Details

analyze209.0ms (1.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19
0	1	1
1	1	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 (0.2%)

Algorithm

1×

intervals

Results

10.0ms	65×	body	1024	valid
6.0ms	148×	body	128	valid
3.0ms	27×	body	512	valid
1.0ms	12×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify110.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune9.0ms (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

27.0b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
2.4b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite368.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

26.6b

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-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `associate-/l*_binary64_1728`
6×	`associate-/r/_binary64_1729`
5×	`add-log-exp_binary64_1822`
3×	`pow1_binary64_1844` `flip3--_binary64_1787` `flip--_binary64_1758` `div-inv_binary64_1780`
2×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-/l/_binary64_1730`
1×	`diff-log_binary64_1875` `frac-sub_binary64_1792` `sub-neg_binary64_1776`

Counts

3 → 147

Calls

3 calls:

53.0ms	(-.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))

Compiler

Compiled 3337 to 2419 computations (27.5% saved)

series170.0ms (1.3%)

Error

0.0b

Counts

3 → 32

Calls

3 calls:

75.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
38.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
27.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 992 to 825 computations (16.8% saved)

simplify125.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5572	3013

prune239.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	174	5	179
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	5	180

Error

0.0b

Counts

180 → 5

Compiler

Compiled 3411 to 2403 computations (29.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 1 x))
0.1b	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
2.4b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
21.0b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3))

rewrite581.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

119×	`*-un-lft-identity_binary64_1783`
112×	`add-sqr-sqrt_binary64_1805`
99×	`times-frac_binary64_1789`
59×	`add-cube-cbrt_binary64_1818`
54×	`cbrt-prod_binary64_1814`
40×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
34×	`cancel-sign-sub-inv_binary64_1749`
23×	`distribute-lft-out_binary64_1734`
22×	`difference-of-squares_binary64_1752`
12×	`associate-/r/_binary64_1729`
9×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
6×	`add-log-exp_binary64_1822` `div-inv_binary64_1780`
5×	`pow1_binary64_1844` `flip3-+_binary64_1786` `flip-+_binary64_1757` `distribute-lft-out--_binary64_1735`
4×	`sqr-pow_binary64_1755` `difference-of-sqr-1_binary64_1753` `associate-/r*_binary64_1727`
3×	`cube-div_binary64_1812` `pow-unpow_binary64_1860` `associate-/l*_binary64_1728`
2×	`cbrt-div_binary64_1815` `unpow3_binary64_1849` `cube-mult_binary64_1813` `flip3--_binary64_1787` `flip--_binary64_1758` `div-exp_binary64_1834` `pow-exp_binary64_1851` `rem-cube-cbrt_binary64_1806` `cbrt-undiv_binary64_1817`
1×	`pow1/3_binary64_1865` `rem-cbrt-cube_binary64_1807` `diff-log_binary64_1875` `frac-sub_binary64_1792` `sub-neg_binary64_1776` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `frac-2neg_binary64_1794` `clear-num_binary64_1782`

Counts

4 → 202

Calls

4 calls:

92.0ms	(-.f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
16.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3))
8.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
5.0ms	(/.f64 x (+.f64 1 x))

Compiler

Compiled 5504 to 4145 computations (24.7% saved)

series268.0ms (2%)

Error

0.0b

Counts

4 → 41

Calls

4 calls:

73.0ms	(-.f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
59.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
53.0ms	(/.f64 x (+.f64 1 x))
37.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3))

Compiler

Compiled 1508 to 1276 computations (15.4% saved)

simplify118.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5138	4260

prune369.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	243	5	248

Error

0.0b

Counts

248 → 5

Compiler

Compiled 5197 to 3780 computations (27.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))
0.0b	(*.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)))
0.0b	(*.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
2.4b	(-.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (/.f64 (+.f64 1 x) (+.f64 x -1))))

rewrite1.8s (13.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

544×	`*-un-lft-identity_binary64_1783`
320×	`times-frac_binary64_1789`
193×	`distribute-lft-out_binary64_1734`
150×	`add-sqr-sqrt_binary64_1805`
106×	`add-cube-cbrt_binary64_1818`
72×	`swap-sqr_binary64_1750`
44×	`associate-l_binary64_1724` `associate-r_binary64_1723`
30×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
20×	`difference-of-sqr--1_binary64_1754`
19×	`associate-/r/_binary64_1729`
18×	`pow1_binary64_1844` `frac-sub_binary64_1792`
14×	`frac-times_binary64_1793` `associate-l/_binary64_1726` `associate-r/_binary64_1725` `difference-of-squares_binary64_1752`
12×	`associate-/r*_binary64_1727`
11×	`associate-/l/_binary64_1730`
9×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `div-inv_binary64_1780` `flip3-+_binary64_1786` `flip-+_binary64_1757`
8×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751`
6×	`add-log-exp_binary64_1822`
4×	`associate-/l*_binary64_1728`
2×	`flip3--_binary64_1787` `flip--_binary64_1758` `pow2_binary64_1864` `pow-prod-down_binary64_1854` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `pow-sqr_binary64_1756` `*-commutative_binary64_1714`
1×	`diff-log_binary64_1875` `sub-neg_binary64_1776` `cancel-sign-sub-inv_binary64_1749` `frac-2neg_binary64_1794` `div-sub_binary64_1788` `clear-num_binary64_1782` `frac-add_binary64_1791`

