Details

analyze2.7s (16%)

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
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

Compiler

Compiled 29 to 22 computations (24.1% saved)

sample5.2s (30.4%)

Results

2.7s	2846×	body	1024	valid
872.0ms	3613×	body	128	valid
750.0ms	1161×	body	512	valid
343.0ms	1488×	body	128	invalid
264.0ms	626×	body	256	valid
83.0ms	137×	body	512	invalid
64.0ms	114×	body	256	invalid
42.0ms	50×	body	1024	invalid
17.0ms	10×	body	2048	valid

Compiler

Compiled 86 to 65 computations (24.4% saved)

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

627×	`distribute-rgt-in_binary64`
623×	`distribute-lft-in_binary64`
431×	`associate-/r/_binary64`
404×	`associate-/r*_binary64`
395×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	54	35
2	181	35
3	898	35
4	3262	35
5	4861	35
6	4933	35
7	5155	35

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

38.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	38.5b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

Compiler

Compiled 103 to 71 computations (31.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.2b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
✓	4.3b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
✓	16.4b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
✓	18.7b	(/.f64 (pow.f64 t 3) (*.f64 l l))

series422.0ms (2.5%)

Counts

4 → 132

Calls

4 calls:

188.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
123.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
78.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
32.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-exp-log_binary64`
58×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
28×	`times-frac_binary64`
26×	`add-sqr-sqrt_binary64`

Counts

4 → 167

Calls

4 calls:

18.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
11.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
7.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
5.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify190.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
569×	`associate-l_binary64`
436×	`associate-r_binary64`
248×	`*-commutative_binary64`
210×	`log-prod_binary64`

Counts

299 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	7807
1	869	7006
2	3862	6945
3	4830	6945
4	5036	6945

prune356.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	223	12	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	224	12	236

Error

14.8b

Counts

236 → 12

Alt Table

Status	Error	Program
	33.9b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	44.1b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) l) (.f64 (sin.f64 k) (/.f64 (*.f64 t (sqrt.f64 t)) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	38.9b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (pow.f64 t 3) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 l l)))
	57.0b	(/.f64 2 (exp.f64 (+.f64 (+.f64 (+.f64 (-.f64 (.f64 (log.f64 t) 3) (log.f64 (.f64 l l))) (log.f64 (sin.f64 k))) (log.f64 (tan.f64 k))) (log.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	47.0b	(/.f64 2 (fma.f64 (/.f64 t l) (/.f64 (pow.f64 k 4) l) (fma.f64 1/3 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 4)) (.f64 l l)) (fma.f64 31/180 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 6)) (.f64 l l)) (fma.f64 2 (/.f64 (.f64 (pow.f64 t 3) (.f64 k k)) (.f64 l l)) (.f64 1/6 (/.f64 (.f64 t (pow.f64 k 6)) (.f64 l l))))))))
	58.8b	(/.f64 2 (.f64 (exp.f64 (+.f64 (+.f64 (-.f64 (.f64 (log.f64 t) 3) (+.f64 (log.f64 l) (log.f64 l))) (log.f64 (sin.f64 k))) (log.f64 (tan.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	41.4b	(/.f64 2 (.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) 3)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	44.1b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	33.8b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 1 l) (.f64 (/.f64 (pow.f64 t 3) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	48.7b	(/.f64 2 (.f64 (.f64 (.f64 (exp.f64 (-.f64 (.f64 (log.f64 t) 3) (log.f64 (*.f64 l l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	51.6b	(/.f64 2 (.f64 (.f64 (.f64 (exp.f64 (-.f64 (.f64 (log.f64 t) 3) (+.f64 (log.f64 l) (log.f64 l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
▶	29.4b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

Compiler

Compiled 8527 to 4818 computations (43.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.2b	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
✓	3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	9.2b	(/.f64 (*.f64 t t) l)
✓	16.4b	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series342.0ms (2%)

Counts

4 → 132

Calls

4 calls:

191.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
118.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
20.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
12.0ms	(/.f64 (*.f64 t t) l)

rewrite62.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`add-cbrt-cube_binary64`
120×	`add-exp-log_binary64`
70×	`cbrt-unprod_binary64`
70×	`prod-exp_binary64`
44×	`associate-*l/_binary64`

Counts

4 → 167

Calls

4 calls:

18.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
11.0ms	(.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
5.0ms	(*.f64 (/.f64 t l) (sin.f64 k))
5.0ms	(/.f64 (*.f64 t t) l)

simplify234.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-def_binary64`
668×	`associate-r_binary64`
357×	`*-commutative_binary64`
255×	`associate-*l/_binary64`
183×	`distribute-rgt-in_binary64`

Counts

299 → 266

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	366	8901
1	1100	7091
2	3652	7057
3	4718	7057
4	4971	7057
5	4931	7057

prune387.0ms (2.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	258	8	266
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	264	14	278

