Details

analyze71.0ms (1.3%)

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)

sample1.8s (32.4%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 72 to 60 computations (16.7% saved)

preprocess77.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

545×	`*-commutative_binary64`
493×	`associate-l_binary64`
470×	`sqr-pow_binary64`
416×	`unswap-sqr_binary64`
325×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	48
1	59	48
2	110	48
3	207	48
4	495	48
5	1512	48
6	2056	48
7	2701	48
8	2820	48
9	2994	48
10	3213	48
11	3545	48
12	4005	48
13	4604	48
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 19 computations (9.5% saved)

simplify51.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

818×	`unswap-sqr_binary64`
500×	`sqr-pow_binary64`
281×	`cube-prod_binary64`
277×	`*-commutative_binary64`
242×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	24
1	38	24
2	65	24
3	114	24
4	255	24
5	739	24
6	1007	24
7	1337	24
8	2621	24
9	2723	24
10	2884	24
11	3093	24
12	3400	24
13	3828	24
14	4392	24

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(+.f64 (.f64 (.f64 (/.f64 1 6) (pow.f64 (.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (.f64 (*.f64 2 (PI.f64)) u2))) 1/2)
▶	0.4b	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) 1/2)

Status

Error

Program

0.4b

(+.f64 (*.f64 (*.f64 (/.f64 1 6) (pow.f64 (*.f64 -2 (log.f64 u1)) 1/2)) (cos.f64 (*.f64 (*.f64 2 (PI.f64)) u2))) 1/2)

▶

0.4b

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

Compiler

Compiled 112 to 98 computations (12.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/6 (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))))
✓	0.1b	(sqrt.f64 (*.f64 -2 (log.f64 u1)))
✓	0.2b	(*.f64 (PI.f64) u2)
✓	0.4b	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) 1/2)

series179.0ms (3.3%)

Counts

4 → 36

Calls

15 calls:

53.0ms	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) 1/2)	u2	inf
52.0ms	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) 1/2)	u2	-inf
15.0ms	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) 1/2)	u1	inf
14.0ms	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) 1/2)	u1	0
11.0ms	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 2 (.f64 (PI.f64) u2)))) 1/2)	u1	-inf

rewrite56.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`prod-diff_binary64`
276×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
147×	`add-log-exp_binary64`
146×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	50
1	324	50
2	3635	50

Stop Event

1×	node limit

Counts

4 → 76

simplify40.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`
423×	`distribute-lft-neg-in_binary64`
387×	`associate-l_binary64`
351×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	952
1	231	900
2	643	838
3	2796	824

Stop Event

1×	node limit

Counts

112 → 101

prune122.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	6	103

Error

Counts

103 → 6

Alt Table

Status	Error	Program
	0.7b	(cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))) 1/2) 3))
	0.6b	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (exp.f64 (log.f64 (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))))) 1/2)
▶	0.3b	(+.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) (sqrt.f64 2)))))
	0.8b	(pow.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))) 1/2) 3) 1/3)
	0.6b	(/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64)))))) 3) 1/8) (+.f64 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64)))))) (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))))) (-.f64 1/4 (.f64 (.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64)))))) 1/2))))
	0.5b	(exp.f64 (log.f64 (fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))) 1/2)))

Compiler

Compiled 2426 to 1849 computations (23.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series404.0ms (7.4%)

Counts

4 → 68

Calls

18 calls:

126.0ms	(.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (.f64 (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))) (sqrt.f64 2)))	u2	-inf
61.0ms	(.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) (sqrt.f64 2))))	u2	inf
60.0ms	(.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) (sqrt.f64 2))))	u2	-inf
57.0ms	(.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (.f64 (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))) (sqrt.f64 2)))	u2	inf
12.0ms	(.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) (sqrt.f64 2))))	u1	inf

rewrite57.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`prod-diff_binary64`
164×	`add-sqr-sqrt_binary64`
153×	`add-log-exp_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	63
1	346	63
2	4007	63

Stop Event

1×	node limit

Counts

4 → 66

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-neg_binary64`
641×	`associate-l_binary64`
479×	`distribute-lft-neg-in_binary64`
467×	`distribute-rgt-neg-in_binary64`
278×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1664
1	249	1614
2	847	1553
3	2953	1543

Stop Event

1×	node limit

Counts

134 → 96

prune92.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Error

Counts

102 → 5

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) (sqrt.f64 2)))))
	0.4b	(+.f64 1/2 (.f64 1/6 (sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) 2))))))
	0.6b	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (exp.f64 (log.f64 (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))))) 1/2)
	0.8b	(pow.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))) 1/2) 3) 1/3)
▶	0.3b	(+.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) 1/6))))

Compiler

Compiled 2434 to 1806 computations (25.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series300.0ms (5.5%)

Counts

3 → 56

Calls

15 calls:

