Details

analyze2.7s (14.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0.8%	98.9%	0.3%	13
1.2%	98.5%	0.3%	14

Compiler

Compiled 44 to 31 computations (29.5% saved)

sample1.8s (10.1%)

Results

1.6s	8256×	body	128	valid
177.0ms	920×	body	128	invalid

Compiler

Compiled 88 to 62 computations (29.5% saved)

preprocess44.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

524×	`associate-+r+_binary64`
524×	`associate-+l+_binary64`
472×	`fma-def_binary64`
435×	`associate-l_binary64`
390×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	182	656
1	508	656
2	1160	624
3	3497	624
0	6	6

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 43 to 30 computations (30.2% saved)

simplify29.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

704×	`distribute-rgt-in_binary64`
703×	`distribute-lft-in_binary64`
676×	`fma-def_binary64`
308×	`associate-l_binary64`
236×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	41
1	63	41
2	134	39
3	402	39
4	1067	39
5	3164	39
6	4889	39

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

27.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	28.6b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))
▶	27.4b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)

Status

Error

Program

28.6b

(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))

▶

27.4b

(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)

Compiler

Compiled 228 to 150 computations (34.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z 313060547623/100000000000 55833770631/5000000000)
✓	0.1b	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)
✓	0.1b	(fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t)
✓	26.7b	(/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000))

series1.2s (6.9%)

Counts

4 → 156

Calls

39 calls:

74.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)	b	-inf
69.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)	t	-inf
69.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)	b	inf
66.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)	t	inf
64.0ms	(fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x)	a	inf

rewrite53.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`add-sqr-sqrt_binary64`
228×	`log1p-expm1-u_binary64`
228×	`expm1-log1p-u_binary64`
227×	`add-cbrt-cube_binary64`
227×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	88
1	485	88

Stop Event

1×	node limit

Counts

4 → 80

simplify271.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

517×	`associate-l_binary64`
463×	`cancel-sign-sub-inv_binary64`
297×	`fma-def_binary64`
251×	`associate-+r+_binary64`
211×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	16199
1	767	16060
2	2641	13614

Stop Event

1×	node limit

Counts

236 → 162

prune293.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	156	6	162
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	157	7	164

Error

0.0b

Counts

164 → 7

Alt Table

Status	Error	Program
	29.4b	(fma.f64 y (/.f64 (+.f64 (.f64 a z) (+.f64 (.f64 313060547623/100000000000 (pow.f64 z 4)) (+.f64 b (.f64 55833770631/5000000000 (pow.f64 z 3))))) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z)))))) x)
	32.0b	(fma.f64 y (-.f64 (+.f64 (.f64 1000000000000/607771387771 (.f64 a z)) (+.f64 (.f64 1000000000000/607771387771 (.f64 t (pow.f64 z 2))) (+.f64 (.f64 1000000000000/607771387771 b) (.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 (pow.f64 z 2) b))))) (+.f64 (.f64 11940090572100000000000000/369386059793087248348441 (.f64 z b)) (.f64 11940090572100000000000000/369386059793087248348441 (*.f64 a (pow.f64 z 2))))) x)
	30.0b	(+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (.f64 z z)) x)) (.f64 (/.f64 y z) (-.f64 (/.f64 t z) 3652704169880641883561/100000000000000000000)))
	31.9b	(+.f64 (+.f64 (.f64 (.f64 1000000000000/607771387771 y) (+.f64 b (.f64 z (+.f64 a (.f64 t z))))) (fma.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 b (.f64 (.f64 z z) y)) x)) (.f64 -11940090572100000000000000/369386059793087248348441 (.f64 y (.f64 z (fma.f64 a z b)))))
▶	28.6b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))
	30.4b	(fma.f64 y (+.f64 (+.f64 313060547623/100000000000 (/.f64 t (.f64 z z))) (-.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (.f64 z z)) (/.f64 a (pow.f64 z 3))) (+.f64 (/.f64 3652704169880641883561/100000000000000000000 z) (fma.f64 15234687407/1000000000 (/.f64 t (pow.f64 z 3)) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (pow.f64 z 3)))))) x)
	32.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (pow.f64 z 2)) (+.f64 (.f64 313060547623/100000000000 y) (+.f64 (.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (pow.f64 z 2))) x))) (.f64 3652704169880641883561/100000000000000000000 (/.f64 y z)))

Compiler

Compiled 7672 to 5016 computations (34.6% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z)
✓	0.3b	(.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z)
✓	1.7b	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b))
✓	27.9b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))

series758.0ms (4.2%)