Error

10.6b

Counts

278 → 14

Alt Table

Status	Error	Program
	33.9b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
▶	21.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	37.7b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t t) (.f64 t (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 l l)))
	21.9b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	58.8b	(/.f64 2 (.f64 (exp.f64 (+.f64 (+.f64 (-.f64 (.f64 (log.f64 t) 3) (+.f64 (log.f64 l) (log.f64 l))) (log.f64 (sin.f64 k))) (log.f64 (tan.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	22.1b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 t (cbrt.f64 l))) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	48.7b	(/.f64 2 (.f64 (.f64 (.f64 (exp.f64 (-.f64 (.f64 (log.f64 t) 3) (log.f64 (*.f64 l l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	30.0b	(/.f64 2 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 (*.f64 t (sin.f64 k)) l) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	57.0b	(/.f64 2 (exp.f64 (+.f64 (+.f64 (+.f64 (-.f64 (.f64 (log.f64 t) 3) (log.f64 (.f64 l l))) (log.f64 (sin.f64 k))) (log.f64 (tan.f64 k))) (log.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	47.0b	(/.f64 2 (fma.f64 (/.f64 t l) (/.f64 (pow.f64 k 4) l) (fma.f64 1/3 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 4)) (.f64 l l)) (fma.f64 31/180 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 6)) (.f64 l l)) (fma.f64 2 (/.f64 (.f64 (pow.f64 t 3) (.f64 k k)) (.f64 l l)) (.f64 1/6 (/.f64 (.f64 t (pow.f64 k 6)) (.f64 l l))))))))
	29.1b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 t (sin.f64 k))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 l (cos.f64 k))))
	44.1b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t (/.f64 3 2)) l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	58.0b	(/.f64 2 (exp.f64 (+.f64 (+.f64 (+.f64 (-.f64 (log.f64 (.f64 t t)) (log.f64 l)) (log.f64 (.f64 (/.f64 t l) (sin.f64 k)))) (log.f64 (tan.f64 k))) (log.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	29.5b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))) (*.f64 (cbrt.f64 (/.f64 t l)) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

Compiler

Compiled 10522 to 4511 computations (57.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.5b	(.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k)))
✓	3.2b	(.f64 (.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
	3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	16.4b	(.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series380.0ms (2.2%)

Counts

3 → 108

Calls

3 calls:

189.0ms

(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

119.0ms

(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))

72.0ms

(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))

rewrite86.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-cbrt-cube_binary64`
145×	`add-exp-log_binary64`
76×	`cbrt-unprod_binary64`
76×	`prod-exp_binary64`
66×	`times-frac_binary64`

Counts

3 → 188

Calls

3 calls:

24.0ms

(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

15.0ms

(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k)))

12.0ms

(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))

simplify183.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
546×	`*-commutative_binary64`
533×	`distribute-rgt-in_binary64`
350×	`associate-*l/_binary64`
220×	`associate-/l*_binary64`

Counts

296 → 325

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	415	10198
1	1359	8093
2	3659	8029
3	5190	8029

prune651.0ms (3.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	381	6	387
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	387	14	401

Error

7.7b

Counts

401 → 14

Alt Table

Status	Error	Program
	20.5b	(/.f64 2 (.f64 (.f64 (/.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (/.f64 l t)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	47.0b	(/.f64 2 (fma.f64 (/.f64 t l) (/.f64 (pow.f64 k 4) l) (fma.f64 1/3 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 4)) (.f64 l l)) (fma.f64 31/180 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 6)) (.f64 l l)) (fma.f64 2 (/.f64 (.f64 (pow.f64 t 3) (.f64 k k)) (.f64 l l)) (.f64 1/6 (/.f64 (.f64 t (pow.f64 k 6)) (.f64 l l))))))))
	37.7b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t t) (.f64 t (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 l l)))
	21.9b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	20.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 1) (.f64 (/.f64 (cbrt.f64 t) (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	28.3b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 t (.f64 t (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 l t) l)))
	48.7b	(/.f64 2 (.f64 (.f64 (.f64 (exp.f64 (-.f64 (.f64 (log.f64 t) 3) (log.f64 (*.f64 l l)))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	30.0b	(/.f64 2 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (/.f64 (*.f64 t (sin.f64 k)) l) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	40.3b	(/.f64 2 (.f64 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (sqrt.f64 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	33.9b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	21.7b	(/.f64 2 (.f64 (.f64 (/.f64 t (/.f64 l t)) (.f64 (/.f64 t l) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
▶	16.6b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t)))
	58.0b	(/.f64 2 (exp.f64 (+.f64 (+.f64 (+.f64 (-.f64 (log.f64 (.f64 t t)) (log.f64 l)) (log.f64 (.f64 (/.f64 t l) (sin.f64 k)))) (log.f64 (tan.f64 k))) (log.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	29.5b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))) (*.f64 (cbrt.f64 (/.f64 t l)) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

