Details

analyze2.2s (12.4%)

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
0%	99.9%	0.1%	6
1.6%	95.2%	3.2%	7
1.6%	94.4%	4%	8
3.5%	85.9%	10.6%	9
3.5%	84.9%	11.6%	10
4.8%	79.4%	15.8%	11
5.3%	78.2%	16.4%	12
6%	74.9%	19.1%	13
6.1%	74.5%	19.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample8.4s (48.1%)

Results

2.9s	1816×	body	2048	valid
2.2s	2671×	body	1024	valid
1.9s	775×	body	8192	exit
567.0ms	1239×	body	512	valid
292.0ms	1913×	body	128	valid
158.0ms	583×	body	256	valid
82.0ms	34×	body	4096	valid
78.0ms	90×	body	1024	invalid
66.0ms	107×	body	512	invalid
64.0ms	430×	body	128	invalid
25.0ms	73×	body	256	invalid
12.0ms	10×	body	2048	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify44.0ms (0.3%)

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

46.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	47.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
	47.0b	(*.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)

localize8.0ms (0%)

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)))
✓	2.0b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
✓	7.7b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
✓	9.9b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

series316.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

122.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
100.0ms	(/.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)
35.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

rewrite150.0ms (0.9%)

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:

39.0ms	(*.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))
9.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify397.0ms (2.3%)

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

prune701.0ms (4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	782	11	793
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	783	12	795

Error

0.1b

Counts

795 → 12

Alt Table

Status	Error	Program
	28.3b	(-.f64 (fma.f64 (.f64 n (.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (.f64 n i) 50 (.f64 (/.f64 (.f64 i i) n) 100/3)))) (.f64 50 (+.f64 i (*.f64 i i))))
	28.3b	(.f64 100 (-.f64 (fma.f64 1/6 (.f64 n (.f64 i i)) (+.f64 n (fma.f64 1/2 (.f64 n i) (.f64 1/3 (/.f64 (.f64 i i) n))))) (.f64 1/2 (+.f64 i (.f64 i i)))))
	57.7b	(.f64 100 (/.f64 (-.f64 (fma.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 n) 2)) (fma.f64 n (log.f64 i) (fma.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 i) 2)) (/.f64 (.f64 n n) i)))) (fma.f64 n (log.f64 n) (.f64 (.f64 n n) (*.f64 (log.f64 i) (log.f64 n))))) (/.f64 i n)))
	58.7b	(.f64 100 (-.f64 (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 2)) (.f64 i i)) (fma.f64 1/3 (/.f64 (pow.f64 n 5) (pow.f64 i 4)) (fma.f64 1/2 (/.f64 (pow.f64 n 5) (pow.f64 i 3)) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 i) 3)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 i) 2)) i) (+.f64 (/.f64 (.f64 (.f64 n n) (log.f64 i)) i) (+.f64 (/.f64 (pow.f64 n 3) (.f64 i i)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 4)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 4) (.f64 (log.f64 i) (pow.f64 (log.f64 n) 2))) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 4)) i) (+.f64 (/.f64 (.f64 (pow.f64 n 4) (log.f64 i)) (.f64 i i)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 2)) (.f64 i i)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (log.f64 n)) (pow.f64 i 3)) (.f64 1/4 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 2))) i)))))))))))))))) (+.f64 (/.f64 (.f64 (pow.f64 n 4) (log.f64 n)) (.f64 i i)) (fma.f64 1/6 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 3))) i) (fma.f64 1/2 (/.f64 (pow.f64 n 4) (pow.f64 i 3)) (+.f64 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 3) (log.f64 n))) i) (+.f64 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 5) (log.f64 n))) (.f64 i i)) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 i) 3) (.f64 (pow.f64 n 5) (log.f64 n))) i) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 n) 3)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 4) (.f64 (log.f64 n) (pow.f64 (log.f64 i) 2))) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (log.f64 i)) (pow.f64 i 3)) (/.f64 (.f64 (.f64 n n) (log.f64 n)) i))))))))))))
	44.0b	(.f64 100 (/.f64 (expm1.f64 (.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
	47.0b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
	33.3b	(.f64 100 (/.f64 (-.f64 (expm1.f64 i) (.f64 1/2 (/.f64 (.f64 (.f64 i i) (exp.f64 i)) n))) (/.f64 i n)))
	47.0b	(.f64 100 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) i) n))
▶	19.5b	(.f64 100 (/.f64 (.f64 n (expm1.f64 i)) i))
	55.6b	(.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (.f64 n n))))
	58.2b	(.f64 100 (/.f64 (.f64 (pow.f64 n 2) (-.f64 (log.f64 i) (log.f64 n))) i))
	50.0b	(.f64 100 (/.f64 (expm1.f64 (.f64 n (-.f64 (log.f64 (/.f64 -1 n)) (log.f64 (/.f64 -1 i))))) (/.f64 i n)))