Counts

4 → 144

Calls

36 calls:

66.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))	y	-inf
64.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))	y	inf
61.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))	t	inf
58.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))	y	0
57.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))	b	-inf

rewrite51.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

331×	`log1p-expm1-u_binary64`
331×	`expm1-log1p-u_binary64`
330×	`add-cbrt-cube_binary64`
320×	`add-log-exp_binary64`
319×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	81
1	683	81

Stop Event

1×	node limit

Counts

4 → 57

simplify147.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

515×	`associate-l_binary64`
470×	`associate-r_binary64`
273×	`fma-def_binary64`
265×	`cancel-sign-sub-inv_binary64`
165×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	8490
1	626	8454
2	1965	7183

Stop Event

1×	node limit

Counts

201 → 141

prune235.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	141	7	148

Error

0.0b

Counts

148 → 7

Alt Table

Status	Error	Program
	29.4b	(fma.f64 y (/.f64 (+.f64 (.f64 a z) (+.f64 (.f64 313060547623/100000000000 (pow.f64 z 4)) (+.f64 b (.f64 55833770631/5000000000 (pow.f64 z 3))))) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z)))))) x)
	32.0b	(fma.f64 y (-.f64 (+.f64 (.f64 1000000000000/607771387771 (.f64 a z)) (+.f64 (.f64 1000000000000/607771387771 (.f64 t (pow.f64 z 2))) (+.f64 (.f64 1000000000000/607771387771 b) (.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 (pow.f64 z 2) b))))) (+.f64 (.f64 11940090572100000000000000/369386059793087248348441 (.f64 z b)) (.f64 11940090572100000000000000/369386059793087248348441 (*.f64 a (pow.f64 z 2))))) x)
	31.9b	(+.f64 (+.f64 (.f64 (.f64 1000000000000/607771387771 y) (+.f64 b (.f64 z (+.f64 a (.f64 t z))))) (fma.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 b (.f64 (.f64 z z) y)) x)) (.f64 -11940090572100000000000000/369386059793087248348441 (.f64 y (.f64 z (fma.f64 a z b)))))
✓	28.6b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))
▶	28.4b	(+.f64 x (.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (.f64 z (+.f64 (.f64 z 314690115749/10000000000) 119400905721/10000000000))))) (fma.f64 a z (fma.f64 t (*.f64 z z) (fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b))))))
	30.4b	(fma.f64 y (+.f64 (+.f64 313060547623/100000000000 (/.f64 t (.f64 z z))) (-.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (.f64 z z)) (/.f64 a (pow.f64 z 3))) (+.f64 (/.f64 3652704169880641883561/100000000000000000000 z) (fma.f64 15234687407/1000000000 (/.f64 t (pow.f64 z 3)) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (pow.f64 z 3)))))) x)
	32.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (pow.f64 z 2)) (+.f64 (.f64 313060547623/100000000000 y) (+.f64 (.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (pow.f64 z 2))) x))) (.f64 3652704169880641883561/100000000000000000000 (/.f64 y z)))

Compiler

Compiled 5974 to 3914 computations (34.5% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.1b	(/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (.f64 z (+.f64 (*.f64 z 314690115749/10000000000) 119400905721/10000000000)))))
✓	6.8b	(fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b))
✓	7.6b	(fma.f64 t (*.f64 z z) (fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b)))
✓	28.8b	(.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (.f64 z (+.f64 (.f64 z 314690115749/10000000000) 119400905721/10000000000))))) (fma.f64 a z (fma.f64 t (*.f64 z z) (fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b)))))

series789.0ms (4.4%)

Counts

4 → 144

Calls

36 calls:

66.0ms	(.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (.f64 z (+.f64 (.f64 z 314690115749/10000000000) 119400905721/10000000000))))) (fma.f64 a z (fma.f64 t (*.f64 z z) (fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b)))))	y	-inf
59.0ms	(.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (.f64 z (+.f64 (.f64 z 314690115749/10000000000) 119400905721/10000000000))))) (fma.f64 a z (fma.f64 t (*.f64 z z) (fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b)))))	y	inf
57.0ms	(.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (.f64 z (+.f64 (.f64 z 314690115749/10000000000) 119400905721/10000000000))))) (fma.f64 a z (fma.f64 t (*.f64 z z) (fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b)))))	y	0
52.0ms	(.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (.f64 z (+.f64 (.f64 z 314690115749/10000000000) 119400905721/10000000000))))) (fma.f64 a z (fma.f64 t (*.f64 z z) (fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b)))))	t	inf
51.0ms	(.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (.f64 z (+.f64 (.f64 z 314690115749/10000000000) 119400905721/10000000000))))) (fma.f64 a z (fma.f64 t (*.f64 z z) (fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b)))))	b	-inf

rewrite60.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

316×	`log1p-expm1-u_binary64`
316×	`expm1-log1p-u_binary64`
311×	`add-cbrt-cube_binary64`
306×	`add-log-exp_binary64`
305×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	113
1	676	113

