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)

sample87.0ms (1.7%)

Algorithm

1×

intervals

Results

39.0ms	111×	body	1024	valid
26.0ms	35×	body	2048	valid
9.0ms	45×	body	512	valid
3.0ms	52×	body	128	valid
2.0ms	13×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify176.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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: 35.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.3b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.5b	(sin.f64 (+.f64 x eps))

rewrite13.0ms (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:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

series97.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

65.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
31.0ms	(sin.f64 (+.f64 x eps))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4839	426
1	4839	426

prune27.0ms (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: 0.3b

Counts

30 → 3

Compiler

Compiled 404 to 129 computations (68.1% saved)

localize12.0ms (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)))
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 41

Calls

3 calls:

8.0ms	(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))

series157.0ms (3%)

Counts

3 → 9

Calls

3 calls:

86.0ms	(*.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))
34.0ms	(+.f64 x (+.f64 x eps))

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4886	830
1	4886	830

prune64.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	46	7	53

Merged error: 0.2b

Counts

53 → 7

Compiler

Compiled 1138 to 737 computations (35.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.4b	(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)
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite34.0ms (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	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
10.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

series262.0ms (5%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
74.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
35.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
32.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4829	1942
1	4829	1942

prune128.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	96	8	104

Merged error: 0.2b

Counts

104 → 8

Compiler

Compiled 2408 to 1595 computations (33.8% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64_1798` `add-sqr-sqrt_binary64_1783` `*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820`
1×	`pow1/3_binary64_1841` `cbrt-prod_binary64_1790` `cos-mult_binary64_1913` `cbrt-div_binary64_1791`

Counts

4 → 31

Calls

4 calls:

10.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
3.0ms	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))

series313.0ms (6%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(cbrt.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
33.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
30.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
29.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5239	572

prune73.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	42	9	51

Merged error: 0.2b

Counts

51 → 9

Compiler

Compiled 1540 to 971 computations (36.9% saved)

regimes99.0ms (1.9%)

Compiler: Compiled 438 to 354 computations (19.2% saved)

bsearch96.0ms (1.8%)

Steps

Iters	Range		Point
6	3.399893619986278e-45	2.058855698569637e-44	2.0358793251829584e-44
11	-697988.6142033994	-1.144111223116443e-20	-8.519919949486787e-09

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%)

sample3.2s (60.8%)

Algorithm

1×

intervals

Results

1.3s	3466×	body	1024	valid
943.0ms	1217×	body	2048	valid
303.0ms	1433×	body	512	valid
88.0ms	1270×	body	128	valid
84.0ms	614×	body	256	valid

Compiler

Compiled 276 to 222 computations (19.6% saved)

Details

analyze2.0ms (0%)

sample87.0ms (1.7%)

simplify176.0ms (3.4%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite13.0ms (0.3%)

series97.0ms (1.8%)

simplify80.0ms (1.5%)

prune27.0ms (0.5%)

localize12.0ms (0.2%)

rewrite24.0ms (0.4%)

series157.0ms (3%)

simplify81.0ms (1.5%)

prune64.0ms (1.2%)

localize16.0ms (0.3%)

rewrite34.0ms (0.6%)

series262.0ms (5%)

simplify76.0ms (1.5%)

prune128.0ms (2.5%)

localize18.0ms (0.3%)

rewrite33.0ms (0.6%)

series313.0ms (6%)

simplify69.0ms (1.3%)

prune73.0ms (1.4%)

regimes99.0ms (1.9%)

bsearch96.0ms (1.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.2s (60.8%)

Profiling