Details

analyze121.0ms (3.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	1.6%	48.5%	9
50.4%	1.2%	48.5%	10
50.4%	1.2%	48.5%	11
50.4%	1.1%	48.6%	12
50.4%	1%	48.6%	13
50.5%	0.9%	48.6%	14

Compiler

Compiled 15 to 8 computations (46.7% saved)

sample56.0ms (1.6%)

Algorithm

1×

intervals

Results

31.0ms	127×	body	1024	valid
9.0ms	64×	body	512	valid
4.0ms	13×	body	2048	valid
2.0ms	25×	body	256	valid
1.0ms	27×	body	128	valid

Compiler

Compiled 30 to 16 computations (46.7% saved)

simplify76.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

464×	`times-frac_binary64`
407×	`neg-mul-1_binary64`
388×	`neg-sub0_binary64` `associate-/r/_binary64`
311×	`associate-/l/_binary64`
286×	`unswap-sqr_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	20	22
2	34	22
3	57	22
4	116	22
5	263	22
6	561	22
7	1419	22
8	3334	22
9	4405	22
10	4797	22

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

58.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	58.9b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 28 to 14 computations (50% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.5b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
6.2b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite54.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

44×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64` `times-frac_binary64`
16×	`add-cube-cbrt_binary64`
7×	`sinh-undef_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `cosh-undef_binary64` `distribute-lft-out_binary64`
6×	`associate-/l*_binary64`

Counts

2 → 76

Calls

2 calls:

12.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
5.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 1465 to 231 computations (84.2% saved)

series42.0ms (1.2%)

Error

1.3b

Counts

2 → 12

Calls

2 calls:

19.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
11.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 401 to 259 computations (35.4% saved)

simplify138.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

756×	`div-sub_binary64`
320×	`cancel-sign-sub-inv_binary64`
201×	`unswap-sqr_binary64`
195×	`exp-prod_binary64`
186×	`cube-prod_binary64`

Counts

88 → 48

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	148	2388
1	346	2245
2	826	2236
3	2341	2236
4	3884	2223
5	5304	2223

prune34.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Error

0.7b

Counts

49 → 4

Alt Table

Status	Error	Program
	1.7b	(/.f64 (+.f64 (+.f64 x x) (+.f64 (+.f64 (.f64 1/3 (pow.f64 x 3)) (.f64 1/60 (pow.f64 x 5))) (*.f64 1/2520 (pow.f64 x 7)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
	1.8b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
	58.1b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
▶	1.5b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 792 to 330 computations (58.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sinh.f64 x)
1.5b	(/.f64 (sinh.f64 x) (cosh.f64 x))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`times-frac_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l_binary64` `associate-/r_binary64`
2×	`pow1_binary64` `add-log-exp_binary64` `sinh-def_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
1.0ms	(sinh.f64 x)

Compiler

Compiled 420 to 117 computations (72.1% saved)

series51.0ms (1.4%)

Error

0.7b

Counts

2 → 12

Calls

2 calls:

26.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
12.0ms	(sinh.f64 x)

Compiler

Compiled 354 to 241 computations (31.9% saved)

simplify93.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/l/_binary64`
536×	`times-frac_binary64`
430×	`associate-/l*_binary64`
354×	`associate-/r/_binary64`
248×	`cancel-sign-sub-inv_binary64`

Counts

49 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	98	714
1	194	673
2	494	673
3	1285	627
4	4051	615
5	4735	615
6	4874	615

prune20.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	18	1	19
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	19	4	23

Error

0.7b

Counts

23 → 4

Alt Table

Status	Error	Program
▶	1.7b	(/.f64 (+.f64 x (+.f64 (+.f64 (.f64 (pow.f64 x 3) 1/6) (.f64 (pow.f64 x 5) 1/120)) (*.f64 (pow.f64 x 7) 1/5040))) (cosh.f64 x))
	1.8b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
	58.1b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
✓	1.5b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 293 to 188 computations (35.8% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 (pow.f64 x 3) 1/6) (.f64 (pow.f64 x 5) 1/120)) (*.f64 (pow.f64 x 7) 1/5040))
0.0b	(*.f64 (pow.f64 x 7) 1/5040)
0.0b	(*.f64 (pow.f64 x 5) 1/120)
0.1b	(*.f64 (pow.f64 x 3) 1/6)

rewrite165.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

31×	`add-sqr-sqrt_binary64`
26×	`associate-l_binary64`
19×	`add-exp-log_binary64`
14×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
12×	`unpow-prod-down_binary64`

Counts

4 → 94

Calls

4 calls:

9.0ms	(+.f64 (+.f64 (.f64 (pow.f64 x 3) 1/6) (.f64 (pow.f64 x 5) 1/120)) (*.f64 (pow.f64 x 7) 1/5040))
7.0ms	(*.f64 (pow.f64 x 3) 1/6)
5.0ms	(*.f64 (pow.f64 x 5) 1/120)
5.0ms	(*.f64 (pow.f64 x 7) 1/5040)

Compiler

Compiled 2514 to 1902 computations (24.3% saved)

series62.0ms (1.7%)

Error

0.7b

Counts

4 → 14

Calls

4 calls:

