Details

analyze2.1s (12.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	74.7%	25.3%	8
0%	74.7%	25.3%	9
0%	65.4%	34.6%	10
0%	51.4%	48.6%	11
0%	51.4%	48.6%	12
0%	51.4%	48.6%	13
0%	51.4%	48.6%	14

Compiler

Compiled 30 to 21 computations (30% saved)

sample4.5s (26.5%)

Symmetry

(sort z t a)

Results

2.5s	11499×	body	128	invalid
1.8s	8254×	body	128	valid
1.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 89 to 62 computations (30.3% saved)

simplify84.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

2664×	`associate-+l+_binary64`
1041×	`associate-+r+_binary64`
923×	`+-commutative_binary64`
750×	`fma-def_binary64`
5×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	30
1	41	26
2	109	26
3	376	26
4	1118	26
5	1592	26
6	1698	26
7	1698	26
8	1698	26
9	1698	26
10	2706	26
11	2958	26
12	2958	26
13	2910	26
14	2910	26
15	2540	26
16	2524	26

prune4.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))

Compiler

Compiled 99 to 61 computations (38.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 x (log.f64 y) z) t)
✓	0.0b	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
✓	0.1b	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))
✓	0.1b	(fma.f64 x (log.f64 y) z)

series1.1s (6.7%)

Counts

4 → 228

Calls

4 calls:

738.0ms	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))
166.0ms	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
127.0ms	(+.f64 (fma.f64 x (log.f64 y) z) t)
102.0ms	(fma.f64 x (log.f64 y) z)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
11×	`add-log-exp_binary64`
7×	`fma-def_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

4 → 59

Calls

4 calls:

4.0ms	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
2.0ms	(+.f64 (fma.f64 x (log.f64 y) z) t)
0.0ms	(fma.f64 x (log.f64 y) z)
0.0ms	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))

simplify144.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-neg_binary64`
616×	`distribute-rgt-in_binary64`
580×	`distribute-lft-in_binary64`
507×	`fma-def_binary64`
416×	`associate--l+_binary64`

Counts

287 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	4579
1	414	4467
2	1201	4079
3	4906	4071
4	5553	4071

prune343.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	5	141

Error

0.1b

Counts

141 → 5

Alt Table

Status	Error	Program
	31.0b	(fma.f64 y i (*.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
	1.2b	(fma.f64 y i (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
▶	0.1b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	14.6b	(fma.f64 y i (+.f64 (fma.f64 (log.f64 y) x z) (+.f64 a (fma.f64 (log.f64 c) -1/2 t))))
	37.4b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (expm1.f64 (log1p.f64 (+.f64 (fma.f64 x (log.f64 y) z) t))) a)))

Compiler

Compiled 3663 to 1294 computations (64.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z))
✓	0.0b	(+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z))))
✓	0.3b	(*.f64 (log.f64 y) x)
✓	0.3b	(*.f64 (log.f64 c) b)

series1.8s (10.6%)

Counts

4 → 110

Calls

4 calls:

745.0ms	(+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z))))
586.0ms	(+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z))
250.0ms	(*.f64 (log.f64 y) x)
216.0ms	(*.f64 (log.f64 c) b)

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-log-exp_binary64`
14×	`*-un-lft-identity_binary64`
13×	`sum-log_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`

Counts

4 → 80

Calls

4 calls:

8.0ms	(+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z))))
5.0ms	(+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z))
4.0ms	(*.f64 (log.f64 c) b)
3.0ms	(*.f64 (log.f64 y) x)

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

978×	`fma-neg_binary64`
781×	`fma-def_binary64`
569×	`associate-+l+_binary64`
188×	`associate--l+_binary64`
186×	`cancel-sign-sub-inv_binary64`

Counts

190 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2655
1	481	2443
2	1544	2441
3	4449	2441
4	5295	2441

prune241.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	145	7	152
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	147	10	157

Error

0.0b

Counts

157 → 10

Alt Table

Status	Error	Program
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) z)))) (*.f64 1/2 (log.f64 c))))
	37.4b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (expm1.f64 (log1p.f64 (+.f64 (fma.f64 x (log.f64 y) z) t))) a)))
	32.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (sqrt.f64 (log.f64 c)) (.f64 (sqrt.f64 (log.f64 c)) b)) z)))) (.f64 1/2 (log.f64 c))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 c)) (cbrt.f64 (log.f64 c))) (.f64 (cbrt.f64 (log.f64 c)) b)) z)))) (*.f64 1/2 (log.f64 c))))
	31.0b	(fma.f64 y i (*.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
	14.6b	(fma.f64 y i (+.f64 (fma.f64 (log.f64 y) x z) (+.f64 a (fma.f64 (log.f64 c) -1/2 t))))
▶	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (log.f64 y) x)) (cbrt.f64 (.f64 (log.f64 y) x))) (cbrt.f64 (.f64 (log.f64 y) x))) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (.f64 (log.f64 y) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	31.6b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (sqrt.f64 b)) (sqrt.f64 b)) z)))) (.f64 1/2 (log.f64 c))))

Compiler

Compiled 4976 to 1766 computations (64.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (log.f64 c) b)
✓	0.4b	(.f64 (.f64 (cbrt.f64 (.f64 (log.f64 y) x)) (cbrt.f64 (.f64 (log.f64 y) x))) (cbrt.f64 (*.f64 (log.f64 y) x)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (log.f64 y) x)) (cbrt.f64 (*.f64 (log.f64 y) x)))
✓	0.6b	(cbrt.f64 (*.f64 (log.f64 y) x))

series2.3s (13.6%)