Stop Event

1×	node limit

Counts

4 → 62

simplify156.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

543×	`associate-l_binary64`
354×	`cancel-sign-sub-inv_binary64`
219×	`fma-def_binary64`
158×	`distribute-rgt-out_binary64`
150×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	8223
1	614	8183
2	2024	6928

Stop Event

1×	node limit

Counts

206 → 134

prune191.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	134	7	141

Error

0.0b

Counts

141 → 7

Alt Table

Status	Error	Program
	29.4b	(fma.f64 y (/.f64 (+.f64 (.f64 a z) (+.f64 (.f64 313060547623/100000000000 (pow.f64 z 4)) (+.f64 b (.f64 55833770631/5000000000 (pow.f64 z 3))))) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z)))))) x)
	32.0b	(fma.f64 y (-.f64 (+.f64 (.f64 1000000000000/607771387771 (.f64 a z)) (+.f64 (.f64 1000000000000/607771387771 (.f64 t (pow.f64 z 2))) (+.f64 (.f64 1000000000000/607771387771 b) (.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 (pow.f64 z 2) b))))) (+.f64 (.f64 11940090572100000000000000/369386059793087248348441 (.f64 z b)) (.f64 11940090572100000000000000/369386059793087248348441 (*.f64 a (pow.f64 z 2))))) x)
▶	24.5b	(+.f64 x (.f64 b (.f64 y 1000000000000/607771387771)))
✓	28.6b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))
✓	28.4b	(+.f64 x (.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (.f64 z (+.f64 (.f64 z 314690115749/10000000000) 119400905721/10000000000))))) (fma.f64 a z (fma.f64 t (*.f64 z z) (fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b))))))
	30.4b	(fma.f64 y (+.f64 (+.f64 313060547623/100000000000 (/.f64 t (.f64 z z))) (-.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (.f64 z z)) (/.f64 a (pow.f64 z 3))) (+.f64 (/.f64 3652704169880641883561/100000000000000000000 z) (fma.f64 15234687407/1000000000 (/.f64 t (pow.f64 z 3)) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (pow.f64 z 3)))))) x)
	32.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (pow.f64 z 2)) (+.f64 (.f64 313060547623/100000000000 y) (+.f64 (.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (pow.f64 z 2))) x))) (.f64 3652704169880641883561/100000000000000000000 (/.f64 y z)))

Compiler

Compiled 6208 to 4102 computations (33.9% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 b (.f64 y 1000000000000/607771387771)))
✓	0.2b	(.f64 b (.f64 y 1000000000000/607771387771))

series11.0ms (0.1%)

Counts

2 → 60

Calls

15 calls:

1.0ms	(+.f64 x (.f64 b (.f64 y 1000000000000/607771387771)))	x	inf
1.0ms	(+.f64 x (.f64 b (.f64 y 1000000000000/607771387771)))	x	-inf
1.0ms	(.f64 b (.f64 y 1000000000000/607771387771))	b	inf
1.0ms	(.f64 b (.f64 y 1000000000000/607771387771))	b	0
1.0ms	(.f64 b (.f64 y 1000000000000/607771387771))	y	inf

rewrite46.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

956×	`prod-diff_binary64`
845×	`expm1-log1p-u_binary64`
87×	`add-sqr-sqrt_binary64`
83×	`log1p-expm1-u_binary64`
82×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	171	15
2	2259	15

Stop Event

1×	node limit

Counts

2 → 51

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`*-commutative_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	423
1	14	423
2	23	423
3	29	423