17.0ms	(+.f64 (+.f64 (.f64 (pow.f64 x 3) 1/6) (.f64 (pow.f64 x 5) 1/120)) (*.f64 (pow.f64 x 7) 1/5040))
12.0ms	(*.f64 (pow.f64 x 7) 1/5040)
12.0ms	(*.f64 (pow.f64 x 5) 1/120)
10.0ms	(*.f64 (pow.f64 x 3) 1/6)

Compiler

Compiled 669 to 512 computations (23.5% saved)

simplify111.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

459×	`*-commutative_binary64`
409×	`unswap-sqr_binary64`
315×	`log-prod_binary64` `exp-prod_binary64`
287×	`distribute-rgt-in_binary64`
274×	`distribute-lft-in_binary64`

Counts

108 → 75

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	170	1493
1	360	1418
2	1236	1388
3	2808	1364
4	4666	1340
5	4926	1340

prune79.0ms (2.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	75	4	79

Error

0.7b

Counts

79 → 4

Alt Table

Status	Error	Program
✓	1.7b	(/.f64 (+.f64 x (+.f64 (+.f64 (.f64 (pow.f64 x 3) 1/6) (.f64 (pow.f64 x 5) 1/120)) (*.f64 (pow.f64 x 7) 1/5040))) (cosh.f64 x))
▶	1.8b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
	58.1b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
✓	1.5b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 1569 to 1175 computations (25.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
0.0b	(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
0.0b	(*.f64 (pow.f64 x 5) 2/15)
0.1b	(*.f64 1/3 (pow.f64 x 3))

rewrite136.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

23×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
14×	`add-exp-log_binary64`
11×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
10×	`associate-l_binary64`

Counts

4 → 83

Calls

4 calls:

7.0ms	(*.f64 1/3 (pow.f64 x 3))
6.0ms	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
5.0ms	(*.f64 (pow.f64 x 5) 2/15)
3.0ms	(-.f64 x (*.f64 1/3 (pow.f64 x 3)))

Compiler

Compiled 1554 to 1223 computations (21.3% saved)

series57.0ms (1.6%)

Error

0.7b

Counts

4 → 17

Calls

4 calls:

17.0ms	(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
12.0ms	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
11.0ms	(*.f64 (pow.f64 x 5) 2/15)
9.0ms	(*.f64 1/3 (pow.f64 x 3))

Compiler

Compiled 429 to 337 computations (21.4% saved)

simplify135.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

488×	`cancel-sign-sub-inv_binary64`
483×	`unswap-sqr_binary64`
337×	`log-prod_binary64`
327×	`*-commutative_binary64`
282×	`exp-prod_binary64`

Counts

100 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	145	1335
1	319	1268
2	956	1228
3	2404	1228
4	4216	1219
5	4931	1219
6	4931	1219

prune64.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	61	6	67

Error

0.7b

Counts

67 → 6

Alt Table

Status	Error	Program
	1.7b	(/.f64 (+.f64 x (+.f64 (+.f64 (.f64 (pow.f64 x 3) 1/6) (.f64 (pow.f64 x 5) 1/120)) (*.f64 (pow.f64 x 7) 1/5040))) (cosh.f64 x))
	60.7b	(+.f64 (.f64 (pow.f64 x 3) -1/3) (.f64 (pow.f64 x 5) 2/15))
	1.8b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))) (.f64 2/15 (cbrt.f64 (pow.f64 x 5)))))
	6.0b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (exp.f64 (log.f64 (.f64 2/15 (pow.f64 x 5)))))
	58.1b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
	1.5b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 947 to 729 computations (23% saved)

regimes151.0ms (4.2%)

Accuracy

Total -0.6b remaining (-4639.7%)

Threshold costs -0.6b (-4639.7%)

Compiler

Compiled 1816 to 1320 computations (27.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	3	3

end1.0ms (0%)

Compiler: Compiled 3 to 2 computations (33.3% saved)

sample1.9s (52.3%)

Algorithm

1×

intervals

Results

992.0ms	3852×	body	1024	valid
265.0ms	1970×	body	512	valid
121.0ms	401×	body	2048	valid
86.0ms	986×	body	256	valid
32.0ms	791×	body	128	valid
0.0ms	3×	body	128	overflowed

Compiler

Compiled 120 to 89 computations (25.8% saved)

Details

analyze121.0ms (3.4%)

sample56.0ms (1.6%)

simplify76.0ms (2.1%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite54.0ms (1.5%)

series42.0ms (1.2%)

simplify138.0ms (3.8%)

prune34.0ms (1%)

localize4.0ms (0.1%)

rewrite33.0ms (0.9%)

series51.0ms (1.4%)

simplify93.0ms (2.6%)

prune20.0ms (0.6%)

localize16.0ms (0.4%)

rewrite165.0ms (4.6%)

series62.0ms (1.7%)

simplify111.0ms (3.1%)

prune79.0ms (2.2%)

localize8.0ms (0.2%)

rewrite136.0ms (3.8%)

series57.0ms (1.6%)

simplify135.0ms (3.7%)

prune64.0ms (1.8%)

regimes151.0ms (4.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.9s (52.3%)

Profiling