Details

analyze1.4s (15.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample199.0ms (2.1%)

Algorithm

1×

intervals

Results

127.0ms	72×	body	2048	valid
40.0ms	87×	body	1024	valid
8.0ms	43×	body	512	valid
5.0ms	5×	body	4096	valid
4.0ms	34×	body	256	valid
1.0ms	15×	body	128	valid

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

450×	`div-sub_binary64`
335×	`times-frac_binary64`
172×	`sub-neg_binary64`
155×	`associate-/l*_binary64`
135×	`associate-/l/_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	39	14
4	62	14
5	105	14
6	193	14
7	374	14
8	614	14
9	989	14
10	1101	14
11	1124	14
12	1093	14
13	1100	14
14	1102	14
15	1106	14
16	1106	14
17	1005	14

prune4.0ms (0%)

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

34.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	34.8b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 20 to 12 computations (40% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.6b	(-.f64 x (tan.f64 x))
1.6b	(-.f64 x (sin.f64 x))

rewrite98.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

33.8b

Rules

45×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
25×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 84

Calls

3 calls:

8.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 1296 to 257 computations (80.2% saved)

series89.0ms (1%)

Error

0.0b

Counts

3 → 28

Calls

3 calls:

28.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
20.0ms	(-.f64 x (sin.f64 x))
17.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 933 to 603 computations (35.4% saved)

simplify184.0ms (2%)

Algorithm

1×	egg-herbie

Rules

498×	`times-frac_binary64`
453×	`associate-l_binary64`
357×	`associate-/l*_binary64`
183×	`associate-/r*_binary64`
174×	`distribute-rgt-in_binary64`

Counts

112 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	2358
1	524	2268
2	1408	2256
3	4868	2250
4	4986	2250
5	4999	2250
6	4999	2250
7	4920	2250

prune33.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	3	46

Error

0.0b

Counts

46 → 3

Alt Table

Status	Error	Program
	63.5b	(/.f64 (-.f64 (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 1/5040 (pow.f64 x 7))) (+.f64 (.f64 1/120 (pow.f64 x 5)) (.f64 1/362880 (pow.f64 x 9)))) (-.f64 x (tan.f64 x)))
▶	28.8b	(-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
	34.8b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))

Compiler

Compiled 671 to 326 computations (51.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.1b	(.f64 9/40 (.f64 x x))
13.8b	(-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite74.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
6×	`prod-exp_binary64` `associate-l_binary64`

Counts

3 → 60

Calls

3 calls:

7.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
5.0ms	(*.f64 27/2800 (pow.f64 x 4))
5.0ms	(.f64 9/40 (.f64 x x))

Compiler

Compiled 1160 to 850 computations (26.7% saved)

series31.0ms (0.3%)

Error

0.0b

Counts

3 → 11

Calls

3 calls:

11.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
8.0ms	(*.f64 27/2800 (pow.f64 x 4))
8.0ms	(.f64 9/40 (.f64 x x))

Compiler

Compiled 295 to 245 computations (16.9% saved)

simplify115.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

730×	`associate-l_binary64`
607×	`associate-r_binary64`
583×	`cancel-sign-sub-inv_binary64`
263×	`unswap-sqr_binary64`
180×	`exp-prod_binary64`

Counts

71 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	127	954
1	273	895
2	735	865
3	2852	852
4	4703	852
5	4973	852
6	4902	852

prune23.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	40	3	43

Error

0.0b

Counts

43 → 3

Alt Table

Status	Error	Program
	63.5b	(/.f64 (-.f64 (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 1/5040 (pow.f64 x 7))) (+.f64 (.f64 1/120 (pow.f64 x 5)) (.f64 1/362880 (pow.f64 x 9)))) (-.f64 x (tan.f64 x)))
▶	28.8b	(-.f64 (+.f64 -1/2 (.f64 9/40 (.f64 x x))) (*.f64 27/2800 (pow.f64 x 4)))
	34.8b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))

Compiler

Compiled 493 to 368 computations (25.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.1b	(.f64 9/40 (.f64 x x))
13.8b	(-.f64 (+.f64 -1/2 (.f64 9/40 (.f64 x x))) (*.f64 27/2800 (pow.f64 x 4)))

rewrite66.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

13×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `associate-r_binary64`
7×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`prod-exp_binary64` `associate-l_binary64`

Counts

3 → 58

Calls

3 calls:

6.0ms	(-.f64 (+.f64 -1/2 (.f64 9/40 (.f64 x x))) (*.f64 27/2800 (pow.f64 x 4)))
5.0ms	(.f64 9/40 (.f64 x x))
5.0ms	(*.f64 27/2800 (pow.f64 x 4))

Compiler

Compiled 1101 to 802 computations (27.2% saved)

series31.0ms (0.3%)

Error

0.0b

Counts

3 → 11

Calls

3 calls:

12.0ms	(-.f64 (+.f64 -1/2 (.f64 9/40 (.f64 x x))) (*.f64 27/2800 (pow.f64 x 4)))
8.0ms	(*.f64 27/2800 (pow.f64 x 4))
8.0ms	(.f64 9/40 (.f64 x x))