Compiler

Compiled 32322 to 18390 computations (43.1% saved)

localize5.0ms (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))
✓	7.2b	(/.f64 (*.f64 n (expm1.f64 i)) i)

series32.0ms (0.2%)

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)
7.0ms	(*.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))
3.0ms	(/.f64 (*.f64 n (expm1.f64 i)) i)
3.0ms	(*.f64 n (expm1.f64 i))

simplify106.0ms (0.6%)

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

prune125.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	124	13	137

Error

0.0b

Counts

137 → 13

Alt Table

Status	Error	Program
▶	19.3b	(/.f64 -100 (/.f64 i (neg.f64 (*.f64 n (expm1.f64 i)))))
	33.3b	(.f64 100 (/.f64 (-.f64 (expm1.f64 i) (.f64 1/2 (/.f64 (.f64 (.f64 i i) (exp.f64 i)) n))) (/.f64 i n)))
	28.3b	(-.f64 (fma.f64 (.f64 n (.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (.f64 n i) 50 (.f64 (/.f64 (.f64 i i) n) 100/3)))) (.f64 50 (+.f64 i (*.f64 i i))))
	28.3b	(.f64 100 (-.f64 (fma.f64 1/6 (.f64 n (.f64 i i)) (+.f64 n (fma.f64 1/2 (.f64 n i) (.f64 1/3 (/.f64 (.f64 i i) n))))) (.f64 1/2 (+.f64 i (.f64 i i)))))
	57.7b	(.f64 100 (/.f64 (-.f64 (fma.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 n) 2)) (fma.f64 n (log.f64 i) (fma.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 i) 2)) (/.f64 (.f64 n n) i)))) (fma.f64 n (log.f64 n) (.f64 (.f64 n n) (*.f64 (log.f64 i) (log.f64 n))))) (/.f64 i n)))
	58.7b	(.f64 100 (-.f64 (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 2)) (.f64 i i)) (fma.f64 1/3 (/.f64 (pow.f64 n 5) (pow.f64 i 4)) (fma.f64 1/2 (/.f64 (pow.f64 n 5) (pow.f64 i 3)) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 i) 3)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 i) 2)) i) (+.f64 (/.f64 (.f64 (.f64 n n) (log.f64 i)) i) (+.f64 (/.f64 (pow.f64 n 3) (.f64 i i)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 4)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 4) (.f64 (log.f64 i) (pow.f64 (log.f64 n) 2))) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 4)) i) (+.f64 (/.f64 (.f64 (pow.f64 n 4) (log.f64 i)) (.f64 i i)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 2)) (.f64 i i)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (log.f64 n)) (pow.f64 i 3)) (.f64 1/4 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 2))) i)))))))))))))))) (+.f64 (/.f64 (.f64 (pow.f64 n 4) (log.f64 n)) (.f64 i i)) (fma.f64 1/6 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 3))) i) (fma.f64 1/2 (/.f64 (pow.f64 n 4) (pow.f64 i 3)) (+.f64 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 3) (log.f64 n))) i) (+.f64 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 5) (log.f64 n))) (.f64 i i)) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 i) 3) (.f64 (pow.f64 n 5) (log.f64 n))) i) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 n) 3)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 4) (.f64 (log.f64 n) (pow.f64 (log.f64 i) 2))) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (log.f64 i)) (pow.f64 i 3)) (/.f64 (.f64 (.f64 n n) (log.f64 n)) i))))))))))))
	44.0b	(.f64 100 (/.f64 (expm1.f64 (.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
	47.0b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
	47.0b	(.f64 100 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) i) n))
	35.5b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 n (expm1.f64 i)) i) 100) 3))
	55.6b	(.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (.f64 n n))))
	58.2b	(.f64 100 (/.f64 (.f64 (pow.f64 n 2) (-.f64 (log.f64 i) (log.f64 n))) i))
	50.0b	(.f64 100 (/.f64 (expm1.f64 (.f64 n (-.f64 (log.f64 (/.f64 -1 n)) (log.f64 (/.f64 -1 i))))) (/.f64 i n)))

