Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample30.0ms (0.8%)

Algorithm

1×

intervals

Results

14.0ms	69×	body	1024	valid
4.0ms	126×	body	128	valid
3.0ms	37×	body	512	valid
1.0ms	19×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify168.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune2.0ms (0.1%)

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

Error

31.6b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.4b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite75.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_1783`
88×	`times-frac_binary64_1789`
85×	`add-sqr-sqrt_binary64_1805`
37×	`add-cube-cbrt_binary64_1818`
34×	`cancel-sign-sub-inv_binary64_1749`
27×	`distribute-lft-out_binary64_1734`
22×	`difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`
11×	`associate-/r*_binary64_1727`
9×	`difference-of-sqr-1_binary64_1753`
7×	`add-cbrt-cube_binary64_1819` `associate-/l*_binary64_1728` `add-exp-log_binary64_1821`
6×	`associate-/r/_binary64_1729`
5×	`add-log-exp_binary64_1822`
3×	`flip3--_binary64_1787` `div-inv_binary64_1780` `flip--_binary64_1758` `pow1_binary64_1844`
2×	`associate-/l/_binary64_1730` `flip-+_binary64_1757` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `flip3-+_binary64_1786` `clear-num_binary64_1782`
1×	`diff-log_binary64_1875` `frac-sub_binary64_1792` `sub-neg_binary64_1776`

Counts

3 → 147

Calls

3 calls:

47.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series62.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

36.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
13.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
13.0ms	(/.f64 x (+.f64 x 1))

simplify87.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5658	2774

prune205.0ms (5.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	3	157

Error

0.1b

Counts

157 → 3

Compiler

Compiled 3061 to 2159 computations (29.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.3b	(/.f64 3 (pow.f64 x 3))
0.5b	(/.f64 -1 (*.f64 x x))
7.4b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite93.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64_1783`
68×	`times-frac_binary64_1789`
44×	`add-sqr-sqrt_binary64_1805`
40×	`add-cube-cbrt_binary64_1818`
14×	`add-exp-log_binary64_1821` `unpow3_binary64_1849`
13×	`cancel-sign-sub-inv_binary64_1749` `associate-/r*_binary64_1727`
12×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
11×	`add-cbrt-cube_binary64_1819` `distribute-lft-out_binary64_1734` `add-log-exp_binary64_1822`
8×	`distribute-rgt-out_binary64_1736`
6×	`associate-/l*_binary64_1728` `div-inv_binary64_1780`
5×	`div-exp_binary64_1834`
4×	`sqr-pow_binary64_1755` `cube-mult_binary64_1813` `pow1_binary64_1844`
3×	`frac-sub_binary64_1792` `cbrt-undiv_binary64_1817`
2×	`difference-of-squares_binary64_1752` `frac-add_binary64_1791` `flip-+_binary64_1757` `distribute-lft-out--_binary64_1735` `distribute-rgt1-in_binary64_1739` `diff-log_binary64_1875` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `flip3-+_binary64_1786` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip--_binary64_1758` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `pow-exp_binary64_1851` `associate--r+_binary64_1719`

Counts

4 → 141

Calls

4 calls:

39.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
32.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
5.0ms	(/.f64 3 (pow.f64 x 3))
4.0ms	(/.f64 -1 (*.f64 x x))

series108.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
22.0ms	(/.f64 3 (pow.f64 x 3))
18.0ms	(/.f64 -1 (*.f64 x x))
17.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5045	2493

prune174.0ms (4.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	152	4	156

Error

0.1b

Counts

156 → 4

Compiler

Compiled 3229 to 2248 computations (30.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (-.f64 x 1))
0.0b	(*.f64 (+.f64 x 1) (+.f64 x 1))
0.0b	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 -1 (*.f64 x x)))
20.5b	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))

