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)

sample99.0ms (1.8%)

Algorithm

1×

intervals

Results

41.0ms	117×	body	1024	valid
32.0ms	39×	body	2048	valid
12.0ms	35×	body	512	valid
3.0ms	18×	body	256	valid
3.0ms	47×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify171.0ms (3%)

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)

localize9.0ms (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))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64_1798` `add-sqr-sqrt_binary64_1783` `*-un-lft-identity_binary64_1762`
2×	`add-cube-cbrt_binary64_1794` `sin-sum_binary64_1892` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820`
1×	`flip3--_binary64_1766` `diff-log_binary64_1851` `diff-sin_binary64_1909` `distribute-lft-out--_binary64_1716` `difference-of-squares_binary64_1731` `flip--_binary64_1737` `sub-neg_binary64_1755` `associate--l+_binary64_1701`

Counts

2 → 23

Calls

2 calls:

8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	(sin.f64 (+.f64 x eps))

series104.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

77.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
27.0ms	(sin.f64 (+.f64 x eps))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4839	426
1	4839	426

prune30.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.2b

Counts

30 → 3

Compiler

Compiled 404 to 129 computations (68.1% saved)

localize12.0ms (0.2%)

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))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_1762`
11×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820`
9×	`add-log-exp_binary64_1798` `add-sqr-sqrt_binary64_1783`
7×	`add-cube-cbrt_binary64_1794`
6×	`associate-l_binary64_1705`
4×	`pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `cbrt-unprod_binary64_1792` `associate-r_binary64_1704`
3×	`distribute-lft-out_binary64_1715` `sum-log_binary64_1850`
2×	`sin-cos-mult_binary64_1915` `*-commutative_binary64_1695`
1×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `unswap-sqr_binary64_1730` `+-commutative_binary64_1694` `associate-*r/_binary64_1706` `associate-+r+_binary64_1696`

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

series275.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
101.0ms	(*.f64 (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))
32.0ms	(+.f64 x (+.f64 x eps))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4938	1363
1	4938	1363

prune88.0ms (1.6%)

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 1571 to 1025 computations (34.8% 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))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_1762`
8×	`add-log-exp_binary64_1798` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820`
4×	`add-sqr-sqrt_binary64_1783` `add-cube-cbrt_binary64_1794`
3×	`pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `cbrt-unprod_binary64_1792` `distribute-lft-out_binary64_1715` `sum-log_binary64_1850` `associate-r_binary64_1704`
1×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `+-commutative_binary64_1694` `-commutative_binary64_1695` `associate-+r+_binary64_1696` `associate-l*_binary64_1705`

Counts

3 → 40

Calls

3 calls:

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

series172.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

104.0ms	(.f64 (.f64 2 (sin.f64 (/.f64 eps 2))) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
36.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
31.0ms	(+.f64 x (+.f64 x eps))

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5187	824

prune56.0ms (1%)

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 1070 to 692 computations (35.3% 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_1790`
24×	`add-sqr-sqrt_binary64_1783`
15×	`-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794` `associate-r*_binary64_1704`
10×	`cube-prod_binary64_1787` `unpow-prod-down_binary64_1838`
7×	`add-exp-log_binary64_1797` `pow1_binary64_1820`
6×	`add-cbrt-cube_binary64_1795`
5×	`unswap-sqr_binary64_1730`
4×	`sqr-pow_binary64_1734` `add-log-exp_binary64_1798`
3×	`cube-mult_binary64_1789` `unpow3_binary64_1825` `pow-unpow_binary64_1836` `associate-l_binary64_1705`
1×	`rem-cube-cbrt_binary64_1784` `pow-prod-down_binary64_1830` `pow1/3_binary64_1841` `prod-exp_binary64_1808` `pow-exp_binary64_1827` `cbrt-unprod_binary64_1792` `pow-pow_binary64_1831` `rem-cbrt-cube_binary64_1785` `*-commutative_binary64_1695` `pow-to-exp_binary64_1828`

Counts

4 → 85

Calls

4 calls:

10.0ms	(*.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))
4.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)

series255.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
88.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
33.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
30.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4829	1942
1	4829	1942

prune119.0ms (2.1%)

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 2273 to 1492 computations (34.4% saved)

regimes246.0ms (4.4%)

Compiler: Compiled 1685 to 1229 computations (27.1% saved)

bsearch90.0ms (1.6%)

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%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	60
1	47	60

end0.0ms (0%)

sample3.5s (61.8%)

Algorithm

1×

intervals

Results

1.3s	3470×	body	1024	valid
964.0ms	1253×	body	2048	valid
283.0ms	1300×	body	512	valid
88.0ms	640×	body	256	valid
86.0ms	1333×	body	128	valid
8.0ms	4×	body	4096	valid

Compiler

Compiled 584 to 432 computations (26% saved)

Details

analyze2.0ms (0%)

sample99.0ms (1.8%)

simplify171.0ms (3%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite17.0ms (0.3%)

series104.0ms (1.8%)

simplify78.0ms (1.4%)

prune30.0ms (0.5%)

localize12.0ms (0.2%)

rewrite33.0ms (0.6%)

series275.0ms (4.9%)

simplify74.0ms (1.3%)

prune88.0ms (1.6%)

localize12.0ms (0.2%)

rewrite25.0ms (0.4%)

series172.0ms (3.1%)

simplify55.0ms (1%)

prune56.0ms (1%)

localize15.0ms (0.3%)

rewrite33.0ms (0.6%)

series255.0ms (4.5%)

simplify78.0ms (1.4%)

prune119.0ms (2.1%)

regimes246.0ms (4.4%)

bsearch90.0ms (1.6%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (61.8%)

Profiling