Details

analyze2.9s (14.3%)

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)

sample5.4s (26.4%)

Results

2.7s	2735×	body	1024	valid
922.0ms	3529×	body	128	valid
916.0ms	1368×	body	512	valid
355.0ms	1436×	body	128	invalid
278.0ms	617×	body	256	valid
89.0ms	135×	body	512	invalid
59.0ms	125×	body	256	invalid
51.0ms	52×	body	1024	invalid
11.0ms	7×	body	2048	valid

Compiler

Compiled 86 to 65 computations (24.4% saved)

simplify64.0ms (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

32.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.9b	(/.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
✓	2.5b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
✓	4.1b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
✓	13.9b	(.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)))
✓	15.7b	(/.f64 (pow.f64 t 3) (*.f64 l l))

series459.0ms (2.2%)

Counts

4 → 132

Calls

4 calls:

211.0ms	(.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)))
132.0ms	(.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))
38.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite61.0ms (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))
9.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
5.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify206.0ms (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

prune428.0ms (2.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	217	18	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	218	18	236

Error

12.8b

Counts

236 → 18

Alt Table

Status	Error	Program
	29.6b	(/.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))))
	41.5b	(/.f64 2 (fma.f64 173/2520 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 8)) (.f64 l l)) (fma.f64 31/360 (/.f64 (.f64 t (pow.f64 k 8)) (.f64 l l)) (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))))))))))
	45.6b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (/.f64 (.f64 t (sqrt.f64 t)) l))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	46.8b	(/.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))))
	27.8b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (.f64 t t) (/.f64 l (/.f64 t l))) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	23.2b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) 3) l) (*.f64 (/.f64 (pow.f64 (cbrt.f64 t) 3) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	60.3b	(/.f64 2 (exp.f64 (+.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))) (log.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	57.8b	(/.f64 2 (.f64 (exp.f64 (+.f64 (+.f64 (-.f64 (.f64 (log.f64 t) 3) (log.f64 (*.f64 l l))) (log.f64 (sin.f64 k))) (log.f64 (tan.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	59.6b	(/.f64 2 (.f64 (.f64 (exp.f64 (+.f64 (-.f64 (*.f64 (log.f64 t) 3) (+.f64 (log.f64 l) (log.f64 l))) (log.f64 (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	34.0b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	55.0b	(/.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))))
	43.2b	(/.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))))
	32.6b	(/.f64 2 (.f64 (.f64 (/.f64 (*.f64 (pow.f64 t 3) (sin.f64 k)) (pow.f64 l 2)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
▶	22.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	22.9b	(/.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))))
	33.0b	(/.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)))
	43.2b	(/.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))))
	36.1b	(/.f64 2 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (.f64 (sin.f64 k) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

Compiler

Compiled 8929 to 5094 computations (42.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.5b	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
✓	4.0b	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
✓	7.0b	(/.f64 (*.f64 t t) l)
✓	13.9b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series357.0ms (1.7%)

Counts

4 → 132

Calls

4 calls:

192.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
123.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
30.0ms	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
12.0ms	(/.f64 (*.f64 t t) l)

rewrite68.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 159

Calls

4 calls:

19.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
15.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k))
6.0ms	(.f64 (/.f64 (.f64 t t) l) (sin.f64 k))
5.0ms	(/.f64 (*.f64 t t) l)

simplify229.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

711×	`fma-def_binary64`
669×	`associate-r_binary64`
348×	`*-commutative_binary64`
241×	`associate-*l/_binary64`
183×	`distribute-rgt-in_binary64`

Counts

291 → 254

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	348	8854
1	1070	7129
2	3638	7095
3	4722	7095
4	4980	7095
5	4933	7095

prune448.0ms (2.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	242	12	254
Fresh	12	5	17
Picked	1	0	1
Done	0	0	0
Total	255	17	272