rewrite62.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`associate-*r/_binary64_1725`
39×	`*-un-lft-identity_binary64_1783`
32×	`frac-sub_binary64_1792`
31×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
30×	`add-sqr-sqrt_binary64_1805`
22×	`add-cube-cbrt_binary64_1818`
20×	`frac-times_binary64_1793`
19×	`flip3--_binary64_1787` `flip--_binary64_1758`
18×	`associate-/l/_binary64_1730`
13×	`cancel-sign-sub-inv_binary64_1749` `pow1_binary64_1844`
11×	`associate-r_binary64_1723`
10×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `distribute-lft-in_binary64_1732` `associate-*l/_binary64_1726` `distribute-rgt-in_binary64_1733`
9×	`times-frac_binary64_1789`
8×	`associate--l+_binary64_1720`
7×	`associate-l_binary64_1724`
6×	`swap-sqr_binary64_1750` `distribute-lft-out_binary64_1734` `add-log-exp_binary64_1822`
5×	`sub-neg_binary64_1776`
3×	`associate-/l_binary64_1728` `associate-/r_binary64_1727`
2×	`associate-/r/_binary64_1729` `difference-of-squares_binary64_1752` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `*-commutative_binary64_1714` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `associate--r+_binary64_1719`
1×	`div-sub_binary64_1788` `difference-of-sqr-1_binary64_1753` `pow-plus_binary64_1846` `div-inv_binary64_1780` `pow-prod-up_binary64_1853` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `pow-sqr_binary64_1756` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `pow2_binary64_1864`

Counts

4 → 158

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 -1 (*.f64 x x)))
11.0ms	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))
9.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))
8.0ms	(*.f64 x (-.f64 x 1))

series264.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))
24.0ms	(*.f64 x (-.f64 x 1))
19.0ms	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 -1 (*.f64 x x)))
8.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))

simplify96.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5078	3890

prune238.0ms (6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	172	2	174

Error

Counts

174 → 2

Compiler

Compiled 5140 to 3405 computations (33.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 -1 (*.f64 x 3))
16.2b	(/.f64 (-.f64 -1 (.f64 x 3)) (+.f64 -1 (.f64 x x)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`times-frac_binary64_1789`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-log-exp_binary64_1822`
3×	`associate-/l_binary64_1728` `associate-/r_binary64_1727`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip--_binary64_1758` `pow1_binary64_1844`
1×	`div-sub_binary64_1788` `flip-+_binary64_1757` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `flip3-+_binary64_1786` `clear-num_binary64_1782` `sub-neg_binary64_1776`

Counts

2 → 44

Calls

2 calls:

7.0ms	(/.f64 (-.f64 -1 (.f64 x 3)) (+.f64 -1 (.f64 x x)))
3.0ms	(-.f64 -1 (*.f64 x 3))

series43.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

22.0ms	(-.f64 -1 (*.f64 x 3))
21.0ms	(/.f64 (-.f64 -1 (.f64 x 3)) (+.f64 -1 (.f64 x x)))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4906	987
1	4906	987

prune49.0ms (1.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	50	2	52

Error

Counts

52 → 2

Compiler

Compiled 919 to 639 computations (30.5% saved)

regimes247.0ms (6.3%)

Accuracy

Total 0.0b remaining (91.7%)

Threshold costs 0.0b (91.7%)

Compiler

Compiled 2568 to 1983 computations (22.8% saved)

bsearch34.0ms (0.9%)

Steps

Iters	Range		Point
9	527586723076.3732	1.4724239656240512e+18	23245692697104.223
6	-3.3537279351463606e+50	-5.270554226181804e+49	-1.3460071312632054e+50

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	52
1	79	52

end0.0ms (0%)

sample1.7s (43.4%)

Algorithm

1×

intervals

Results

250.0ms	1996×	body	1024	valid
144.0ms	4266×	body	128	valid
97.0ms	1043×	body	512	valid
32.0ms	208×	body	2048	valid
30.0ms	487×	body	256	valid

Compiler

Compiled 1248 to 964 computations (22.8% saved)

Details

analyze4.0ms (0.1%)

sample30.0ms (0.8%)

simplify168.0ms (4.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite75.0ms (1.9%)

series62.0ms (1.6%)

simplify87.0ms (2.2%)

prune205.0ms (5.2%)

localize9.0ms (0.2%)

rewrite93.0ms (2.4%)

series108.0ms (2.7%)

simplify76.0ms (1.9%)

prune174.0ms (4.4%)

localize10.0ms (0.3%)

rewrite62.0ms (1.6%)

series264.0ms (6.7%)

simplify96.0ms (2.4%)

prune238.0ms (6%)

localize7.0ms (0.2%)

rewrite13.0ms (0.3%)

series43.0ms (1.1%)

simplify67.0ms (1.7%)

prune49.0ms (1.2%)

regimes247.0ms (6.3%)

bsearch34.0ms (0.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.7s (43.4%)

Profiling