Compiler

Compiled 2828 to 1431 computations (49.4% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 n (expm1.f64 i))
✓	0.4b	(/.f64 -100 (/.f64 i (neg.f64 (*.f64 n (expm1.f64 i)))))
✓	7.2b	(/.f64 i (neg.f64 (*.f64 n (expm1.f64 i))))

series39.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(/.f64 i (neg.f64 (*.f64 n (expm1.f64 i))))
13.0ms	(/.f64 -100 (/.f64 i (neg.f64 (*.f64 n (expm1.f64 i)))))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
76×	`*-un-lft-identity_binary64`
76×	`add-sqr-sqrt_binary64`
76×	`add-cube-cbrt_binary64`
28×	`associate-/r*_binary64`

Counts

2 → 149

Calls

2 calls:

6.0ms	(/.f64 -100 (/.f64 i (neg.f64 (*.f64 n (expm1.f64 i)))))
3.0ms	(/.f64 i (neg.f64 (*.f64 n (expm1.f64 i))))

simplify105.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

441×	`distribute-rgt-in_binary64`
430×	`distribute-lft-in_binary64`
259×	`associate-/r/_binary64`
204×	`fma-def_binary64`
162×	`*-commutative_binary64`

Counts

197 → 288

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	4283
1	659	3934
2	2260	3923
3	4932	3923

prune213.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	319	0	319
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	319	13	332

Error

0.0b

Counts

332 → 13

Alt Table

Status	Error	Program
✓	19.3b	(/.f64 -100 (/.f64 i (neg.f64 (*.f64 n (expm1.f64 i)))))
	33.3b	(.f64 100 (/.f64 (-.f64 (expm1.f64 i) (.f64 1/2 (/.f64 (.f64 (.f64 i i) (exp.f64 i)) n))) (/.f64 i n)))
▶	28.3b	(-.f64 (fma.f64 (.f64 n (.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (.f64 n i) 50 (.f64 (/.f64 (.f64 i i) n) 100/3)))) (.f64 50 (+.f64 i (*.f64 i i))))
	28.3b	(.f64 100 (-.f64 (fma.f64 1/6 (.f64 n (.f64 i i)) (+.f64 n (fma.f64 1/2 (.f64 n i) (.f64 1/3 (/.f64 (.f64 i i) n))))) (.f64 1/2 (+.f64 i (.f64 i i)))))
	57.7b	(.f64 100 (/.f64 (-.f64 (fma.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 n) 2)) (fma.f64 n (log.f64 i) (fma.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 i) 2)) (/.f64 (.f64 n n) i)))) (fma.f64 n (log.f64 n) (.f64 (.f64 n n) (*.f64 (log.f64 i) (log.f64 n))))) (/.f64 i n)))
	58.7b	(.f64 100 (-.f64 (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 2)) (.f64 i i)) (fma.f64 1/3 (/.f64 (pow.f64 n 5) (pow.f64 i 4)) (fma.f64 1/2 (/.f64 (pow.f64 n 5) (pow.f64 i 3)) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 i) 3)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 i) 2)) i) (+.f64 (/.f64 (.f64 (.f64 n n) (log.f64 i)) i) (+.f64 (/.f64 (pow.f64 n 3) (.f64 i i)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 4)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 4) (.f64 (log.f64 i) (pow.f64 (log.f64 n) 2))) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 4)) i) (+.f64 (/.f64 (.f64 (pow.f64 n 4) (log.f64 i)) (.f64 i i)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 2)) (.f64 i i)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (log.f64 n)) (pow.f64 i 3)) (.f64 1/4 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 2))) i)))))))))))))))) (+.f64 (/.f64 (.f64 (pow.f64 n 4) (log.f64 n)) (.f64 i i)) (fma.f64 1/6 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 3))) i) (fma.f64 1/2 (/.f64 (pow.f64 n 4) (pow.f64 i 3)) (+.f64 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 3) (log.f64 n))) i) (+.f64 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 5) (log.f64 n))) (.f64 i i)) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 i) 3) (.f64 (pow.f64 n 5) (log.f64 n))) i) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 n) 3)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 4) (.f64 (log.f64 n) (pow.f64 (log.f64 i) 2))) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (log.f64 i)) (pow.f64 i 3)) (/.f64 (.f64 (.f64 n n) (log.f64 n)) i))))))))))))
	44.0b	(.f64 100 (/.f64 (expm1.f64 (.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
	47.0b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
	47.0b	(.f64 100 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) i) n))
	35.5b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 n (expm1.f64 i)) i) 100) 3))
	55.6b	(.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (.f64 n n))))
	58.2b	(.f64 100 (/.f64 (.f64 (pow.f64 n 2) (-.f64 (log.f64 i) (log.f64 n))) i))
	50.0b	(.f64 100 (/.f64 (expm1.f64 (.f64 n (-.f64 (log.f64 (/.f64 -1 n)) (log.f64 (/.f64 -1 i))))) (/.f64 i n)))

