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)

sample97.0ms (1.9%)

Algorithm

1×

intervals

Results

40.0ms	117×	body	1024	valid
36.0ms	39×	body	2048	valid
7.0ms	35×	body	512	valid
3.0ms	47×	body	128	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify167.0ms (3.2%)

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: 36.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.2b	(sin.f64 (+.f64 x eps))
2.2b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

rewrite15.0ms (0.3%)

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 (1.9%)

Counts

2 → 6

Calls

2 calls:

72.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
27.0ms	(sin.f64 (+.f64 x eps))

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5018	441

prune81.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Merged error: 0.2b

Counts

33 → 3

Compiler

Compiled 1225 to 678 computations (44.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
1.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_2143`
11×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
9×	`add-sqr-sqrt_binary64_2165` `add-log-exp_binary64_2182`
7×	`add-cube-cbrt_binary64_2178`
6×	`associate-l_binary64_2084`
4×	`associate-r_binary64_2083` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192`
3×	`sum-log_binary64_2234` `distribute-lft-out_binary64_2094`
2×	`sin-cos-mult_binary64_2299` `*-commutative_binary64_2074`
1×	`+-commutative_binary64_2073` `associate-+r+_binary64_2075` `associate-*r/_binary64_2085` `unswap-sqr_binary64_2111` `flip3-+_binary64_2146` `flip-+_binary64_2117`

Counts

4 → 60

Calls

4 calls:

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

series257.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
84.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
35.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
34.0ms	(+.f64 x (+.f64 x eps))

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4891	1363
1	4891	1363

prune191.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	68	7	75

Merged error: 0.2b

Counts

75 → 7

Compiler

Compiled 3300 to 2366 computations (28.3% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(.f64 (.f64 2 (sin.f64 (/.f64 eps 2))) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
1.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

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

series167.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(.f64 (.f64 2 (sin.f64 (/.f64 eps 2))) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
34.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
30.0ms	(+.f64 x (+.f64 x eps))

simplify55.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4899	824
1	4899	824

prune67.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	49	7	56

Merged error: 0.2b

Counts

56 → 7

Compiler

Compiled 1227 to 818 computations (33.3% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
1.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64_2174`
24×	`add-sqr-sqrt_binary64_2165`
15×	`associate-r_binary64_2083` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
10×	`unpow-prod-down_binary64_2222` `cube-prod_binary64_2171`
7×	`pow1_binary64_2204` `add-exp-log_binary64_2181`
6×	`add-cbrt-cube_binary64_2179`
5×	`unswap-sqr_binary64_2111`
4×	`add-log-exp_binary64_2182` `sqr-pow_binary64_2115`
3×	`pow-unpow_binary64_2220` `cube-mult_binary64_2173` `associate-l_binary64_2084` `unpow3_binary64_2209`
1×	`rem-cbrt-cube_binary64_2167` `pow-to-exp_binary64_2212` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `pow-pow_binary64_2215` `*-commutative_binary64_2074` `rem-cube-cbrt_binary64_2166` `pow-exp_binary64_2211` `pow1/3_binary64_2225`

Counts

4 → 85

Calls

4 calls:

11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

series253.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
79.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
34.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
31.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

simplify91.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4871	1942
1	4871	1942

prune137.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	97	7	104

Merged error: 0.2b

Counts

104 → 7

Compiler

Compiled 2605 to 1756 computations (32.6% saved)

regimes67.0ms (1.3%)

Compiler: Compiled 292 to 236 computations (19.2% saved)

bsearch88.0ms (1.7%)

Steps

Iters	Range		Point
10	4.766648698077205e-19	0.0003693174546992489	7.799591496688593e-09
10	-0.7690085446444335	-8.177773180557729e-15	-1.1949421538796511e-08

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	60
1	47	60

end0.0ms (0%)

sample3.1s (59.3%)

Algorithm

1×

intervals

Results

1.3s	3470×	body	1024	valid
956.0ms	1253×	body	2048	valid
268.0ms	1300×	body	512	valid
86.0ms	640×	body	256	valid
84.0ms	1333×	body	128	valid
7.0ms	4×	body	4096	valid

Compiler

Compiled 203 to 163 computations (19.7% saved)

Details

analyze2.0ms (0%)

sample97.0ms (1.9%)

simplify167.0ms (3.2%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite15.0ms (0.3%)

series100.0ms (1.9%)

simplify58.0ms (1.1%)

prune81.0ms (1.6%)

localize14.0ms (0.3%)

rewrite35.0ms (0.7%)

series257.0ms (4.9%)

simplify76.0ms (1.5%)

prune191.0ms (3.7%)

localize12.0ms (0.2%)

rewrite26.0ms (0.5%)

series167.0ms (3.2%)

simplify55.0ms (1.1%)

prune67.0ms (1.3%)

localize15.0ms (0.3%)

rewrite33.0ms (0.6%)

series253.0ms (4.9%)

simplify91.0ms (1.8%)

prune137.0ms (2.6%)

regimes67.0ms (1.3%)

bsearch88.0ms (1.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.1s (59.3%)

Profiling