Compiler

Compiled 15008 to 6045 computations (59.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.2b	(.f64 (.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
	3.5b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	5.4b	(/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t))
✓	14.4b	(.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series443.0ms (2.6%)

Counts

3 → 108

Calls

3 calls:

198.0ms

(/.f64 (*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t))

164.0ms

(*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

81.0ms

(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))

rewrite70.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-cbrt-cube_binary64`
97×	`add-exp-log_binary64`
51×	`cbrt-unprod_binary64`
51×	`prod-exp_binary64`
31×	`times-frac_binary64`

Counts

3 → 145

Calls

3 calls:

19.0ms

(/.f64 (*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t))

15.0ms

(*.f64 (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

9.0ms

(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))

simplify178.0ms (1%)

Algorithm

1×	egg-herbie

Rules

650×	`associate-l_binary64`
568×	`associate-/l*_binary64`
544×	`fma-def_binary64`
310×	`times-frac_binary64`
205×	`associate-*l/_binary64`

Counts

253 → 277

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	376	9901
1	1170	8597
2	4943	8586
3	5331	8586

prune533.0ms (3.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	331	8	339
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	340	13	353

Error

6.4b

Counts

353 → 13

Alt Table

Status	Error	Program
	37.7b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (.f64 t t) (.f64 t (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (.f64 l l)))
	21.9b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (/.f64 t l)) (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	16.6b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 l t)))
	16.1b	(/.f64 2 (/.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (/.f64 l t)))
	58.0b	(/.f64 2 (exp.f64 (+.f64 (+.f64 (+.f64 (-.f64 (log.f64 (.f64 t t)) (log.f64 l)) (log.f64 (.f64 (/.f64 t l) (sin.f64 k)))) (log.f64 (tan.f64 k))) (log.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	17.0b	(/.f64 2 (/.f64 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 (.f64 (cbrt.f64 l) (cbrt.f64 l)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 (cbrt.f64 l) (cbrt.f64 t))))
	33.3b	(/.f64 2 (/.f64 (/.f64 (.f64 (pow.f64 k 2) (pow.f64 (sin.f64 k) 2)) (.f64 (cos.f64 k) l)) (/.f64 l t)))
	33.9b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	17.8b	(/.f64 2 (/.f64 (.f64 t (.f64 (.f64 (.f64 (sin.f64 k) (/.f64 t l)) (tan.f64 k)) (fma.f64 -1 (pow.f64 (/.f64 k t) 2) -2))) (neg.f64 (/.f64 l t))))
	23.5b	(/.f64 2 (/.f64 (/.f64 (fma.f64 2 (/.f64 (.f64 (pow.f64 (sin.f64 k) 2) (.f64 t t)) (cos.f64 k)) (/.f64 (.f64 (.f64 k k) (pow.f64 (sin.f64 k) 2)) (cos.f64 k))) l) (/.f64 l t)))
	18.9b	(/.f64 2 (/.f64 (/.f64 (.f64 (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 1 (*.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 l (cbrt.f64 t))))
	29.5b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) l) (.f64 (.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))) (*.f64 (cbrt.f64 (/.f64 t l)) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	20.1b	(/.f64 2 (.f64 (/.f64 (.f64 (.f64 t (.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) l) (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) t)))

Compiler

Compiled 12706 to 5150 computations (59.5% saved)

regimes3.9s (23%)

Accuracy

Total 3.0b remaining (31.6%)

Threshold costs 0b (0%)

Counts

282 → 3

Compiler

Compiled 60501 to 40618 computations (32.9% saved)

bsearch227.0ms (1.3%)

Steps

Iters	Range		Point
9	1.512015767100139e-107	1.8892892975381577e-101	1.8046842859133757e-101
8	-5.106592599962365e-30	-1.4512887639072254e-34	-3.85670269519708e-32

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	137
1	55	137
2	55	137

end264.0ms (1.6%)

Compiler: Compiled 587 to 374 computations (36.3% saved)

Details

analyze2.7s (16%)

sample5.2s (30.4%)

simplify56.0ms (0.3%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series422.0ms (2.5%)

rewrite56.0ms (0.3%)

simplify190.0ms (1.1%)

prune356.0ms (2.1%)

localize16.0ms (0.1%)

series342.0ms (2%)

rewrite62.0ms (0.4%)

simplify234.0ms (1.4%)

prune387.0ms (2.3%)

localize16.0ms (0.1%)

series380.0ms (2.2%)

rewrite86.0ms (0.5%)

simplify183.0ms (1.1%)

prune651.0ms (3.8%)

localize17.0ms (0.1%)

series443.0ms (2.6%)

rewrite70.0ms (0.4%)

simplify178.0ms (1%)

prune533.0ms (3.1%)

regimes3.9s (23%)

bsearch227.0ms (1.3%)

simplify5.0ms (0%)

end264.0ms (1.6%)

Profiling