Details

analyze939.0ms (8.3%)

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 (58.9%)

Results

3.0s	1876×	body	2048	valid
2.1s	2732×	body	1024	valid
547.0ms	1152×	body	512	valid
260.0ms	1903×	body	128	valid
166.0ms	187×	body	1024	invalid
149.0ms	565×	body	256	valid
147.0ms	252×	body	512	invalid
72.0ms	28×	body	4096	valid
65.0ms	28×	body	2048	invalid
65.0ms	500×	body	128	invalid
45.0ms	133×	body	256	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify43.0ms (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

46.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	46.3b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
	46.4b	(*.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)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
✓	1.3b	(fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)
✓	5.8b	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series224.0ms (2%)

Counts

3 → 72

Calls

3 calls:

124.0ms	(*.f64 n (/.f64 (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100) i))
67.0ms	(fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)
33.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

6.0ms	(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))
0.0ms	(fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)

simplify119.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-def_binary64`
425×	`associate-/l*_binary64`
319×	`times-frac_binary64`
258×	`*-commutative_binary64`
212×	`+-commutative_binary64`

Counts

136 → 189

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	752	7388
1	2406	7091
2	5042	7091

prune255.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	179	10	189
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	181	10	191

Error

3.9b

Counts

191 → 10

Alt Table

Status	Error	Program
	46.3b	(.f64 n (/.f64 (+.f64 (.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n)) -100) i))
	58.5b	(.f64 n (/.f64 (.f64 n (-.f64 (.f64 100 (log.f64 i)) (.f64 100 (log.f64 n)))) i))
	48.0b	(/.f64 (fma.f64 (exp.f64 i) 100 -100) (/.f64 i n))
	48.2b	(/.f64 (.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) n) i)
	58.4b	(.f64 n (/.f64 (+.f64 (+.f64 (.f64 (.f64 50 (.f64 n n)) (+.f64 (pow.f64 (log.f64 i) 2) (pow.f64 (log.f64 n) 2))) (.f64 100 (fma.f64 n (log.f64 i) (/.f64 (.f64 n n) i)))) (.f64 -100 (.f64 (log.f64 n) (+.f64 n (.f64 (.f64 n n) (log.f64 i)))))) i))
	46.3b	(/.f64 (*.f64 n (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)) i)
	33.2b	(-.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)))))))
	29.3b	(-.f64 (fma.f64 50/3 (.f64 (.f64 i i) n) (fma.f64 n 100 (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50 (.f64 i n))))) (.f64 50 (+.f64 i (*.f64 i i))))
▶	28.3b	(.f64 n (/.f64 (.f64 100 i) i))
	48.8b	(-.f64 (.f64 100 (/.f64 (.f64 n (exp.f64 i)) i)) (+.f64 (.f64 100 (/.f64 n i)) (.f64 50 (*.f64 (exp.f64 i) i))))

Compiler

Compiled 9931 to 6136 computations (38.2% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (*.f64 100 i) i)

series1.0ms (0%)

Counts

1 → 12

Calls

1 calls:

1.0ms

(/.f64 (*.f64 100 i) i)

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
3×	`associate-/r*_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`

Counts

1 → 23

Calls

1 calls:

3.0ms

(/.f64 (*.f64 100 i) i)

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

675×	`unswap-sqr_binary64`
656×	`times-frac_binary64`
630×	`fma-neg_binary64`
450×	`associate-/l*_binary64`
324×	`fma-def_binary64`

Counts

35 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	123
1	105	117
2	310	117
3	734	117
4	1843	117
5	2802	117
6	4897	117

