Details

analyze78.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
3.1%	3.1%	93.8%	2
3.1%	3.1%	93.8%	3
4.7%	1.6%	93.8%	4
4.7%	1.6%	93.8%	5
5.5%	0.8%	93.8%	6
5.5%	0.8%	93.8%	7
5.8%	0.4%	93.8%	8
5.8%	0.4%	93.8%	9
6%	0.2%	93.8%	10
6%	0.2%	93.8%	11
6.1%	0.1%	93.8%	12
6.1%	0.1%	93.8%	13
6.2%	0%	93.8%	14

Compiler

Compiled 36 to 30 computations (16.7% saved)

sample2.4s (42.6%)

Results

2.2s

8256×

body

128

valid

Compiler

Compiled 93 to 79 computations (15.1% saved)

simplify131.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

909×	`cube-prod_binary64`
818×	`unswap-sqr_binary64`
698×	`fabs-mul_binary64`
671×	`sqr-pow_binary64`
541×	`cube-mult_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	24
1	38	24
2	63	24
3	101	24
4	203	24
5	528	24
6	667	24
7	856	24
8	1442	24
9	1481	24
10	1512	24
11	1576	24
12	1582	24
13	1854	24
14	2077	24
15	2498	24
16	3106	24
17	3604	24
18	4037	24
19	4445	24
20	4754	24
21	4859	24

prune4.0ms (0.1%)

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

Compiler

Compiled 70 to 60 computations (14.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
✓	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))

series309.0ms (5.4%)

Counts

4 → 52

Calls

4 calls:

160.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
122.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
24.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
3.0ms	(.f64 (.f64 2 (PI.f64)) u2)

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`

Counts

4 → 64

Calls

4 calls:

6.0ms	(.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1))))
4.0ms	(.f64 (.f64 2 (PI.f64)) u2)
2.0ms	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
0.0ms	(fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)

simplify109.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

621×	`unswap-sqr_binary64`
393×	`cancel-sign-sub-inv_binary64`
381×	`*-commutative_binary64`
263×	`fma-neg_binary64`
249×	`sub-neg_binary64`

Counts

116 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	2057
1	326	1932
2	949	1852
3	1807	1800
4	3478	1800
5	4916	1800
6	4917	1800

prune121.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Error

Counts

105 → 8

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (.f64 (.f64 1/6 (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(exp.f64 (log.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)))
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (expm1.f64 (log1p.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
▶	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)

Compiler

Compiled 2519 to 1920 computations (23.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))))
	0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
✓	0.2b	(*.f64 u2 (PI.f64))
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)

series332.0ms (5.8%)

Counts

3 → 60

Calls

3 calls:

168.0ms

(fma.f64 1/6 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64))))) 1/2)

161.0ms

(*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))

2.0ms

(*.f64 u2 (PI.f64))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
7×	`associate-l_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 51

Calls

3 calls:

5.0ms

(*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64)))))

3.0ms

(*.f64 u2 (PI.f64))

0.0ms

(fma.f64 1/6 (*.f64 (sqrt.f64 (*.f64 -2 (log.f64 u1))) (cos.f64 (*.f64 2 (*.f64 u2 (PI.f64))))) 1/2)

simplify124.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-neg_binary64`
365×	`*-commutative_binary64`
325×	`fma-def_binary64`
324×	`cancel-sign-sub-inv_binary64`
320×	`distribute-rgt-neg-in_binary64`

Counts

111 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	2411
1	326	2268
2	1021	2204
3	2266	2163
4	4806	2163
5	4972	2163
6	4959	2163

prune130.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	124	8	132

Error

Counts

132 → 8

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (.f64 (.f64 1/6 (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(exp.f64 (log.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)))
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (expm1.f64 (log1p.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)

Compiler

Compiled 3064 to 2181 computations (28.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
✓	0.5b	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

series79.0ms (1.4%)

Counts

3 → 32

Calls

3 calls:

29.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
25.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))
25.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
18×	`associate-l_binary64`
17×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`

Counts

3 → 86

Calls

3 calls:

