Details

analyze264.0ms (7.2%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample27.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify63.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
556×	`cancel-sign-sub-inv_binary64`
552×	`unswap-sqr_binary64`
357×	`unsub-neg_binary64`
344×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	168	37
3	492	37
4	1604	33
5	2891	33
6	4309	33
7	5214	33

prune5.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)

Status

Error

Program

▶

0.0b

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	1.2b	(.f64 (.f64 b b) (+.f64 a 3))

series92.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

35.0ms	(pow.f64 (hypot.f64 a b) 4)
35.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
13.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 78

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify96.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-+l+_binary64`
469×	`distribute-rgt-in_binary64`
453×	`distribute-lft-in_binary64`
338×	`associate--l+_binary64`
219×	`cancel-sign-sub-inv_binary64`

Counts

174 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3413
1	464	3143
2	1556	3045
3	5074	3045

prune211.0ms (5.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	156	6	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	6	164

Error

Counts

164 → 6

Alt Table

Status	Error	Program
	50.7b	(+.f64 (.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b)))) (*.f64 (pow.f64 a 3) (-.f64 a 4)))
	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	14.2b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (.f64 4 (pow.f64 a 3)) 1))
	14.2b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
	5.8b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))) -1))
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 b (*.f64 b (+.f64 a 3)))) -1))

Compiler

Compiled 5138 to 3025 computations (41.1% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 b (*.f64 b (+.f64 a 3)))) -1))
✓	0.0b	(*.f64 b (+.f64 a 3))
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 b (*.f64 b (+.f64 a 3))))
✓	0.2b	(.f64 b (.f64 b (+.f64 a 3)))

series60.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

36.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 b (*.f64 b (+.f64 a 3)))) -1))
12.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 b (*.f64 b (+.f64 a 3))))
8.0ms	(.f64 b (.f64 b (+.f64 a 3)))
4.0ms	(*.f64 b (+.f64 a 3))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(*.f64 b (+.f64 a 3))
6.0ms	(.f64 b (.f64 b (+.f64 a 3)))
4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 b (*.f64 b (+.f64 a 3)))) -1))
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 b (*.f64 b (+.f64 a 3))))

simplify99.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

730×	`distribute-rgt-in_binary64`
715×	`distribute-lft-in_binary64`
255×	`fma-neg_binary64`
213×	`cancel-sign-sub-inv_binary64`
142×	`associate-l_binary64`

Counts

179 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	3231
1	461	2938
2	1627	2863
3	4830	2851
4	4987	2851

prune236.0ms (6.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	171	6	177

Error

Counts

177 → 6

Alt Table

Status	Error	Program
	50.7b	(+.f64 (.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b)))) (*.f64 (pow.f64 a 3) (-.f64 a 4)))
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	14.2b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (.f64 4 (pow.f64 a 3)) 1))
	14.2b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
	5.8b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 b (*.f64 b (+.f64 a 3)))) -1))

Compiler

Compiled 5348 to 3232 computations (39.6% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
✓	1.2b	(.f64 (+.f64 3 a) (.f64 b b))

series58.0ms (1.6%)

Counts

3 → 72

Calls

3 calls:

36.0ms

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))

14.0ms

(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))

8.0ms

(*.f64 (+.f64 3 a) (*.f64 b b))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
36×	`prod-diff_binary64`
31×	`add-cube-cbrt_binary64`
16×	`unpow-prod-down_binary64`

Counts

3 → 116

Calls

3 calls:

8.0ms

(-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3))

6.0ms

(*.f64 (+.f64 3 a) (*.f64 b b))

4.0ms

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) -1))

simplify140.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

706×	`fma-neg_binary64`
672×	`distribute-rgt-in_binary64`
514×	`cancel-sign-sub-inv_binary64`
255×	`unswap-sqr_binary64`
176×	`distribute-rgt-out_binary64`

Counts

188 → 179

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	4373
1	532	3968
2	2022	3657
3	4999	3647
4	5258	3647

prune311.0ms (8.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	211	6	217

Error

Counts

217 → 6

Alt Table

Status	Error	Program
	50.7b	(+.f64 (.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b)))) (*.f64 (pow.f64 a 3) (-.f64 a 4)))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	14.2b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (.f64 4 (pow.f64 a 3)) 1))
	14.2b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
▶	5.8b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 b (*.f64 b (+.f64 a 3)))) -1))

Compiler

Compiled 7577 to 4538 computations (40.1% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
	1.2b	(.f64 (.f64 b b) (+.f64 a 3))
✓	4.1b	(exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))))
✓	8.8b	(log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))

series57.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

45.0ms	(log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))
11.0ms	(exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))
2.0ms	(exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))))

simplify120.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

339×	`cancel-sign-sub-inv_binary64`
314×	`fma-neg_binary64`
247×	`distribute-neg-in_binary64`
244×	`distribute-rgt-in_binary64`
240×	`sub-neg_binary64`

Counts

79 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	2908
1	650	2705
2	2514	2676
3	4689	2673
4	4995	2673
5	4939	2673

prune262.0ms (7.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	185	6	191

Error

Counts

191 → 6

Alt Table

Status	Error	Program
	50.7b	(+.f64 (.f64 (.f64 a a) (+.f64 4 (.f64 2 (.f64 b b)))) (*.f64 (pow.f64 a 3) (-.f64 a 4)))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
	14.2b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (pow.f64 a 4)) (+.f64 (.f64 4 (pow.f64 a 3)) 1))
	14.2b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
✓	5.8b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 b (*.f64 b (+.f64 a 3)))) -1))

Compiler

Compiled 7048 to 4485 computations (36.4% saved)

regimes446.0ms (12.1%)

Accuracy

Total 0.0b remaining (56.4%)

Threshold costs 0.0b (56.4%)

Counts

84 → 1

Compiler

Compiled 10192 to 7271 computations (28.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	63
1	28	63
2	31	63
3	33	63
4	34	63
5	33	63

end1.0ms (0%)

Compiler: Compiled 44 to 28 computations (36.4% saved)

sample997.0ms (27.1%)

Algorithm

1×

intervals

Results

627.0ms	8000×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 262 to 176 computations (32.8% saved)

Details

analyze264.0ms (7.2%)

sample27.0ms (0.7%)

simplify63.0ms (1.7%)

prune5.0ms (0.1%)

localize13.0ms (0.4%)

series92.0ms (2.5%)

rewrite16.0ms (0.4%)

simplify96.0ms (2.6%)

prune211.0ms (5.8%)

localize13.0ms (0.4%)

series60.0ms (1.6%)

rewrite19.0ms (0.5%)

simplify99.0ms (2.7%)

prune236.0ms (6.4%)

localize15.0ms (0.4%)

series58.0ms (1.6%)

rewrite26.0ms (0.7%)

simplify140.0ms (3.8%)

prune311.0ms (8.5%)

localize17.0ms (0.5%)

series57.0ms (1.5%)

rewrite5.0ms (0.1%)

simplify120.0ms (3.3%)

prune262.0ms (7.1%)

regimes446.0ms (12.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample997.0ms (27.1%)

Profiling