prune71.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	37	11	48

Error

3.9b

Counts

48 → 11

Alt Table

Status	Error	Program
	46.3b	(/.f64 (*.f64 n (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)) i)
▶	29.0b	(.f64 n (.f64 (*.f64 (cbrt.f64 100) (cbrt.f64 100)) (cbrt.f64 100)))
	46.3b	(.f64 n (/.f64 (+.f64 (.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n)) -100) i))
	58.5b	(.f64 n (/.f64 (.f64 n (-.f64 (.f64 100 (log.f64 i)) (.f64 100 (log.f64 n)))) i))
	48.0b	(/.f64 (fma.f64 (exp.f64 i) 100 -100) (/.f64 i n))
	48.2b	(/.f64 (.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) n) i)
	58.4b	(.f64 n (/.f64 (+.f64 (+.f64 (.f64 (.f64 50 (.f64 n n)) (+.f64 (pow.f64 (log.f64 i) 2) (pow.f64 (log.f64 n) 2))) (.f64 100 (fma.f64 n (log.f64 i) (/.f64 (.f64 n n) i)))) (.f64 -100 (.f64 (log.f64 n) (+.f64 n (.f64 (.f64 n n) (log.f64 i)))))) i))
	33.2b	(-.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)))))))
	29.3b	(-.f64 (fma.f64 50/3 (.f64 (.f64 i i) n) (fma.f64 n 100 (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50 (.f64 i n))))) (.f64 50 (+.f64 i (*.f64 i i))))
	29.2b	(.f64 n (exp.f64 (log.f64 (/.f64 (.f64 100 i) i))))
	48.8b	(-.f64 (.f64 100 (/.f64 (.f64 n (exp.f64 i)) i)) (+.f64 (.f64 100 (/.f64 n i)) (.f64 50 (*.f64 (exp.f64 i) i))))

Compiler

Compiled 907 to 596 computations (34.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 n (.f64 (*.f64 (cbrt.f64 100) (cbrt.f64 100)) (cbrt.f64 100)))
✓	1.0b	(cbrt.f64 100)
✓	1.6b	(*.f64 (cbrt.f64 100) (cbrt.f64 100))

series13.0ms (0.1%)

Counts

3 → 12

Calls

3 calls:

13.0ms	(.f64 n (.f64 (*.f64 (cbrt.f64 100) (cbrt.f64 100)) (cbrt.f64 100)))
0.0ms	(*.f64 (cbrt.f64 100) (cbrt.f64 100))
0.0ms	(cbrt.f64 100)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
19×	`pow1_binary64`
14×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`

Counts

3 → 78

Calls

3 calls:

9.0ms	(.f64 n (.f64 (*.f64 (cbrt.f64 100) (cbrt.f64 100)) (cbrt.f64 100)))
5.0ms	(*.f64 (cbrt.f64 100) (cbrt.f64 100))
1.0ms	(cbrt.f64 100)

simplify84.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
385×	`unswap-sqr_binary64`
381×	`*-commutative_binary64`
377×	`associate-/l*_binary64`
360×	`sqr-pow_binary64`

Counts

90 → 99

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	84	704
1	133	658
2	322	654
3	1005	640
4	1731	560
5	2977	560
6	4572	560
7	4898	560

prune94.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	134	10	144

Error

3.9b

Counts

144 → 10

Alt Table

Status	Error	Program
	46.3b	(.f64 n (/.f64 (+.f64 (.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n)) -100) i))
	58.5b	(.f64 n (/.f64 (.f64 n (-.f64 (.f64 100 (log.f64 i)) (.f64 100 (log.f64 n)))) i))
	48.0b	(/.f64 (fma.f64 (exp.f64 i) 100 -100) (/.f64 i n))
	48.2b	(/.f64 (.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) n) i)
	58.4b	(.f64 n (/.f64 (+.f64 (+.f64 (.f64 (.f64 50 (.f64 n n)) (+.f64 (pow.f64 (log.f64 i) 2) (pow.f64 (log.f64 n) 2))) (.f64 100 (fma.f64 n (log.f64 i) (/.f64 (.f64 n n) i)))) (.f64 -100 (.f64 (log.f64 n) (+.f64 n (.f64 (.f64 n n) (log.f64 i)))))) i))
	46.3b	(/.f64 (*.f64 n (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)) i)
	33.2b	(-.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)))))))
	29.3b	(-.f64 (fma.f64 50/3 (.f64 (.f64 i i) n) (fma.f64 n 100 (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50 (.f64 i n))))) (.f64 50 (+.f64 i (*.f64 i i))))
▶	28.9b	(.f64 (.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (.f64 100 n))) (cbrt.f64 (*.f64 100 n)))
	48.8b	(-.f64 (.f64 100 (/.f64 (.f64 n (exp.f64 i)) i)) (+.f64 (.f64 100 (/.f64 n i)) (.f64 50 (*.f64 (exp.f64 i) i))))

Compiler

Compiled 2383 to 2049 computations (14% saved)

localize5.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (.f64 100 n))) (cbrt.f64 (*.f64 100 n)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (*.f64 100 n)))
✓	0.8b	(cbrt.f64 (*.f64 100 n))

series112.0ms (1%)

Counts

3 → 36

Calls

3 calls:

47.0ms	(.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (*.f64 100 n)))
43.0ms	(cbrt.f64 (*.f64 100 n))
22.0ms	(.f64 (.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (.f64 100 n))) (cbrt.f64 (*.f64 100 n)))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

