Details

analyze1.1s (8%)

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
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 31 to 21 computations (32.3% saved)

sample3.3s (23.8%)

Results

899.0ms	5438×	body	128	valid
647.0ms	1198×	body	1024	valid
444.0ms	863×	body	1024	invalid
436.0ms	958×	body	512	valid
241.0ms	1579×	body	128	invalid
196.0ms	487×	body	512	invalid
163.0ms	574×	body	256	valid
88.0ms	290×	body	256	invalid
59.0ms	88×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% saved)

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-def_binary64`
506×	`fma-neg_binary64`
500×	`distribute-rgt-in_binary64`
420×	`distribute-lft-in_binary64`
403×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	48	39
2	103	39
3	222	39
4	455	39
5	975	39
6	2136	39
7	4390	39
8	4971	39

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

40.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	40.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))

Compiler

Compiled 114 to 72 computations (36.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
✓	0.4b	(*.f64 (sqrt.f64 2) t)
✓	14.7b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	18.6b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

series1.1s (8.3%)

Counts

4 → 120

Calls

4 calls:

863.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
210.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
61.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
3.0ms	(*.f64 (sqrt.f64 2) t)

rewrite90.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`prod-diff_binary64`
193×	`add-sqr-sqrt_binary64`
186×	`log1p-expm1-u_binary64`
186×	`expm1-log1p-u_binary64`
183×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	105
1	397	105
2	4687	105
3	5518	105

Stop Event

1×	node limit

Counts

4 → 144

Calls

4 calls:

85.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
85.0ms	(*.f64 (sqrt.f64 2) t)
85.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
85.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

simplify283.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

632×	`*-commutative_binary64`
385×	`fma-def_binary64`
342×	`associate-+r+_binary64`
278×	`associate-r_binary64`
225×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1507	28688
1	5075	28688

Stop Event

1×	node limit

Counts

264 → 301

prune845.0ms (6.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	291	10	301
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	292	10	302

Error

4.6b

Counts

302 → 10

Alt Table

Status	Error	Program
	36.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))))
	36.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
	40.2b	(.f64 (.f64 t (sqrt.f64 2)) (pow.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) -1/2))
▶	29.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	49.7b	(pow.f64 (sqrt.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))) 2)
	37.2b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 (.f64 l l) (.f64 t (*.f64 x (sqrt.f64 2)))))))
	63.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1)) l))
	52.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (fma.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 x 1))) (/.f64 (fma.f64 2 (.f64 t t) (.f64 l l)) (sqrt.f64 (-.f64 x 1))) (neg.f64 (.f64 l l))) (fma.f64 (neg.f64 l) l (*.f64 l l)))))
	40.0b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))
	40.4b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))))

Compiler

Compiled 43613 to 31997 computations (26.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.6b	(/.f64 (*.f64 t t) x)
✓	13.5b	(/.f64 (.f64 l l) (.f64 x x))
✓	17.7b	(/.f64 (.f64 t t) (.f64 x x))
✓	25.5b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))

series211.0ms (1.5%)

Counts

4 → 108

Calls

4 calls:

149.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))
25.0ms	(/.f64 (.f64 t t) (.f64 x x))
25.0ms	(/.f64 (.f64 l l) (.f64 x x))
11.0ms	(/.f64 (*.f64 t t) x)

rewrite76.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

306×	`prod-diff_binary64`
206×	`add-sqr-sqrt_binary64`
198×	`log1p-expm1-u_binary64`
198×	`expm1-log1p-u_binary64`
196×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	81
1	425	67
2	4793	67
3	5333	67

Stop Event

1×	node limit

Counts

4 → 121

Calls

4 calls:

73.0ms	(/.f64 (*.f64 t t) x)
73.0ms	(/.f64 (.f64 l l) (.f64 x x))
73.0ms	(/.f64 (.f64 t t) (.f64 x x))
73.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))

simplify113.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-def_binary64`
289×	`associate-/r*_binary64`
276×	`associate-r_binary64`
248×	`associate-l_binary64`
221×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	417	7585
1	1334	6486
2	5292	6486

Stop Event

1×	node limit

Counts

229 → 190

prune300.0ms (2.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	184	6	190
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	187	13	200

