Details

analyze1.8s (14.5%)

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
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample4.0s (33.2%)

Results

1.9s	3615×	body	1024	valid
1.1s	1235×	body	2048	valid
594.0ms	1427×	body	512	valid
222.0ms	1352×	body	128	valid
163.0ms	624×	body	256	valid
4.0ms	3×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

37.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	37.5b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.2b	(tan.f64 (+.f64 x eps))

series92.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

51.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
41.0ms	(tan.f64 (+.f64 x eps))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 43

Calls

2 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	(tan.f64 (+.f64 x eps))

simplify112.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

936×	`fma-def_binary64`
909×	`times-frac_binary64`
194×	`associate-+r+_binary64`
142×	`unswap-sqr_binary64`
125×	`+-commutative_binary64`

Counts

91 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	2570
1	507	2289
2	1787	2148
3	4965	2145
4	4986	2145
5	4943	2145

prune208.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	6	94

Error

0.2b

Counts

94 → 6

Alt Table

Status	Error	Program
	38.9b	(-.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) x x)) (tan.f64 x))
	23.6b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
▶	23.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	31.1b	(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (.f64 2/3 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	30.9b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
	30.3b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)

Compiler

Compiled 2895 to 1193 computations (58.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
✓	0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
✓	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	2.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series566.0ms (4.7%)

Counts

4 → 96

Calls

4 calls:

318.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
175.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
40.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
33.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`*-un-lft-identity_binary64`
74×	`add-sqr-sqrt_binary64`
67×	`add-cube-cbrt_binary64`
61×	`times-frac_binary64`
54×	`prod-diff_binary64`

Counts

4 → 171

Calls

4 calls:

13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
8.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify241.0ms (2%)

Algorithm

1×	egg-herbie

Rules

228×	`unswap-sqr_binary64`
225×	`associate-+r+_binary64`
225×	`distribute-rgt-in_binary64`
203×	`distribute-lft-in_binary64`
184×	`associate-l_binary64`

Counts

267 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	10657
1	925	9025
2	3170	8501
3	4767	8501
4	4923	8501

prune283.0ms (2.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	235	10	245
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	238	13	251

Error

0.1b

Counts

251 → 13

Alt Table

Status	Error	Program
	23.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (tan.f64 x)) (.f64 (*.f64 (tan.f64 eps) (tan.f64 eps)) (tan.f64 eps)))))) (tan.f64 x))
	24.2b	(+.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (neg.f64 (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))) (cbrt.f64 (tan.f64 x))))
	30.9b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
	23.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
	23.8b	(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	24.6b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	28.5b	(-.f64 (cbrt.f64 (/.f64 (.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	28.5b	(cbrt.f64 (.f64 (.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))) (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
▶	23.6b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x))) 0)
	31.1b	(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (.f64 2/3 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	30.3b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	27.8b	(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
	23.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (tan.f64 x))

Compiler

Compiled 9705 to 3338 computations (65.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
✓	2.8b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x)))

series773.0ms (6.4%)

Counts

2 → 48

Calls

2 calls:

684.0ms

(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x)))

89.0ms

(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`
5×	`pow1_binary64`
4×	`tan-quot_binary64`
3×	`cube-div_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms

(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)

0.0ms

(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x)))

simplify156.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-def_binary64`
371×	`unswap-sqr_binary64`
275×	`times-frac_binary64`
184×	`associate-r_binary64`
179×	`associate-/l*_binary64`

Counts

85 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	7508
1	630	7272
2	2999	7156
3	5018	7156

prune292.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	199	10	209

Error

0.1b

Counts

209 → 10

Alt Table

Status	Error	Program
	30.9b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
	23.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
	23.6b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 eps)) 3) (pow.f64 (cos.f64 x) 3)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x))) 0)
	27.8b	(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
▶	23.6b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x))) 0)
	28.5b	(cbrt.f64 (.f64 (.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))) (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
	24.2b	(+.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (neg.f64 (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))) (cbrt.f64 (tan.f64 x))))
	31.1b	(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (.f64 2/3 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	30.3b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	23.8b	(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))

Compiler

Compiled 9992 to 4210 computations (57.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	0.4b	(pow.f64 (tan.f64 eps) 3)
✓	0.4b	(pow.f64 (tan.f64 x) 3)
✓	2.8b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x)))

series654.0ms (5.4%)

Counts

3 → 48

Calls

3 calls:

619.0ms

(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x)))

18.0ms

(pow.f64 (tan.f64 eps) 3)

16.0ms

(pow.f64 (tan.f64 x) 3)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`
6×	`pow-unpow_binary64`

Counts

3 → 62

Calls

3 calls:

2.0ms

(pow.f64 (tan.f64 x) 3)

2.0ms

(pow.f64 (tan.f64 eps) 3)

0.0ms

(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x)))

simplify178.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
176×	`times-frac_binary64`
173×	`exp-prod_binary64`
164×	`log-prod_binary64`
162×	`associate-r_binary64`

Counts

110 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	7747
1	614	7504
2	2630	6491
3	4713	6491
4	4922	6491

prune220.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	140	11	151

Error

0.1b

Counts

151 → 11

Alt Table

Status	Error	Program
	30.9b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
	23.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
	24.3b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x)))) (cbrt.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x))))) (cbrt.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x))))) 0)
	30.3b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	23.6b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 eps)) 3) (pow.f64 (cos.f64 x) 3)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x))) 0)
	27.8b	(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
✓	23.6b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x))) 0)
	28.5b	(cbrt.f64 (.f64 (.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))) (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
	24.2b	(+.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (neg.f64 (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))) (cbrt.f64 (tan.f64 x))))
	31.1b	(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (.f64 2/3 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	23.8b	(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))

Compiler

Compiled 7112 to 3356 computations (52.8% saved)

regimes2.0s (16.4%)

Accuracy

Total 0.3b remaining (71.4%)

Threshold costs 0.3b (71.4%)

Counts

206 → 3

Compiler

Compiled 19212 to 10478 computations (45.5% saved)

bsearch110.0ms (0.9%)

Steps

Iters	Range		Point
9	8.178505827834829e-18	8.675503229523435e-11	8.542991026995156e-11
10	-0.005325734951448651	-9.496283164410029e-14	-3.511738504762205e-9

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	109
1	52	107
2	63	107
3	70	107
4	74	107
5	75	107
6	73	107

end324.0ms (2.7%)

Compiler: Compiled 647 to 346 computations (46.5% saved)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Details

analyze1.8s (14.5%)

sample4.0s (33.2%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series92.0ms (0.8%)

rewrite14.0ms (0.1%)

simplify112.0ms (0.9%)

prune208.0ms (1.7%)

localize10.0ms (0.1%)

series566.0ms (4.7%)

rewrite48.0ms (0.4%)

simplify241.0ms (2%)

prune283.0ms (2.3%)

localize20.0ms (0.2%)

series773.0ms (6.4%)

rewrite6.0ms (0.1%)

simplify156.0ms (1.3%)

prune292.0ms (2.4%)

localize21.0ms (0.2%)

series654.0ms (5.4%)

rewrite7.0ms (0.1%)

simplify178.0ms (1.5%)

prune220.0ms (1.8%)

regimes2.0s (16.4%)

bsearch110.0ms (0.9%)

simplify5.0ms (0%)

end324.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11