Stop Event

1×

saturated

Counts

111 → 55

prune56.0ms (0.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	55	7	62

Error

0.0b

Counts

62 → 7

Alt Table

Status	Error	Program
	29.4b	(fma.f64 y (/.f64 (+.f64 (.f64 a z) (+.f64 (.f64 313060547623/100000000000 (pow.f64 z 4)) (+.f64 b (.f64 55833770631/5000000000 (pow.f64 z 3))))) (+.f64 607771387771/1000000000000 (+.f64 (.f64 314690115749/10000000000 (pow.f64 z 2)) (+.f64 (pow.f64 z 4) (+.f64 (.f64 15234687407/1000000000 (pow.f64 z 3)) (.f64 119400905721/10000000000 z)))))) x)
	32.0b	(fma.f64 y (-.f64 (+.f64 (.f64 1000000000000/607771387771 (.f64 a z)) (+.f64 (.f64 1000000000000/607771387771 (.f64 t (pow.f64 z 2))) (+.f64 (.f64 1000000000000/607771387771 b) (.f64 123439798033292669987862100000000000000/224502278183706222041215714334315011 (.f64 (pow.f64 z 2) b))))) (+.f64 (.f64 11940090572100000000000000/369386059793087248348441 (.f64 z b)) (.f64 11940090572100000000000000/369386059793087248348441 (*.f64 a (pow.f64 z 2))))) x)
✓	24.5b	(+.f64 x (.f64 b (.f64 y 1000000000000/607771387771)))
✓	28.6b	(+.f64 x (/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))
✓	28.4b	(+.f64 x (.f64 (/.f64 y (+.f64 607771387771/1000000000000 (+.f64 (.f64 (pow.f64 z 3) (+.f64 z 15234687407/1000000000)) (.f64 z (+.f64 (.f64 z 314690115749/10000000000) 119400905721/10000000000))))) (fma.f64 a z (fma.f64 t (*.f64 z z) (fma.f64 313060547623/100000000000 (pow.f64 z 4) (fma.f64 55833770631/5000000000 (pow.f64 z 3) b))))))
	30.4b	(fma.f64 y (+.f64 (+.f64 313060547623/100000000000 (/.f64 t (.f64 z z))) (-.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (.f64 z z)) (/.f64 a (pow.f64 z 3))) (+.f64 (/.f64 3652704169880641883561/100000000000000000000 z) (fma.f64 15234687407/1000000000 (/.f64 t (pow.f64 z 3)) (/.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (pow.f64 z 3)))))) x)
	32.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (pow.f64 z 2)) (+.f64 (.f64 313060547623/100000000000 y) (+.f64 (.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 y (pow.f64 z 2))) x))) (.f64 3652704169880641883561/100000000000000000000 (/.f64 y z)))

Compiler

Compiled 977 to 582 computations (40.4% saved)

regimes8.6s (48%)

Accuracy

Total 0.9b remaining (94.9%)

Threshold costs 0.9b (94.9%)

Counts

272 → 3

Compiler

Compiled 73488 to 51244 computations (30.3% saved)

bsearch76.0ms (0.4%)

Algorithm

2×	binary-search

Calls

2 calls:

37.0ms	z
26.0ms	z

Steps

Iters	Point		Range
2.4931360690352395e+58	∈ [	2.4727257050537976e+58	,	2.66180037408946e+63	]
-2.0907612101454143e+75	∈ [	-1.914443265420582e+76	,	-2.0456427294003e+75	]

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	141
1	74	141
2	83	141
3	92	141
4	97	141
5	99	141

Stop Event

1×

saturated

end204.0ms (1.1%)

Stop Event

1×

fuel

Compiler

Compiled 487 to 332 computations (31.8% saved)

Details

analyze2.7s (14.9%)

sample1.8s (10.1%)

preprocess44.0ms (0.2%)

simplify29.0ms (0.2%)

prune5.0ms (0%)

localize20.0ms (0.1%)

series1.2s (6.9%)

rewrite53.0ms (0.3%)

simplify271.0ms (1.5%)

prune293.0ms (1.6%)

localize35.0ms (0.2%)

series758.0ms (4.2%)

rewrite51.0ms (0.3%)

simplify147.0ms (0.8%)

prune235.0ms (1.3%)

localize28.0ms (0.2%)

series789.0ms (4.4%)

rewrite60.0ms (0.3%)

simplify156.0ms (0.9%)

prune191.0ms (1.1%)

localize6.0ms (0%)

series11.0ms (0.1%)

rewrite46.0ms (0.3%)

simplify16.0ms (0.1%)

prune56.0ms (0.3%)

regimes8.6s (48%)

bsearch76.0ms (0.4%)

simplify9.0ms (0.1%)

end204.0ms (1.1%)

Profiling