Compiler

Compiled 6854 to 2869 computations (58.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.3b	(-.f64 (fma.f64 (.f64 n (.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (.f64 n i) 50 (.f64 (/.f64 (.f64 i i) n) 100/3)))) (.f64 50 (+.f64 i (*.f64 i i))))
✓	4.0b	(fma.f64 (.f64 n (.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (.f64 n i) 50 (.f64 (/.f64 (*.f64 i i) n) 100/3))))
✓	8.0b	(.f64 n (.f64 i i))
✓	8.1b	(/.f64 (*.f64 i i) n)

series61.0ms (0.4%)

Counts

4 → 96

Calls

4 calls:

22.0ms	(-.f64 (fma.f64 (.f64 n (.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (.f64 n i) 50 (.f64 (/.f64 (.f64 i i) n) 100/3)))) (.f64 50 (+.f64 i (*.f64 i i))))
21.0ms	(fma.f64 (.f64 n (.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (.f64 n i) 50 (.f64 (/.f64 (*.f64 i i) n) 100/3))))
10.0ms	(/.f64 (*.f64 i i) n)
8.0ms	(.f64 n (.f64 i i))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 77

Calls

4 calls:

4.0ms	(.f64 n (.f64 i i))
3.0ms	(/.f64 (*.f64 i i) n)
3.0ms	(-.f64 (fma.f64 (.f64 n (.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (.f64 n i) 50 (.f64 (/.f64 (.f64 i i) n) 100/3)))) (.f64 50 (+.f64 i (*.f64 i i))))
0.0ms	(fma.f64 (.f64 n (.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (.f64 n i) 50 (.f64 (/.f64 (*.f64 i i) n) 100/3))))

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

702×	`distribute-rgt-in_binary64`
688×	`distribute-lft-in_binary64`
686×	`fma-def_binary64`
164×	`times-frac_binary64`
125×	`cancel-sign-sub-inv_binary64`

Counts

173 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	3789
1	388	3343
2	1356	2962
3	5165	2962