7.0ms	(*.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))
6.0ms	(.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2)))
2.0ms	(sqrt.f64 (neg.f64 (log.f64 u1)))

simplify120.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-l_binary64`
460×	`neg-sub0_binary64`
445×	`neg-mul-1_binary64`
380×	`associate-r_binary64`
355×	`distribute-rgt-neg-in_binary64`

Counts

118 → 119

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	113	1620
1	194	1566
2	496	1566
3	1396	1566
4	2549	1566
5	4114	1566
6	4381	1566
7	4851	1566

prune139.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	147	8	155

Error

Counts

155 → 8

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (.f64 (.f64 1/6 (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(exp.f64 (log.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)))
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
▶	0.3b	(fma.f64 (.f64 (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) (sqrt.f64 2)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.7b	(fma.f64 (exp.f64 (+.f64 (log.f64 1/6) (log.f64 (sqrt.f64 (.f64 -2 (log.f64 u1)))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)

Compiler

Compiled 3556 to 2361 computations (33.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (neg.f64 (log.f64 u1)))
	0.2b	(.f64 (.f64 2 (PI.f64)) u2)
✓	0.4b	(*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1))))
✓	0.4b	(.f64 (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) (sqrt.f64 2))

series48.0ms (0.8%)

Counts

2 → 20

Calls

2 calls:

26.0ms	(.f64 (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) (sqrt.f64 2))
23.0ms	(*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1))))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`associate-r_binary64`
16×	`sqrt-prod_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`

Counts

2 → 56

Calls

2 calls:

7.0ms	(.f64 (.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1)))) (sqrt.f64 2))
5.0ms	(*.f64 1/6 (sqrt.f64 (neg.f64 (log.f64 u1))))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-r_binary64`
450×	`associate-*l/_binary64`
448×	`*-commutative_binary64`
381×	`neg-mul-1_binary64`
379×	`neg-sub0_binary64`

Counts

76 → 67

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	106	1064
1	193	1020
2	506	1020
3	1226	1020
4	2474	1020
5	3766	1020
6	4938	1020

prune120.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	123	7	130

Error

Counts

130 → 7

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 (.f64 1/6 (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (sqrt.f64 2))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.6b	(fma.f64 (.f64 (.f64 1/6 (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (sqrt.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(exp.f64 (log.f64 (fma.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)))
	0.5b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 1/6 (sqrt.f64 (.f64 -2 (log.f64 u1)))) 3)) (cos.f64 (.f64 (.f64 2 (PI.f64)) u2)) 1/2)
	0.3b	(fma.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (.f64 -2 (log.f64 u1))))) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
	0.5b	(fma.f64 (.f64 (.f64 (sqrt.f64 1/6) (.f64 (sqrt.f64 1/6) (sqrt.f64 (neg.f64 (log.f64 u1))))) (sqrt.f64 2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2)) 1/2)
✓	0.3b	(fma.f64 1/6 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (cos.f64 (.f64 2 (.f64 u2 (PI.f64))))) 1/2)

Compiler

Compiled 2882 to 1900 computations (34.1% saved)

regimes1.1s (19.3%)

Accuracy

Total 0.3b remaining (93.3%)

Threshold costs 0.3b (93.3%)

Counts

90 → 1

Compiler

Compiled 21056 to 18767 computations (10.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	32
1	27	32
2	29	32
3	30	32
4	30	32

end132.0ms (2.3%)

Compiler: Compiled 186 to 166 computations (10.8% saved)

Details

analyze78.0ms (1.4%)

sample2.4s (42.6%)

simplify131.0ms (2.3%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series309.0ms (5.4%)

rewrite14.0ms (0.2%)

simplify109.0ms (1.9%)

prune121.0ms (2.1%)

localize12.0ms (0.2%)

series332.0ms (5.8%)

rewrite13.0ms (0.2%)

simplify124.0ms (2.2%)

prune130.0ms (2.3%)

localize13.0ms (0.2%)

series79.0ms (1.4%)

rewrite19.0ms (0.3%)

simplify120.0ms (2.1%)

prune139.0ms (2.4%)

localize13.0ms (0.2%)

series48.0ms (0.8%)

rewrite15.0ms (0.3%)

simplify80.0ms (1.4%)

prune120.0ms (2.1%)

regimes1.1s (19.3%)

simplify3.0ms (0%)

end132.0ms (2.3%)

Profiling