52.0ms	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) 1/6)))	u2	inf
50.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 1/6))	u2	-inf
49.0ms	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) 1/6)))	u2	-inf
48.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (.f64 (PI.f64) u2))) 1/6))	u2	inf
13.0ms	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) 1/6)))	u1	-inf

rewrite56.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`prod-diff_binary64`
268×	`log1p-udef_binary64`
160×	`add-sqr-sqrt_binary64`
155×	`associate-r_binary64`
150×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	56
1	330	48
2	3953	48

Stop Event

1×	node limit

Counts

3 → 55

simplify50.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

983×	`fma-neg_binary64`
648×	`distribute-rgt-neg-in_binary64`
600×	`associate-l_binary64`
560×	`associate-r_binary64`
211×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1526
1	234	1518
2	705	1442
3	3428	1430

Stop Event

1×	node limit

Counts

111 → 85

prune69.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	100	5	105

Error

Counts

105 → 5

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) (sqrt.f64 2)))))
▶	0.4b	(+.f64 1/2 (.f64 1/6 (sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) 2))))))
	0.6b	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (exp.f64 (log.f64 (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))))) 1/2)
	0.8b	(pow.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))) 1/2) 3) 1/3)
✓	0.3b	(+.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) 1/6))))

Compiler

Compiled 2378 to 1683 computations (29.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (.f64 1/6 (sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) 2))))))
✓	0.1b	(sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))) 2))))
	0.2b	(*.f64 u2 (PI.f64))
✓	0.4b	(.f64 1/6 (sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) 2)))))

series476.0ms (8.7%)

Counts

3 → 72

Calls

18 calls:

53.0ms	(+.f64 1/2 (.f64 1/6 (sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) 2))))))	u2	-inf
53.0ms	(+.f64 1/2 (.f64 1/6 (sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) 2))))))	u2	inf
53.0ms	(.f64 1/6 (sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) 2)))))	u2	inf
52.0ms	(.f64 1/6 (sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) 2)))))	u2	-inf
51.0ms	(sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (.f64 u2 (PI.f64)))) 2))))	u2	inf

rewrite67.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

695×	`prod-diff_binary64`
186×	`add-sqr-sqrt_binary64`
177×	`log1p-expm1-u_binary64`
177×	`expm1-log1p-u_binary64`
174×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	84
1	385	67
2	4702	67

Stop Event

1×	node limit

Counts

3 → 74

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Rules

854×	`times-frac_binary64`
624×	`associate-/l*_binary64`
383×	`associate-/r*_binary64`
256×	`fma-def_binary64`
180×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	2756
1	383	2710
2	1409	2648

Stop Event

1×	node limit

Counts

146 → 114

prune103.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	130	5	135

Error

Counts

135 → 5

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 1/2 (.f64 1/6 (.f64 (sqrt.f64 (log.f64 (/.f64 1 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) (sqrt.f64 2)))))
✓	0.4b	(+.f64 1/2 (.f64 1/6 (sqrt.f64 (.f64 (neg.f64 (log.f64 u1)) (.f64 2 (pow.f64 (cos.f64 (.f64 2 (*.f64 u2 (PI.f64)))) 2))))))
	0.6b	(fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (exp.f64 (log.f64 (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))))) 1/2)
	0.8b	(pow.f64 (pow.f64 (fma.f64 (sqrt.f64 (.f64 -2 (log.f64 u1))) (.f64 1/6 (cos.f64 (.f64 u2 (.f64 2 (PI.f64))))) 1/2) 3) 1/3)
✓	0.3b	(+.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (neg.f64 (log.f64 u1))) (.f64 (cos.f64 (.f64 2 (*.f64 (PI.f64) u2))) 1/6))))

Compiler

Compiled 4001 to 2892 computations (27.7% saved)

regimes1.1s (20.9%)

Accuracy

Total 0.3b remaining (97.8%)

Threshold costs 0.3b (97.8%)

Counts

92 → 1

Compiler

Compiled 20856 to 18524 computations (11.2% saved)

simplify2.0ms (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	17	28
1	25	28
2	27	28
3	28	28

Stop Event

1×

saturated

end108.0ms (2%)

Stop Event

1×

fuel

Compiler

Compiled 140 to 126 computations (10% saved)

Details

analyze71.0ms (1.3%)

sample1.8s (32.4%)

preprocess77.0ms (1.4%)

simplify51.0ms (0.9%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series179.0ms (3.3%)

rewrite56.0ms (1%)

simplify40.0ms (0.7%)

prune122.0ms (2.2%)

localize13.0ms (0.2%)

series404.0ms (7.4%)

rewrite57.0ms (1%)

simplify57.0ms (1%)

prune92.0ms (1.7%)

localize14.0ms (0.3%)

series300.0ms (5.5%)

rewrite56.0ms (1%)

simplify50.0ms (0.9%)

prune69.0ms (1.3%)

localize13.0ms (0.2%)

series476.0ms (8.7%)

rewrite67.0ms (1.2%)

simplify56.0ms (1%)

prune103.0ms (1.9%)

regimes1.1s (20.9%)

simplify2.0ms (0%)

end108.0ms (2%)

Profiling