Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample93.0ms (1.5%)

Algorithm

1×

intervals

Results

43.0ms	122×	body	1024	valid
29.0ms	41×	body	2048	valid
9.0ms	42×	body	512	valid
2.0ms	35×	body	128	valid
2.0ms	16×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify176.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (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

Merged error: 39.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.5b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.9b	(sin.f64 (+.f64 x eps))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2165` `*-un-lft-identity_binary64_2143`
4×	`add-log-exp_binary64_2182`
3×	`add-cube-cbrt_binary64_2178` `cancel-sign-sub-inv_binary64_2109`
2×	`pow1_binary64_2204` `sin-sum_binary64_2276` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
1×	`diff-log_binary64_2235` `flip--_binary64_2118` `sub-neg_binary64_2136` `distribute-lft-out--_binary64_2095` `diff-sin_binary64_2293` `flip3--_binary64_2147` `associate--l+_binary64_2080` `difference-of-squares_binary64_2112`

Counts

2 → 26

Calls

2 calls:

8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

series100.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

70.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
30.0ms	(sin.f64 (+.f64 x eps))

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5018	441

prune65.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	4	33

Merged error: 0.4b

Counts

33 → 4

Compiler

Compiled 883 to 467 computations (47.1% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_2143`
8×	`add-log-exp_binary64_2182`
7×	`add-sqr-sqrt_binary64_2165`
5×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cube-cbrt_binary64_2178` `add-cbrt-cube_binary64_2179`
3×	`associate-r_binary64_2083` `sum-log_binary64_2234` `associate-l_binary64_2084` `distribute-lft-out_binary64_2094`
1×	`+-commutative_binary64_2073` `sin-cos-mult_binary64_2299` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `associate-+r+_binary64_2075` `unswap-sqr_binary64_2111` `flip3-+_binary64_2146` `flip-+_binary64_2117` `*-commutative_binary64_2074`

Counts

3 → 41

Calls

3 calls:

8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(+.f64 x (+.f64 x eps))

series150.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

82.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
37.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
31.0ms	(+.f64 x (+.f64 x eps))

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4821	830
1	4821	830

prune219.0ms (3.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	41	9	50
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	43	11	54

Merged error: 0.3b

Counts

54 → 11

Compiler

Compiled 3575 to 2649 computations (25.9% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.3b	(.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (+.f64 x (.f64 eps 1/2))))
3.0b	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_2165`
4×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143` `add-cbrt-cube_binary64_2179`
3×	`associate-r_binary64_2083` `associate-l_binary64_2084`
2×	`add-log-exp_binary64_2182`
1×	`sin-cos-mult_binary64_2299` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `unswap-sqr_binary64_2111` `cos-sum_binary64_2277` `*-commutative_binary64_2074`

Counts

2 → 27

Calls

2 calls:

7.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (+.f64 x (.f64 eps 1/2))))
5.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

series114.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

83.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (+.f64 x (.f64 eps 1/2))))
31.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4833	582
1	4833	582

prune225.0ms (3.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	25	8	33
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	34	10	44

Merged error: 0.1b

Counts

44 → 10

Compiler

Compiled 3698 to 2950 computations (20.2% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2))))
0.1b	(.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2)))
0.2b	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))
0.3b	(.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_2165`
10×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143` `add-cbrt-cube_binary64_2179`
9×	`associate-r_binary64_2083` `associate-l_binary64_2084`
6×	`add-log-exp_binary64_2182`
5×	`cos-mult_binary64_2297` `sin-mult_binary64_2298`
4×	`associate-*r/_binary64_2085`
3×	`sub-neg_binary64_2136` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `unswap-sqr_binary64_2111` `cancel-sign-sub-inv_binary64_2109` `*-commutative_binary64_2074`
2×	`sub-div_binary64_2150` `flip--_binary64_2118` `distribute-rgt-in_binary64_2093` `flip3--_binary64_2147` `frac-sub_binary64_2152` `distribute-lft-in_binary64_2092`
1×	`diff-log_binary64_2235`

Counts

4 → 78

Calls

4 calls:

13.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))))
7.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2))))
6.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))
5.0ms	(.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2)))

series545.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

232.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))))
165.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2))))
75.0ms	(.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2)))
73.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))

simplify85.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4919	2160
1	4919	2160

prune597.0ms (9.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	7	2	9
Picked	0	1	1
Done	0	0	0
Total	88	12	100

Merged error: 0.0b

Counts

100 → 12

Compiler

Compiled 10741 to 8294 computations (22.8% saved)

regimes81.0ms (1.3%)

Compiler: Compiled 916 to 718 computations (21.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	35
1	48	35

end0.0ms (0%)

sample3.3s (54.2%)

Algorithm

1×

intervals

Results

1.3s	3509×	body	1024	valid
937.0ms	1223×	body	2048	valid
280.0ms	1337×	body	512	valid
84.0ms	1345×	body	128	valid
77.0ms	584×	body	256	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 499 to 395 computations (20.8% saved)

Details

analyze2.0ms (0%)

sample93.0ms (1.5%)

simplify176.0ms (2.9%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite14.0ms (0.2%)

series100.0ms (1.6%)

simplify61.0ms (1%)

prune65.0ms (1.1%)

localize13.0ms (0.2%)

rewrite25.0ms (0.4%)

series150.0ms (2.4%)

simplify86.0ms (1.4%)

prune219.0ms (3.6%)

localize12.0ms (0.2%)

rewrite14.0ms (0.2%)

series114.0ms (1.8%)

simplify75.0ms (1.2%)

prune225.0ms (3.7%)

localize20.0ms (0.3%)

rewrite40.0ms (0.7%)

series545.0ms (8.8%)

simplify85.0ms (1.4%)

prune597.0ms (9.7%)

regimes81.0ms (1.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (54.2%)

Profiling