Error

8.4b

Counts

272 → 17

Alt Table

Status	Error	Program
	17.2b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (.f64 (/.f64 t (cbrt.f64 l)) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	34.7b	(/.f64 2 (/.f64 (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (/.f64 (/.f64 (.f64 (pow.f64 (sin.f64 k) 2) (pow.f64 t 3)) l) l)) (cos.f64 k)))
	48.7b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (fma.f64 (/.f64 (.f64 (.f64 t t) (pow.f64 k 3)) l) -1/6 (/.f64 (.f64 k (*.f64 t t)) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	22.9b	(/.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))))
	17.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (/.f64 l t)) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
▶	17.0b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	34.0b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	22.3b	(/.f64 2 (/.f64 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (*.f64 t t) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) l))
	27.9b	(/.f64 2 (/.f64 (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (tan.f64 k) (/.f64 (*.f64 (sin.f64 k) (pow.f64 t 3)) l))) l))
	41.5b	(/.f64 2 (fma.f64 173/2520 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 8)) (.f64 l l)) (fma.f64 31/360 (/.f64 (.f64 t (pow.f64 k 8)) (.f64 l l)) (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))))))))))
	43.2b	(/.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))))
	46.8b	(/.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))))
	31.4b	(/.f64 2 (.f64 (/.f64 (.f64 (.f64 t (.f64 (.f64 t t) (sin.f64 k))) (tan.f64 k)) (.f64 l l)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	23.0b	(/.f64 2 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (cbrt.f64 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))) (cbrt.f64 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	18.1b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (.f64 (/.f64 t (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 t (cbrt.f64 l))) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	60.3b	(/.f64 2 (exp.f64 (+.f64 (+.f64 (+.f64 (-.f64 (log.f64 t) (log.f64 l)) (+.f64 (-.f64 (+.f64 (log.f64 t) (log.f64 t)) (log.f64 l)) (log.f64 (sin.f64 k)))) (log.f64 (tan.f64 k))) (log.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	42.6b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t (sqrt.f64 l)) (*.f64 (/.f64 t (sqrt.f64 l)) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

Compiler

Compiled 10387 to 4565 computations (56.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
✓	2.5b	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
✓	3.1b	(*.f64 (/.f64 t l) (sin.f64 k))
✓	13.9b	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series637.0ms (3.1%)

Counts

4 → 144

Calls

4 calls:

302.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
190.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
124.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
21.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

rewrite162.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

421×	`add-exp-log_binary64`
304×	`add-cbrt-cube_binary64`
259×	`prod-exp_binary64`
181×	`cbrt-unprod_binary64`
179×	`frac-times_binary64`

Counts

4 → 316

Calls

4 calls:

28.0ms	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
24.0ms	(.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
13.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
7.0ms	(*.f64 (/.f64 t l) (sin.f64 k))

simplify334.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
544×	`associate-/r*_binary64`
462×	`times-frac_binary64`
383×	`associate-/l*_binary64`
229×	`*-commutative_binary64`

Counts

460 → 521

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	673	19026
1	1654	16342
2	4585	16329
3	5011	16329

prune1.0s (4.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	511	10	521
Fresh	11	5	16
Picked	1	0	1
Done	0	0	0
Total	523	15	538