Counts

3 → 72

Calls

3 calls:

1.2s

(*.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) (cbrt.f64 (*.f64 (log.f64 y) x)))

884.0ms

(cbrt.f64 (*.f64 (log.f64 y) x))

229.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) (cbrt.f64 (*.f64 (log.f64 y) x))) (cbrt.f64 (*.f64 (log.f64 y) x)))

rewrite16.0ms (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 (log.f64 y) x)) (cbrt.f64 (*.f64 (log.f64 y) x))) (cbrt.f64 (*.f64 (log.f64 y) x)))

4.0ms

(*.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) (cbrt.f64 (*.f64 (log.f64 y) x)))

2.0ms

(cbrt.f64 (*.f64 (log.f64 y) x))

simplify100.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

555×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
302×	`log-prod_binary64`
294×	`fma-def_binary64`
247×	`unswap-sqr_binary64`

Counts

151 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1809
1	265	1570
2	679	1394
3	1441	1271
4	4717	1271
5	4981	1271

prune273.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	184	9	193

Error

0.0b

Counts

193 → 9

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (pow.f64 (cbrt.f64 (.f64 (log.f64 y) x)) 3) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	31.6b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (sqrt.f64 b)) (sqrt.f64 b)) z)))) (.f64 1/2 (log.f64 c))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) z)))) (*.f64 1/2 (log.f64 c))))
	37.4b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (expm1.f64 (log1p.f64 (+.f64 (fma.f64 x (log.f64 y) z) t))) a)))
	32.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (sqrt.f64 (log.f64 c)) (.f64 (sqrt.f64 (log.f64 c)) b)) z)))) (.f64 1/2 (log.f64 c))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 c)) (cbrt.f64 (log.f64 c))) (.f64 (cbrt.f64 (log.f64 c)) b)) z)))) (*.f64 1/2 (log.f64 c))))
	31.0b	(fma.f64 y i (*.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
	14.6b	(fma.f64 y i (+.f64 (fma.f64 (log.f64 y) x z) (+.f64 a (fma.f64 (log.f64 c) -1/2 t))))

Compiler

Compiled 7856 to 2450 computations (68.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (log.f64 y) x)
	0.3b	(*.f64 (log.f64 c) b)
	0.6b	(cbrt.f64 (*.f64 (log.f64 y) x))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 3)

series750.0ms (4.4%)

Counts

1 → 24

Calls

1 calls:

750.0ms

(pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 3)

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`cube-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`unpow-prod-down_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 28

Calls

1 calls:

2.0ms

(pow.f64 (cbrt.f64 (*.f64 (log.f64 y) x)) 3)

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

706×	`associate-l_binary64`
611×	`associate-r_binary64`
375×	`exp-prod_binary64`
347×	`fma-def_binary64`
339×	`log-prod_binary64`

Counts

52 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	620
1	179	571
2	549	497
3	3319	469
4	4877	469

prune164.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	123	9	132

Error

0.0b

Counts

132 → 9

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (pow.f64 (cbrt.f64 (.f64 (log.f64 y) x)) 3) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	31.6b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (sqrt.f64 b)) (sqrt.f64 b)) z)))) (.f64 1/2 (log.f64 c))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) x)) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) z)))) (*.f64 1/2 (log.f64 c))))
	37.4b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (expm1.f64 (log1p.f64 (+.f64 (fma.f64 x (log.f64 y) z) t))) a)))
	32.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (sqrt.f64 (log.f64 c)) (.f64 (sqrt.f64 (log.f64 c)) b)) z)))) (.f64 1/2 (log.f64 c))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 c)) (cbrt.f64 (log.f64 c))) (.f64 (cbrt.f64 (log.f64 c)) b)) z)))) (*.f64 1/2 (log.f64 c))))
	31.0b	(fma.f64 y i (*.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
	14.6b	(fma.f64 y i (+.f64 (fma.f64 (log.f64 y) x z) (+.f64 a (fma.f64 (log.f64 c) -1/2 t))))

Compiler

Compiled 4097 to 1721 computations (58% saved)

regimes2.5s (14.7%)

Accuracy

Total 0.0b remaining (49.5%)

Threshold costs 0.0b (49.5%)

Counts

147 → 1

Compiler

Compiled 55580 to 34654 computations (37.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	26
1	23	26
2	24	26
3	23	26

end183.0ms (1.1%)

Remove: (sort z t a)
Compiler: Compiled 423 to 262 computations (38.1% saved)

Details

analyze2.1s (12.6%)

sample4.5s (26.5%)

simplify84.0ms (0.5%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series1.1s (6.7%)

rewrite10.0ms (0.1%)

simplify144.0ms (0.9%)

prune343.0ms (2%)

localize19.0ms (0.1%)

series1.8s (10.6%)

rewrite24.0ms (0.1%)

simplify99.0ms (0.6%)

prune241.0ms (1.4%)

localize23.0ms (0.1%)

series2.3s (13.6%)

rewrite16.0ms (0.1%)

simplify100.0ms (0.6%)

prune273.0ms (1.6%)

localize21.0ms (0.1%)

series750.0ms (4.4%)

rewrite3.0ms (0%)

simplify56.0ms (0.3%)

prune164.0ms (1%)

regimes2.5s (14.7%)

simplify3.0ms (0%)

end183.0ms (1.1%)

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