Details

analyze269.0ms (6.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample54.0ms (1.4%)

Algorithm

1×

intervals

Results

26.0ms	63×	body	2048	valid
8.0ms	35×	body	1024	valid
6.0ms	52×	body	512	valid
3.0ms	89×	body	128	valid
1.0ms	15×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify22.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

87×	`div-sub_binary64`
74×	`associate-/l*_binary64`
63×	`times-frac_binary64`
56×	`unsub-neg_binary64`
50×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	39	12
4	69	12
5	101	12
6	141	12
7	218	12
8	331	12
9	433	12
10	453	12
11	421	12
12	366	12

prune2.0ms (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

32.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	32.2b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.7b	(-.f64 1 (cos.f64 x))
14.3b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite75.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

31.0b

Rules

14×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`times-frac_binary64` `difference-of-squares_binary64` `associate-/l*_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 47

Calls

2 calls:

8.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 669 to 336 computations (49.8% saved)

series31.0ms (0.8%)

Error

0.5b

Counts

2 → 12

Calls

2 calls:

11.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
7.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 321 to 243 computations (24.3% saved)

simplify83.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

904×	`div-sub_binary64`
624×	`cancel-sign-sub-inv_binary64`
267×	`associate-r_binary64`
260×	`times-frac_binary64`
256×	`associate-l_binary64`

Counts

59 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	107	901
1	263	811
2	665	811
3	2490	811
4	4553	811
5	6295	811

prune33.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	25	7	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	8	33

Error

0.3b

Counts

33 → 8

Alt Table

Status	Error	Program
✓	32.2b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
	31.8b	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 x (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))
	40.5b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x)) 3))
	48.8b	(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
	32.2b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (.f64 x x) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))))
▶	14.9b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	31.7b	(/.f64 1 (/.f64 x (/.f64 (-.f64 1 (cos.f64 x)) x)))
	30.4b	(+.f64 (-.f64 1/2 (.f64 1/24 (.f64 x x))) (*.f64 1/720 (pow.f64 x 4)))

Compiler

Compiled 566 to 346 computations (38.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.3b	(+.f64 1 (cos.f64 x))
14.2b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite145.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 111

Calls

4 calls:

10.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
7.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 2337 to 893 computations (61.8% saved)

series69.0ms (1.7%)

Error

0.3b

Counts

4 → 24

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
16.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
9.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
7.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 850 to 589 computations (30.7% saved)

simplify103.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-*l/_binary64`
540×	`associate-/r/_binary64`
452×	`associate-*r/_binary64`
218×	`cancel-sign-sub-inv_binary64`
170×	`log-div_binary64`

Counts

135 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	197	2598
1	490	1983
2	1693	1971
3	4364	1960
4	4933	1960

prune94.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	4	2	6
Picked	0	1	1
Done	1	0	1
Total	119	6	125

Error

Counts

125 → 6

Alt Table

Status	Error	Program
	0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
▶	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	14.7b	(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (.f64 x x))
	32.2b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (.f64 x x) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))))
✓	14.9b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	30.4b	(+.f64 (-.f64 1/2 (.f64 1/24 (.f64 x x))) (*.f64 1/720 (pow.f64 x 4)))

Compiler

Compiled 1715 to 911 computations (46.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.1b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

rewrite124.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-l_binary64`

Counts

3 → 87

Calls

3 calls:

8.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
8.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
3.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 1585 to 735 computations (53.6% saved)

series67.0ms (1.7%)

Error

Counts

3 → 18

Calls

3 calls:

21.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
21.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
10.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 568 to 433 computations (23.8% saved)

simplify113.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

589×	`associate-/l/_binary64`
541×	`associate-*l/_binary64`
464×	`cancel-sign-sub-inv_binary64`
443×	`associate-l_binary64`
393×	`associate-/r*_binary64`

Counts

105 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	1928
1	420	1669
2	1285	1669
3	4178	1665
4	4878	1665
5	4938	1665

prune52.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	55	6	61

Error

Counts

61 → 6

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	14.7b	(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (.f64 x x))
	32.2b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (.f64 x x) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))))
✓	14.9b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	30.4b	(+.f64 (-.f64 1/2 (.f64 1/24 (.f64 x x))) (*.f64 1/720 (pow.f64 x 4)))

Compiler

Compiled 899 to 485 computations (46.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
0.2b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.2b	(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))

rewrite113.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-r_binary64`

Counts

3 → 84

Calls

3 calls:

7.0ms	(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
6.0ms	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

Compiler

Compiled 1593 to 929 computations (41.7% saved)

series67.0ms (1.7%)

Error

Counts

3 → 18

Calls

3 calls:

19.0ms	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
19.0ms	(*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x))
15.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

Compiler

Compiled 577 to 433 computations (25% saved)

simplify136.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

571×	`associate-/l/_binary64`
522×	`associate-*l/_binary64`
423×	`associate-l_binary64`
411×	`associate-*r/_binary64`
374×	`associate-r_binary64`

Counts

102 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	2035
1	396	1770
2	1338	1770
3	4245	1766
4	4719	1766
5	4963	1766
6	4948	1766

prune39.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	47	6	53

Error

Counts

53 → 6

Alt Table

Status	Error	Program
	0.1b	(/.f64 (*.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) x)) x)
	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	14.7b	(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) (.f64 x x))
	32.2b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (.f64 x x) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 1 (cos.f64 x))))))
	14.9b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	30.4b	(+.f64 (-.f64 1/2 (.f64 1/24 (.f64 x x))) (*.f64 1/720 (pow.f64 x 4)))

Compiler

Compiled 596 to 373 computations (37.4% saved)

regimes384.0ms (9.8%)

Accuracy

Total 0.1b remaining (80.1%)

Threshold costs 0.1b (80.1%)

Compiler

Compiled 5366 to 3503 computations (34.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	10	17
2	10	17

end1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample1.8s (46.4%)

Algorithm

1×

intervals

Results

857.0ms	1924×	body	2048	valid
215.0ms	1137×	body	1024	valid
207.0ms	1499×	body	512	valid
95.0ms	2608×	body	128	valid
67.0ms	733×	body	256	valid
38.0ms	99×	body	4096	valid

Compiler

Compiled 111 to 76 computations (31.5% saved)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	39	12
4	69	12
5	101	12
6	141	12
7	218	12
8	331	12
9	433	12
10	453	12
11	421	12
12	366	12

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	39	12
4	69	12
5	101	12
6	141	12
7	218	12
8	331	12
9	433	12
10	453	12
11	421	12
12	366	12

Details

analyze269.0ms (6.8%)

sample54.0ms (1.4%)

simplify22.0ms (0.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite75.0ms (1.9%)

series31.0ms (0.8%)

simplify83.0ms (2.1%)

prune33.0ms (0.8%)

localize9.0ms (0.2%)

rewrite145.0ms (3.7%)

series69.0ms (1.7%)

simplify103.0ms (2.6%)

prune94.0ms (2.4%)

localize8.0ms (0.2%)

rewrite124.0ms (3.1%)

series67.0ms (1.7%)

simplify113.0ms (2.9%)

prune52.0ms (1.3%)

localize8.0ms (0.2%)

rewrite113.0ms (2.9%)

series67.0ms (1.7%)

simplify136.0ms (3.5%)

prune39.0ms (1%)

regimes384.0ms (9.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.8s (46.4%)

Profiling

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	39	12
4	69	12
5	101	12
6	141	12
7	218	12
8	331	12
9	433	12
10	453	12
11	421	12
12	366	12