Error

7.6b

Counts

538 → 15

Alt Table

Status	Error	Program
	17.1b	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (sqrt.f64 2)))
	48.7b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (fma.f64 (/.f64 (.f64 (.f64 t t) (pow.f64 k 3)) l) -1/6 (/.f64 (.f64 k (*.f64 t t)) l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	17.0b	(.f64 (/.f64 1 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))
▶	15.9b	(/.f64 2 (.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	17.0b	(.f64 (/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (cos.f64 k))
	17.3b	(.f64 (/.f64 (sqrt.f64 2) (.f64 (.f64 (/.f64 t l) (.f64 t (/.f64 (*.f64 t (sin.f64 k)) l))) (tan.f64 k))) (/.f64 (sqrt.f64 2) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	17.0b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (sqrt.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (sqrt.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
	41.5b	(/.f64 2 (fma.f64 173/2520 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 8)) (.f64 l l)) (fma.f64 31/360 (/.f64 (.f64 t (pow.f64 k 8)) (.f64 l l)) (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))))))))))
	60.3b	(/.f64 2 (exp.f64 (+.f64 (+.f64 (+.f64 (-.f64 (log.f64 t) (log.f64 l)) (+.f64 (-.f64 (+.f64 (log.f64 t) (log.f64 t)) (log.f64 l)) (log.f64 (sin.f64 k)))) (log.f64 (tan.f64 k))) (log.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	31.4b	(.f64 (/.f64 2 (.f64 (+.f64 8 (pow.f64 (pow.f64 (/.f64 k t) 2) 3)) (.f64 (tan.f64 k) (.f64 t (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)))))) (.f64 l (+.f64 (.f64 2 2) (-.f64 (.f64 (pow.f64 (/.f64 k t) 2) (pow.f64 (/.f64 k t) 2)) (.f64 2 (pow.f64 (/.f64 k t) 2))))))
	33.8b	(.f64 2 (/.f64 (.f64 (cos.f64 k) (pow.f64 l 2)) (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))))
	34.0b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	20.8b	(.f64 (/.f64 2 (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (tan.f64 k) (.f64 t (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)))))) l)
	46.8b	(/.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))))
	21.1b	(.f64 (/.f64 2 (.f64 (.f64 (.f64 t (.f64 t (.f64 (/.f64 t l) (sin.f64 k)))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (.f64 (.f64 l 1) (cos.f64 k)))

Compiler

Compiled 22624 to 10471 computations (53.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 (*.f64 t (sin.f64 k)) l)
✓	1.3b	(.f64 (/.f64 t l) (.f64 (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)) (tan.f64 k)))
✓	2.6b	(.f64 (.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)) (tan.f64 k))
✓	13.9b	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

series426.0ms (2.1%)

Counts

4 → 112

Calls

4 calls:

195.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
125.0ms	(.f64 (/.f64 t l) (.f64 (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)) (tan.f64 k)))
83.0ms	(.f64 (.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)) (tan.f64 k))
22.0ms	(/.f64 (*.f64 t (sin.f64 k)) l)

rewrite72.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

125×	`add-cbrt-cube_binary64`
125×	`add-exp-log_binary64`
72×	`cbrt-unprod_binary64`
72×	`prod-exp_binary64`
41×	`associate-*r/_binary64`

Counts

4 → 170

Calls

4 calls:

21.0ms	(.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
13.0ms	(.f64 (/.f64 t l) (.f64 (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)) (tan.f64 k)))
7.0ms	(.f64 (.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)) (tan.f64 k))
3.0ms	(/.f64 (*.f64 t (sin.f64 k)) l)

simplify222.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
620×	`distribute-rgt-in_binary64`
479×	`*-commutative_binary64`
307×	`associate-*l/_binary64`
229×	`associate-/l*_binary64`

Counts

282 → 285

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	9846
1	1204	8164
2	3568	8124
3	4916	8124
4	5209	8124

prune514.0ms (2.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	278	7	285
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	284	16	300