prune142.0ms (0.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	147	13	160

Error

0.0b

Counts

160 → 13

Alt Table

Status	Error	Program
✓	19.3b	(/.f64 -100 (/.f64 i (neg.f64 (*.f64 n (expm1.f64 i)))))
	33.3b	(.f64 100 (/.f64 (-.f64 (expm1.f64 i) (.f64 1/2 (/.f64 (.f64 (.f64 i i) (exp.f64 i)) n))) (/.f64 i n)))
✓	28.3b	(-.f64 (fma.f64 (.f64 n (.f64 i i)) 50/3 (fma.f64 n 100 (fma.f64 (.f64 n i) 50 (.f64 (/.f64 (.f64 i i) n) 100/3)))) (.f64 50 (+.f64 i (*.f64 i i))))
	28.3b	(.f64 100 (-.f64 (fma.f64 1/6 (.f64 n (.f64 i i)) (+.f64 n (fma.f64 1/2 (.f64 n i) (.f64 1/3 (/.f64 (.f64 i i) n))))) (.f64 1/2 (+.f64 i (.f64 i i)))))
	57.7b	(.f64 100 (/.f64 (-.f64 (fma.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 n) 2)) (fma.f64 n (log.f64 i) (fma.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 i) 2)) (/.f64 (.f64 n n) i)))) (fma.f64 n (log.f64 n) (.f64 (.f64 n n) (*.f64 (log.f64 i) (log.f64 n))))) (/.f64 i n)))
	58.7b	(.f64 100 (-.f64 (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 2)) (.f64 i i)) (fma.f64 1/3 (/.f64 (pow.f64 n 5) (pow.f64 i 4)) (fma.f64 1/2 (/.f64 (pow.f64 n 5) (pow.f64 i 3)) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 i) 3)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 i) 2)) i) (+.f64 (/.f64 (.f64 (.f64 n n) (log.f64 i)) i) (+.f64 (/.f64 (pow.f64 n 3) (.f64 i i)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 4)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 4) (.f64 (log.f64 i) (pow.f64 (log.f64 n) 2))) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 4)) i) (+.f64 (/.f64 (.f64 (pow.f64 n 4) (log.f64 i)) (.f64 i i)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 2)) (.f64 i i)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (log.f64 n)) (pow.f64 i 3)) (.f64 1/4 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 2))) i)))))))))))))))) (+.f64 (/.f64 (.f64 (pow.f64 n 4) (log.f64 n)) (.f64 i i)) (fma.f64 1/6 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 5) (pow.f64 (log.f64 n) 3))) i) (fma.f64 1/2 (/.f64 (pow.f64 n 4) (pow.f64 i 3)) (+.f64 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 3) (log.f64 n))) i) (+.f64 (/.f64 (.f64 (log.f64 i) (.f64 (pow.f64 n 5) (log.f64 n))) (.f64 i i)) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 i) 3) (.f64 (pow.f64 n 5) (log.f64 n))) i) (fma.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 n) 3)) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 4) (.f64 (log.f64 n) (pow.f64 (log.f64 i) 2))) i) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 n 5) (log.f64 i)) (pow.f64 i 3)) (/.f64 (.f64 (.f64 n n) (log.f64 n)) i))))))))))))
	44.0b	(.f64 100 (/.f64 (expm1.f64 (.f64 (log.f64 (+.f64 1 (/.f64 i n))) n)) (/.f64 i n)))
	47.0b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
	47.0b	(.f64 100 (.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) i) n))
	35.5b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 n (expm1.f64 i)) i) 100) 3))
	55.6b	(.f64 100 (/.f64 (log.f64 (/.f64 i n)) (/.f64 i (.f64 n n))))
	58.2b	(.f64 100 (/.f64 (.f64 (pow.f64 n 2) (-.f64 (log.f64 i) (log.f64 n))) i))
	50.0b	(.f64 100 (/.f64 (expm1.f64 (.f64 n (-.f64 (log.f64 (/.f64 -1 n)) (log.f64 (/.f64 -1 i))))) (/.f64 i n)))

Compiler

Compiled 5914 to 2616 computations (55.8% saved)

regimes2.9s (16.6%)

Accuracy

Total 10.3b remaining (98.7%)

Threshold costs 0b (0%)

Counts

313 → 5

Compiler

Compiled 26186 to 17194 computations (34.3% saved)

bsearch1.0s (5.9%)

Steps

Iters	Range		Point
9	3.9159840747297776e+262	2.2218715682348202e+268	5.028729354167085e+265
12	4.459481869274049e+85	1.566983006261577e+130	6.869232008206506e+129
9	40.07322357397244	3274961.0599709423	339.51119695591177
8	-6458.698515588834	-3.8845736936505464	-3.9261148805468635

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	169
1	77	169
2	82	169
3	84	169
4	85	169
5	83	169

end336.0ms (1.9%)

Compiler: Compiled 796 to 481 computations (39.6% saved)

Details

analyze2.2s (12.4%)

sample8.4s (48.1%)

simplify44.0ms (0.3%)

prune4.0ms (0%)

localize8.0ms (0%)

series316.0ms (1.8%)

rewrite150.0ms (0.9%)

simplify397.0ms (2.3%)

prune701.0ms (4%)

localize5.0ms (0%)

series32.0ms (0.2%)

rewrite15.0ms (0.1%)

simplify106.0ms (0.6%)

prune125.0ms (0.7%)

localize7.0ms (0%)

series39.0ms (0.2%)

rewrite22.0ms (0.1%)

simplify105.0ms (0.6%)

prune213.0ms (1.2%)

localize16.0ms (0.1%)

series61.0ms (0.4%)

rewrite14.0ms (0.1%)

simplify82.0ms (0.5%)

prune142.0ms (0.8%)

regimes2.9s (16.6%)

bsearch1.0s (5.9%)

simplify7.0ms (0%)

end336.0ms (1.9%)

Profiling