Error

0.3b

Counts

200 → 13

Alt Table

Status	Error	Program
	36.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))))
	36.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
▶	27.9b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))) 1/4) 2))
	40.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x))))))))
	49.7b	(pow.f64 (sqrt.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))) 2)
	54.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	40.4b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))))
	40.2b	(.f64 (.f64 t (sqrt.f64 2)) (pow.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) -1/2))
	38.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 x t)) (/.f64 (.f64 l l) (.f64 x (.f64 x t))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
✓	29.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	28.4b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))))) 3))
	52.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (fma.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 x 1))) (/.f64 (fma.f64 2 (.f64 t t) (.f64 l l)) (sqrt.f64 (-.f64 x 1))) (neg.f64 (.f64 l l))) (fma.f64 (neg.f64 l) l (*.f64 l l)))))
	55.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))

Compiler

Compiled 15537 to 9402 computations (39.5% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.2b	(fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))
✓	6.0b	(/.f64 (*.f64 l l) x)
	7.6b	(/.f64 (*.f64 t t) x)
✓	26.2b	(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))) 1/4)

series304.0ms (2.2%)

Counts

3 → 96

Calls

3 calls:

247.0ms

(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))) 1/4)

48.0ms

(fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))

9.0ms

(/.f64 (*.f64 l l) x)

rewrite62.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

215×	`prod-diff_binary64`
208×	`add-sqr-sqrt_binary64`
202×	`log1p-expm1-u_binary64`
202×	`expm1-log1p-u_binary64`
198×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	88
1	448	86
2	4681	86
3	5112	86

Stop Event

1×	node limit

Counts

3 → 66

Calls

3 calls:

60.0ms

(fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))

60.0ms

(/.f64 (*.f64 l l) x)

60.0ms

(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))) 1/4)

simplify148.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

598×	`times-frac_binary64`
583×	`associate-/r*_binary64`
576×	`fma-def_binary64`
447×	`associate-/l*_binary64`
232×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	585	11205
1	1972	10433
2	5442	10433

Stop Event

1×	node limit

Counts

162 → 151

prune409.0ms (3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	177	15	192

Error

0.3b

Counts

192 → 15

Alt Table

Status	Error	Program
	36.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))))
	36.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
✓	27.9b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))) 1/4) 2))
	40.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x))))))))
	49.7b	(pow.f64 (sqrt.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))) 2)
	40.2b	(.f64 (.f64 t (sqrt.f64 2)) (pow.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) -1/2))
	38.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 x t)) (/.f64 (.f64 l l) (.f64 x (.f64 x t))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
✓	29.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	26.8b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (expm1.f64 (log1p.f64 (.f64 l (/.f64 l x))))))))) 1/4) 2))
	42.7b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x))))) (.f64 2 (log.f64 (/.f64 -1 t)))))) 2))
▶	26.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (pow.f64 (cbrt.f64 (.f64 l (/.f64 l x))) 3)))))) 1/4) 2))
	39.5b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 2 (log.f64 (/.f64 1 t)))))) 2))
	52.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (fma.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 x 1))) (/.f64 (fma.f64 2 (.f64 t t) (.f64 l l)) (sqrt.f64 (-.f64 x 1))) (neg.f64 (.f64 l l))) (fma.f64 (neg.f64 l) l (*.f64 l l)))))
	55.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	54.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))

Compiler

Compiled 19753 to 13842 computations (29.9% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.2b	(fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (pow.f64 (cbrt.f64 (*.f64 l (/.f64 l x))) 3)))))
	7.6b	(/.f64 (*.f64 t t) x)
✓	26.2b	(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (pow.f64 (cbrt.f64 (*.f64 l (/.f64 l x))) 3)))))) 1/4)
✓	31.7b	(cbrt.f64 (*.f64 l (/.f64 l x)))

series928.0ms (6.8%)

Counts

3 → 96

Calls

3 calls:

395.0ms

(cbrt.f64 (*.f64 l (/.f64 l x)))

338.0ms

(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (pow.f64 (cbrt.f64 (*.f64 l (/.f64 l x))) 3)))))) 1/4)

194.0ms

(fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (pow.f64 (cbrt.f64 (*.f64 l (/.f64 l x))) 3)))))

rewrite59.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

214×	`add-sqr-sqrt_binary64`
212×	`log1p-expm1-u_binary64`
212×	`expm1-log1p-u_binary64`
206×	`add-log-exp_binary64`
205×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	90
1	473	90
2	4656	90
3	4907	90

Stop Event

1×	node limit

Counts

3 → 58

Calls

3 calls:

58.0ms

(fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (pow.f64 (cbrt.f64 (*.f64 l (/.f64 l x))) 3)))))

58.0ms

(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (pow.f64 (cbrt.f64 (*.f64 l (/.f64 l x))) 3)))))) 1/4)

