.f64 n (pow.f64 i 2))) (.f64 100/3 (/.f64 (pow.f64 i 2) n))))))) (+.f64 (.f64 25 (pow.f64 i 3)) (+.f64 (.f64 50 i) (+.f64 (.f64 50 (pow.f64 i 2)) (*.f64 25 (/.f64 (pow.f64 i 3) (pow.f64 n 2)))))))
▶	20.5b	(.f64 (sqrt.f64 100) (.f64 (/.f64 (*.f64 n (expm1.f64 i)) i) 10))
	28.3b	(-.f64 (fma.f64 n 100 (.f64 (.f64 n i) 50)) (*.f64 i 50))
	57.3b	(-.f64 (+.f64 (.f64 50 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 3)) i)) (+.f64 (.f64 100 (/.f64 (.f64 (pow.f64 n 2) (log.f64 i)) i)) (+.f64 (.f64 100 (/.f64 (pow.f64 n 3) (pow.f64 i 2))) (.f64 50 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i))))) (+.f64 (.f64 100 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 3) (log.f64 n))) i)) (.f64 100 (/.f64 (.f64 (pow.f64 n 2) (log.f64 n)) i))))
	47.6b	(/.f64 (*.f64 100 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)) (/.f64 i n))
	47.6b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
	47.6b	(.f64 100 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) i) n))

Compiler

Compiled 1780 to 1032 computations (42% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 n (expm1.f64 i))
✓	0.1b	(.f64 (/.f64 (.f64 n (expm1.f64 i)) i) 10)
✓	0.2b	(.f64 (sqrt.f64 100) (.f64 (/.f64 (*.f64 n (expm1.f64 i)) i) 10))
	7.8b	(/.f64 (*.f64 n (expm1.f64 i)) i)

series29.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(.f64 (sqrt.f64 100) (.f64 (/.f64 (*.f64 n (expm1.f64 i)) i) 10))
13.0ms	(.f64 (/.f64 (.f64 n (expm1.f64 i)) i) 10)

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-cbrt-cube_binary64`
25×	`add-exp-log_binary64`
13×	`associate-l_binary64`
12×	`cbrt-unprod_binary64`
12×	`prod-exp_binary64`

Counts

2 → 57

Calls

2 calls:

8.0ms	(.f64 (sqrt.f64 100) (.f64 (/.f64 (*.f64 n (expm1.f64 i)) i) 10))
5.0ms	(.f64 (/.f64 (.f64 n (expm1.f64 i)) i) 10)

simplify56.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

694×	`times-frac_binary64`
654×	`associate-*l/_binary64`
573×	`associate-/l*_binary64`
264×	`fma-def_binary64`
214×	`associate-/r*_binary64`

Counts

105 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1722
1	365	1436
2	1249	1422
3	5422	1422

prune128.0ms (1.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	180	10	190

Error

0.1b

Counts

190 → 10

Alt Table

Status	Error	Program
✓	20.3b	(/.f64 (.f64 (expm1.f64 i) (.f64 n 100)) i)
	56.0b	(.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (.f64 n n))))
	44.7b	(.f64 100 (/.f64 (expm1.f64 (.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
	30.4b	(-.f64 (+.f64 (.f64 100 n) (+.f64 (.f64 275/6 (/.f64 (pow.f64 i 3) n)) (+.f64 (.f64 50 (.f64 n i)) (+.f64 (.f64 25/6 (.f64 n (pow.f64 i 3))) (+.f64 (.f64 50/3 (.f64 n (pow.f64 i 2))) (.f64 100/3 (/.f64 (pow.f64 i 2) n))))))) (+.f64 (.f64 25 (pow.f64 i 3)) (+.f64 (.f64 50 i) (+.f64 (.f64 50 (pow.f64 i 2)) (*.f64 25 (/.f64 (pow.f64 i 3) (pow.f64 n 2)))))))
✓	20.5b	(.f64 (sqrt.f64 100) (.f64 (/.f64 (*.f64 n (expm1.f64 i)) i) 10))
	28.3b	(-.f64 (fma.f64 n 100 (.f64 (.f64 n i) 50)) (*.f64 i 50))
	57.3b	(-.f64 (+.f64 (.f64 50 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 3)) i)) (+.f64 (.f64 100 (/.f64 (.f64 (pow.f64 n 2) (log.f64 i)) i)) (+.f64 (.f64 100 (/.f64 (pow.f64 n 3) (pow.f64 i 2))) (.f64 50 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i))))) (+.f64 (.f64 100 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 3) (log.f64 n))) i)) (.f64 100 (/.f64 (.f64 (pow.f64 n 2) (log.f64 n)) i))))
	47.6b	(/.f64 (*.f64 100 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)) (/.f64 i n))
	47.6b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
	47.6b	(.f64 100 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) i) n))

Compiler

Compiled 3250 to 1751 computations (46.1% saved)

regimes1.5s (12.5%)

Accuracy

Total 11.2b remaining (98.9%)

Threshold costs 0b (0%)

Counts

207 → 5

Compiler

Compiled 16184 to 11369 computations (29.8% saved)

bsearch325.0ms (2.7%)

Steps

Iters	Range		Point
9	1.8020499276394604e-12	0.002412083276118996	0.0023543790910373224
9	4.777910616278625e-166	4.2680398943733136e-161	1.1323542808442225e-164
11	-2.4560703488983795e-279	7.956679807108224e-307	-5.21080278599253e-310
10	-4.9299807929003833e-191	-7.070022185313673e-201	-1.8422714442376505e-192

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	101
1	48	101
2	52	101
3	54	101
4	55	101
5	54	101

end178.0ms (1.5%)

Compiler: Compiled 398 to 265 computations (33.4% saved)

Details

analyze1.0s (8.6%)

sample6.7s (55.5%)

simplify44.0ms (0.4%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series317.0ms (2.6%)

rewrite151.0ms (1.3%)

simplify404.0ms (3.4%)

prune689.0ms (5.8%)

localize6.0ms (0%)

series32.0ms (0.3%)

rewrite15.0ms (0.1%)

simplify113.0ms (0.9%)

prune92.0ms (0.8%)

localize7.0ms (0.1%)

series26.0ms (0.2%)

rewrite11.0ms (0.1%)

simplify67.0ms (0.6%)

prune70.0ms (0.6%)

localize9.0ms (0.1%)

series29.0ms (0.2%)

rewrite17.0ms (0.1%)

simplify56.0ms (0.5%)

prune128.0ms (1.1%)

regimes1.5s (12.5%)

bsearch325.0ms (2.7%)

simplify5.0ms (0%)

end178.0ms (1.5%)

Profiling