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)

sample79.0ms (1.6%)

Algorithm

1×

intervals

Results

30.0ms	100×	body	1024	valid
27.0ms	47×	body	2048	valid
8.0ms	39×	body	512	valid
3.0ms	54×	body	128	valid
2.0ms	16×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify102.0ms (2.1%)

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: 36.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.9b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.7b	(sin.f64 (+.f64 x eps))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`add-log-exp_binary64_1822`
3×	`add-cube-cbrt_binary64_1818` `cancel-sign-sub-inv_binary64_1749`
2×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `sin-sum_binary64_1916` `pow1_binary64_1844`
1×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `diff-sin_binary64_1933` `associate--l+_binary64_1720` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

series55.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

38.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
16.0ms	(sin.f64 (+.f64 x eps))

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5196	441

prune26.0ms (0.5%)

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: 0.3b

Counts

33 → 3

Compiler

Compiled 428 to 129 computations (69.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.7b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1783`
8×	`add-log-exp_binary64_1822`
7×	`add-sqr-sqrt_binary64_1805`
5×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `pow1_binary64_1844`
3×	`distribute-lft-out_binary64_1734` `associate-l_binary64_1724` `sum-log_binary64_1874` `associate-r_binary64_1723`
1×	`associate-+r+_binary64_1715` `+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `sin-cos-mult_binary64_1939` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`

Counts

3 → 41

Calls

3 calls:

9.0ms	(+.f64 x (+.f64 x eps))
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)))

series81.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

46.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
19.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
16.0ms	(+.f64 x (+.f64 x eps))

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5266	830

prune67.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	44	9	53

Merged error: 0.3b

Counts

53 → 9

Compiler

Compiled 1196 to 783 computations (34.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
3.7b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite42.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1805`
12×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`log-prod_binary64_1869` `exp-prod_binary64_1835`
8×	`log-pow_binary64_1872` `pow1_binary64_1844`
7×	`associate-r_binary64_1723`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
5×	`add-log-exp_binary64_1822`
3×	`distribute-lft-in_binary64_1732` `associate-l_binary64_1724` `distribute-rgt-in_binary64_1733`
1×	`rem-exp-log_binary64_1823` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `*-commutative_binary64_1714` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `rem-log-exp_binary64_1824`

Counts

4 → 61

Calls

4 calls:

14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
8.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
8.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series203.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
62.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
35.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
18.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4989	1476
1	4989	1476

prune93.0ms (1.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	73	9	82

Merged error: 0.3b

Counts

82 → 9

Compiler

Compiled 1830 to 1218 computations (33.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) 3))
0.5b	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) 3)))
0.8b	(pow.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) 3)
3.7b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64_1814`
15×	`log-prod_binary64_1869` `add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
6×	`pow1_binary64_1844`
5×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
4×	`pow-pow_binary64_1855` `add-log-exp_binary64_1822`
3×	`sqr-pow_binary64_1755` `cube-mult_binary64_1813` `pow-unpow_binary64_1860` `unpow3_binary64_1849` `exp-prod_binary64_1835`
2×	`log-pow_binary64_1872` `pow1/3_binary64_1865`
1×	`rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `rem-log-exp_binary64_1824`

Counts

4 → 79

Calls

4 calls:

11.0ms	(pow.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) 3)
11.0ms	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) 3)))
10.0ms	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) 3))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series194.0ms (4%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) 3)
55.0ms	(log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) 3)))
34.0ms	(cbrt.f64 (pow.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) 3))
20.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify80.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5008	1843

prune120.0ms (2.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	90	10	100

Merged error: 0.3b

Counts

100 → 10

Compiler

Compiled 2249 to 1523 computations (32.3% saved)

regimes236.0ms (4.9%)

Compiler: Compiled 1722 to 1370 computations (20.4% saved)

bsearch79.0ms (1.6%)

Steps

Iters	Range		Point
10	2.4014625307099903e-26	2.1370823519636745e-16	2.1191567652653345e-16
9	-0.00020344265452465967	-9.707864883246397e-11	-8.705293557889514e-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	49	81
1	49	81

end0.0ms (0%)

sample3.0s (62.7%)

Algorithm

1×

intervals

Results

1.1s	3497×	body	1024	valid
670.0ms	1229×	body	2048	valid
269.0ms	1360×	body	512	valid
86.0ms	1330×	body	128	valid
76.0ms	581×	body	256	valid
3.0ms	3×	body	4096	valid

Compiler

Compiled 640 to 500 computations (21.9% saved)

Details

analyze2.0ms (0%)

sample79.0ms (1.6%)

simplify102.0ms (2.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite13.0ms (0.3%)

series55.0ms (1.1%)

simplify54.0ms (1.1%)

prune26.0ms (0.5%)

localize11.0ms (0.2%)

rewrite26.0ms (0.5%)

series81.0ms (1.7%)

simplify76.0ms (1.6%)

prune67.0ms (1.4%)

localize15.0ms (0.3%)

rewrite42.0ms (0.9%)

series203.0ms (4.2%)

simplify69.0ms (1.4%)

prune93.0ms (1.9%)

localize17.0ms (0.3%)

rewrite46.0ms (1%)

series194.0ms (4%)

simplify80.0ms (1.7%)

prune120.0ms (2.5%)

regimes236.0ms (4.9%)

bsearch79.0ms (1.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample3.0s (62.7%)

Profiling