58.0ms

(cbrt.f64 (*.f64 l (/.f64 l x)))

simplify232.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
672×	`times-frac_binary64`
319×	`*-commutative_binary64`
192×	`+-commutative_binary64`
146×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	786	13976
1	2592	13219
2	4948	13069
3	4969	13069

Stop Event

1×	node limit

Counts

154 → 168

prune457.0ms (3.3%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	196	15	211

Error

0.3b

Counts

211 → 15

Alt Table

Status	Error	Program
	36.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))))
	36.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
✓	27.9b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))) 1/4) 2))
	40.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x))))))))
	49.7b	(pow.f64 (sqrt.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))) 2)
	40.2b	(.f64 (.f64 t (sqrt.f64 2)) (pow.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) -1/2))
	38.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 x t)) (/.f64 (.f64 l l) (.f64 x (.f64 x t))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
✓	29.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	26.8b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (expm1.f64 (log1p.f64 (.f64 l (/.f64 l x))))))))) 1/4) 2))
	42.7b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x))))) (.f64 2 (log.f64 (/.f64 -1 t)))))) 2))
✓	26.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (pow.f64 (cbrt.f64 (.f64 l (/.f64 l x))) 3)))))) 1/4) 2))
	39.5b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 2 (log.f64 (/.f64 1 t)))))) 2))
	52.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (fma.f64 (/.f64 (+.f64 x 1) (sqrt.f64 (-.f64 x 1))) (/.f64 (fma.f64 2 (.f64 t t) (.f64 l l)) (sqrt.f64 (-.f64 x 1))) (neg.f64 (.f64 l l))) (fma.f64 (neg.f64 l) l (*.f64 l l)))))
	55.4b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	54.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))

Compiler

Compiled 22981 to 16356 computations (28.8% saved)

regimes2.2s (16.2%)

Accuracy

Total 8.5b remaining (95.1%)

Threshold costs 0b (0%)

Counts

144 → 7

Compiler

Compiled 37539 to 26225 computations (30.1% saved)

bsearch932.0ms (6.8%)

Steps

Iters	Range		Point
7	2.1619762343420863e+61	1.762798061039258e+63	1.7217277470457817e+63
8	1.6741206551946781e-186	7.468234788858256e-184	1.6898595657411804e-186
7	-3.3485930915106366e-307	8.3187306561638e-310	4.04367196613585e-310
9	-5.858506782973357e-274	-1.7561552091000522e-280	-5.760693106007019e-274
8	-2.0905511634183514e-206	-1.344818396963145e-209	-1.3699428530136365e-209
10	-0.008866260243616425	-2.77151334505108e-20	-0.008644579131846854

Compiler

Compiled 4 to 3 computations (25% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
20×	`+-commutative_binary64`
14×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	103	393
1	140	393
2	168	393
3	189	393
4	208	393
5	220	393
6	226	393
7	229	393
8	230	393
9	228	393

Stop Event

1×

saturated

end399.0ms (2.9%)

Compiler: Compiled 1048 to 722 computations (31.1% saved)

Iter	Nodes	Cost
0	103	393
1	140	393
2	168	393
3	189	393
4	208	393
5	220	393
6	226	393
7	229	393
8	230	393
9	228	393

Iter	Nodes	Cost
0	103	393
1	140	393
2	168	393
3	189	393
4	208	393
5	220	393
6	226	393
7	229	393
8	230	393
9	228	393

Details

analyze1.1s (8%)

sample3.3s (23.8%)

simplify48.0ms (0.3%)

prune3.0ms (0%)

localize14.0ms (0.1%)

series1.1s (8.3%)

rewrite90.0ms (0.7%)

simplify283.0ms (2.1%)

prune845.0ms (6.2%)

localize22.0ms (0.2%)

series211.0ms (1.5%)

rewrite76.0ms (0.6%)

simplify113.0ms (0.8%)

prune300.0ms (2.2%)

localize27.0ms (0.2%)

series304.0ms (2.2%)

rewrite62.0ms (0.5%)

simplify148.0ms (1.1%)

prune409.0ms (3%)

localize28.0ms (0.2%)

series928.0ms (6.8%)

rewrite59.0ms (0.4%)

simplify232.0ms (1.7%)

prune457.0ms (3.3%)

regimes2.2s (16.2%)

bsearch932.0ms (6.8%)

simplify19.0ms (0.1%)

end399.0ms (2.9%)

Profiling

Iter	Nodes	Cost
0	103	393
1	140	393
2	168	393
3	189	393
4	208	393
5	220	393
6	226	393
7	229	393
8	230	393
9	228	393