Compiler

Compiled 295 to 245 computations (16.9% saved)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Rules

683×	`associate-l_binary64`
605×	`associate-r_binary64`
594×	`cancel-sign-sub-inv_binary64`
495×	`distribute-rgt-neg-in_binary64`
181×	`unswap-sqr_binary64`

Counts

69 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	944
1	244	887
2	734	848
3	3021	839
4	4944	839
5	4983	839

prune27.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	42	3	45

Error

0.0b

Counts

45 → 3

Alt Table

Status	Error	Program
	63.5b	(/.f64 (-.f64 (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 1/5040 (pow.f64 x 7))) (+.f64 (.f64 1/120 (pow.f64 x 5)) (.f64 1/362880 (pow.f64 x 9)))) (-.f64 x (tan.f64 x)))
✓	28.8b	(-.f64 (+.f64 -1/2 (.f64 9/40 (.f64 x x))) (*.f64 27/2800 (pow.f64 x 4)))
▶	34.8b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))

Compiler

Compiled 585 to 426 computations (27.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3)
0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))
1.6b	(-.f64 x (tan.f64 x))
1.6b	(-.f64 x (sin.f64 x))

rewrite137.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

136×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
100×	`times-frac_binary64`
68×	`cbrt-prod_binary64`
62×	`unpow-prod-down_binary64` `cube-prod_binary64`
52×	`add-cube-cbrt_binary64`

Counts

4 → 192

Calls

4 calls:

12.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))
11.0ms	(pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3)
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 2547 to 796 computations (68.7% saved)

series130.0ms (1.4%)

Error

0.0b

Counts

4 → 40

Calls

4 calls:

50.0ms	(pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3)
24.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))
15.0ms	(-.f64 x (tan.f64 x))
14.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 1717 to 1174 computations (31.6% saved)

simplify260.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

364×	`unswap-sqr_binary64`
229×	`log-prod_binary64`
224×	`cancel-sign-sub-inv_binary64`
197×	`sqr-pow_binary64`
177×	`sub-neg_binary64`

Counts

232 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	6687
1	941	6318
2	2914	6171
3	4549	6171
4	4972	6171
5	4935	6171

prune47.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	168	3	171

Error

0.0b

Counts

171 → 3

Alt Table

Status	Error	Program
	63.5b	(/.f64 (-.f64 (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 1/5040 (pow.f64 x 7))) (+.f64 (.f64 1/120 (pow.f64 x 5)) (.f64 1/362880 (pow.f64 x 9)))) (-.f64 x (tan.f64 x)))
	28.8b	(-.f64 (+.f64 -1/2 (.f64 9/40 (.f64 x x))) (*.f64 27/2800 (pow.f64 x 4)))
	34.8b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))

Compiler

Compiled 1630 to 652 computations (60% saved)

regimes316.0ms (3.4%)

Accuracy

Total 0.0b remaining (10.3%)

Threshold costs 0.0b (10.3%)

Compiler

Compiled 3085 to 2063 computations (33.1% saved)

bsearch39.0ms (0.4%)

Steps

Iters	Range		Point
10	1.1992419585311902e-11	407.22060669436894	0.028616561567871263
7	-0.09936557168756392	-0.001330811998782659	-0.03062657705051721

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
11×	`sub-neg_binary64` `*-commutative_binary64`
7×	`neg-mul-1_binary64` `neg-sub0_binary64`
4×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
1×	`unsub-neg_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	87
1	61	85
2	83	85
3	97	85
4	104	85
5	105	85
6	103	85

end2.0ms (0%)

Compiler: Compiled 55 to 33 computations (40% saved)

sample5.7s (61.5%)

Algorithm

1×

intervals

Results

3.7s	2050×	body	2048	valid
1.0s	3058×	body	1024	valid
273.0ms	1443×	body	512	valid
93.0ms	758×	body	256	valid
93.0ms	89×	body	4096	valid
49.0ms	602×	body	128	valid

Compiler

Compiled 123 to 84 computations (31.7% saved)

Details

analyze1.4s (15.6%)

sample199.0ms (2.1%)

simplify78.0ms (0.8%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite98.0ms (1.1%)

series89.0ms (1%)

simplify184.0ms (2%)

prune33.0ms (0.4%)

localize8.0ms (0.1%)

rewrite74.0ms (0.8%)

series31.0ms (0.3%)

simplify115.0ms (1.2%)

prune23.0ms (0.3%)

localize8.0ms (0.1%)

rewrite66.0ms (0.7%)

series31.0ms (0.3%)

simplify93.0ms (1%)

prune27.0ms (0.3%)

localize10.0ms (0.1%)

rewrite137.0ms (1.5%)

series130.0ms (1.4%)

simplify260.0ms (2.8%)

prune47.0ms (0.5%)

regimes316.0ms (3.4%)

bsearch39.0ms (0.4%)

simplify6.0ms (0.1%)

end2.0ms (0%)

sample5.7s (61.5%)

Profiling