Error

7.3b

Counts

300 → 16

Alt Table

Status	Error	Program
	17.1b	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (sqrt.f64 2)))
	30.9b	(/.f64 2 (fma.f64 2 (/.f64 (.f64 (pow.f64 (sin.f64 k) 2) (pow.f64 t 3)) (.f64 (cos.f64 k) (.f64 l l))) (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (cos.f64 k) (.f64 l l)))))
	17.0b	(.f64 (/.f64 1 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))) (/.f64 2 (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	17.0b	(.f64 (/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (/.f64 t 1) (.f64 (/.f64 t l) (sin.f64 k)))) (sin.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (cos.f64 k))
	60.3b	(/.f64 2 (exp.f64 (+.f64 (+.f64 (-.f64 (log.f64 t) (log.f64 l)) (+.f64 (+.f64 (log.f64 t) (-.f64 (log.f64 (*.f64 t (sin.f64 k))) (log.f64 l))) (log.f64 (tan.f64 k)))) (log.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	17.3b	(.f64 (/.f64 (sqrt.f64 2) (.f64 (.f64 (/.f64 t l) (.f64 t (/.f64 (*.f64 t (sin.f64 k)) l))) (tan.f64 k))) (/.f64 (sqrt.f64 2) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	41.5b	(/.f64 2 (fma.f64 173/2520 (/.f64 (.f64 (pow.f64 t 3) (pow.f64 k 8)) (.f64 l l)) (fma.f64 31/360 (/.f64 (.f64 t (pow.f64 k 8)) (.f64 l l)) (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))))))))))
	15.9b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (sqrt.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)))) (sqrt.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)))))
	46.8b	(/.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))))
	15.7b	(/.f64 2 (.f64 (.f64 (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (.f64 (/.f64 (cbrt.f64 t) (cbrt.f64 l)) (.f64 (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)) (tan.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	36.5b	(/.f64 2 (.f64 (.f64 (/.f64 t l) (fma.f64 1/6 (/.f64 (.f64 (.f64 t t) (pow.f64 k 4)) l) (/.f64 (.f64 (.f64 k k) (*.f64 t t)) l))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	17.9b	(/.f64 2 (.f64 (.f64 t (.f64 (/.f64 1 l) (.f64 (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)) (tan.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	20.8b	(.f64 (/.f64 2 (.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (.f64 (tan.f64 k) (.f64 t (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)))))) l)
	16.1b	(/.f64 2 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)) (tan.f64 k)))) (cbrt.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)) (tan.f64 k))))) (cbrt.f64 (.f64 (/.f64 t l) (.f64 (.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)) (tan.f64 k))))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
	31.4b	(.f64 (/.f64 2 (.f64 (+.f64 8 (pow.f64 (pow.f64 (/.f64 k t) 2) 3)) (.f64 (tan.f64 k) (.f64 t (.f64 t (/.f64 (.f64 t (sin.f64 k)) l)))))) (.f64 l (+.f64 (.f64 2 2) (-.f64 (.f64 (pow.f64 (/.f64 k t) 2) (pow.f64 (/.f64 k t) 2)) (.f64 2 (pow.f64 (/.f64 k t) 2))))))
	33.8b	(.f64 2 (/.f64 (.f64 (cos.f64 k) (pow.f64 l 2)) (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))))

Compiler

Compiled 11054 to 4330 computations (60.8% saved)

regimes5.7s (27.9%)

Accuracy

Total 4.1b remaining (34.9%)

Threshold costs 0b (0%)

Counts

378 → 3

Compiler

Compiled 81199 to 54512 computations (32.9% saved)

bsearch252.0ms (1.2%)

Steps

Iters	Range		Point
10	3.666081356116588e-127	1.7554894801233848e-115	1.0916995414116273e-121
6	-1.8520961261353278e-155	-1.3345886362358392e-156	-1.8241171965154315e-155

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	132
1	58	132
2	57	132

end413.0ms (2%)

Compiler: Compiled 815 to 506 computations (37.9% saved)

Details

analyze2.9s (14.3%)

sample5.4s (26.4%)

simplify64.0ms (0.3%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series459.0ms (2.2%)

rewrite61.0ms (0.3%)

simplify206.0ms (1%)

prune428.0ms (2.1%)

localize18.0ms (0.1%)

series357.0ms (1.7%)

rewrite68.0ms (0.3%)

simplify229.0ms (1.1%)

prune448.0ms (2.2%)

localize18.0ms (0.1%)

series637.0ms (3.1%)

rewrite162.0ms (0.8%)

simplify334.0ms (1.6%)

prune1.0s (4.9%)

localize17.0ms (0.1%)

series426.0ms (2.1%)

rewrite72.0ms (0.4%)

simplify222.0ms (1.1%)

prune514.0ms (2.5%)

regimes5.7s (27.9%)

bsearch252.0ms (1.2%)

simplify4.0ms (0%)

end413.0ms (2%)

Profiling