6.0ms	(.f64 (.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (.f64 100 n))) (cbrt.f64 (*.f64 100 n)))
5.0ms	(.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (*.f64 100 n)))
2.0ms	(cbrt.f64 (*.f64 100 n))

simplify97.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
489×	`*-commutative_binary64`
469×	`associate-r_binary64`
415×	`sqr-pow_binary64`
368×	`unswap-sqr_binary64`

Counts

115 → 117

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	81	1128
1	150	1049
2	421	986
3	1175	925
4	2302	831
5	3355	831
6	4449	831
7	4849	831

prune128.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	160	11	171

Error

3.9b

Counts

171 → 11

Alt Table

Status	Error	Program
	29.0b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (.f64 100 n))) (cbrt.f64 (.f64 100 n)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (.f64 100 n))) (cbrt.f64 (.f64 100 n))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (.f64 100 n))) (cbrt.f64 (*.f64 100 n)))))
	48.0b	(/.f64 (fma.f64 (exp.f64 i) 100 -100) (/.f64 i n))
	46.3b	(.f64 n (/.f64 (+.f64 (.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n)) -100) i))
	58.5b	(.f64 n (/.f64 (.f64 n (-.f64 (.f64 100 (log.f64 i)) (.f64 100 (log.f64 n)))) i))
	48.2b	(/.f64 (.f64 (-.f64 (.f64 100 (exp.f64 i)) 100) n) i)
	58.4b	(.f64 n (/.f64 (+.f64 (+.f64 (.f64 (.f64 50 (.f64 n n)) (+.f64 (pow.f64 (log.f64 i) 2) (pow.f64 (log.f64 n) 2))) (.f64 100 (fma.f64 n (log.f64 i) (/.f64 (.f64 n n) i)))) (.f64 -100 (.f64 (log.f64 n) (+.f64 n (.f64 (.f64 n n) (log.f64 i)))))) i))
	46.3b	(/.f64 (*.f64 n (fma.f64 100 (pow.f64 (+.f64 1 (/.f64 i n)) n) -100)) i)
	33.2b	(-.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)))))))
	29.3b	(-.f64 (fma.f64 50/3 (.f64 (.f64 i i) n) (fma.f64 n 100 (fma.f64 (/.f64 (.f64 i i) n) 100/3 (.f64 50 (.f64 i n))))) (.f64 50 (+.f64 i (*.f64 i i))))
	30.8b	(.f64 (exp.f64 (log.f64 (.f64 (cbrt.f64 (.f64 100 n)) (cbrt.f64 (.f64 100 n))))) (cbrt.f64 (*.f64 100 n)))
	48.8b	(-.f64 (.f64 100 (/.f64 (.f64 n (exp.f64 i)) i)) (+.f64 (.f64 100 (/.f64 n i)) (.f64 50 (*.f64 (exp.f64 i) i))))

Compiler

Compiled 2967 to 2360 computations (20.5% saved)

regimes1.9s (17%)

Accuracy

Total 8.5b remaining (73.9%)

Threshold costs 0b (0%)

Counts

236 → 3

Compiler

Compiled 17712 to 14028 computations (20.8% saved)

bsearch173.0ms (1.5%)

Steps

Iters	Range		Point
11	1.1114993555773914e-22	844023021969352.0	0.8920348598017706
7	-2.517519002575135e-10	-9.941326879530895e-13	-1.2241496397660598e-10

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	96
1	56	96
2	63	96
3	71	96
4	82	96
5	87	96
6	89	96
7	87	96

end232.0ms (2.1%)

Compiler: Compiled 447 to 301 computations (32.7% saved)

Details

analyze939.0ms (8.3%)

sample6.7s (58.9%)

simplify43.0ms (0.4%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series224.0ms (2%)

rewrite16.0ms (0.1%)

simplify119.0ms (1.1%)

prune255.0ms (2.3%)

localize5.0ms (0%)

series1.0ms (0%)

rewrite4.0ms (0%)

simplify50.0ms (0.4%)

prune71.0ms (0.6%)

localize6.0ms (0.1%)

series13.0ms (0.1%)

rewrite18.0ms (0.2%)

simplify84.0ms (0.7%)

prune94.0ms (0.8%)

localize5.0ms (0%)

series112.0ms (1%)

rewrite17.0ms (0.1%)

simplify97.0ms (0.9%)

prune128.0ms (1.1%)

regimes1.9s (17%)

bsearch173.0ms (1.5%)

simplify5.0ms (0%)

end232.0ms (2.1%)

Profiling