Counts

4 → 329

Calls

4 calls:

65.0ms	(/.f64 (-.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))
36.0ms	(*.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
22.0ms	(*.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)))
20.0ms	(-.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (/.f64 (+.f64 1 x) (+.f64 x -1))))

Compiler

Compiled 18824 to 13573 computations (27.9% saved)

series388.0ms (2.9%)

Error

0.0b

Counts

4 → 43

Calls

4 calls:

129.0ms	(/.f64 (-.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))
107.0ms	(-.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (/.f64 (+.f64 1 x) (+.f64 x -1))))
45.0ms	(*.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
41.0ms	(*.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x)))

Compiler

Compiled 2629 to 2069 computations (21.3% saved)

simplify202.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4945	12014
1	4945	12014

prune1.6s (11.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	369	3	372
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	371	6	377

Error

0.0b

Counts

377 → 6

Compiler

Compiled 17142 to 12473 computations (27.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 1 x))
0.0b	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
2.4b	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
2.4b	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))

rewrite1.3s (9.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

983×	`*-un-lft-identity_binary64_1783`
396×	`times-frac_binary64_1789`
262×	`distribute-lft-out_binary64_1734`
186×	`sqrt-prod_binary64_1799`
168×	`distribute-lft-out--_binary64_1735`
135×	`add-sqr-sqrt_binary64_1805`
79×	`swap-sqr_binary64_1750`
52×	`cancel-sign-sub-inv_binary64_1749`
41×	`add-cube-cbrt_binary64_1818`
24×	`difference-of-squares_binary64_1752` `sqrt-div_binary64_1800`
19×	`pow1_binary64_1844` `associate-l_binary64_1724` `associate-r_binary64_1723`
10×	`frac-sub_binary64_1792` `flip3--_binary64_1787` `flip--_binary64_1758`
9×	`frac-times_binary64_1793`
8×	`add-log-exp_binary64_1822` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `difference-of-sqr--1_binary64_1754` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
6×	`associate-/r/_binary64_1729`
5×	`pow-prod-up_binary64_1853`
4×	`unswap-sqr_binary64_1751` `associate-/r*_binary64_1727`
3×	`div-inv_binary64_1780` `flip3-+_binary64_1786` `flip-+_binary64_1757` `pow-prod-down_binary64_1854` `pow-sqr_binary64_1756` `associate-l/_binary64_1726` `associate-r/_binary64_1725` `associate-/l*_binary64_1728`
2×	`diff-log_binary64_1875` `sub-neg_binary64_1776` `rem-sqrt-square_binary64_1796`
1×	`pow2_binary64_1864` `pow-plus_binary64_1846` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `sqrt-unprod_binary64_1803` `sqr-abs_binary64_1798` `rem-square-sqrt_binary64_1795` `*-commutative_binary64_1714` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782`

Counts

4 → 297

Calls

4 calls:

98.0ms	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
48.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
35.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
6.0ms	(/.f64 x (+.f64 1 x))

Compiler

Compiled 12499 to 9409 computations (24.7% saved)

series324.0ms (2.5%)

Error

Counts

4 → 43

Calls

4 calls:

97.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
67.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
62.0ms	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
36.0ms	(/.f64 x (+.f64 1 x))

Compiler

Compiled 2264 to 1822 computations (19.5% saved)

simplify164.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	6131	7694

prune771.0ms (5.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	340	6	346

Error

0.0b

Counts

346 → 6

Compiler

Compiled 9796 to 7111 computations (27.4% saved)

regimes509.0ms (3.9%)

Accuracy

Total 0.0b remaining (70.8%)

Threshold costs 0.0b (70.8%)

Compiler

Compiled 4621 to 3592 computations (22.3% saved)

bsearch52.0ms (0.4%)

Steps

Iters	Range		Point
8	44.79751205509612	87417.7786515175	1889.84365421045
8	-315734.20136470115	-73.04333385933747	-2954.202156251063

Compiler

Compiled 1 to 1 computations (0% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	158	121
1	158	121

end0.0ms (0%)

sample3.5s (26.2%)

Algorithm

1×

intervals

Results

328.0ms	1967×	body	1024	valid
186.0ms	4369×	body	128	valid
126.0ms	952×	body	512	valid
45.0ms	218×	body	2048	valid
41.0ms	494×	body	256	valid

Compiler

Compiled 2298 to 1788 computations (22.2% saved)

Details

analyze209.0ms (1.6%)

sample30.0ms (0.2%)

simplify110.0ms (0.8%)

prune9.0ms (0.1%)

localize13.0ms (0.1%)

rewrite368.0ms (2.8%)

series170.0ms (1.3%)

simplify125.0ms (0.9%)

prune239.0ms (1.8%)

localize21.0ms (0.2%)

rewrite581.0ms (4.4%)

series268.0ms (2%)

simplify118.0ms (0.9%)

prune369.0ms (2.8%)

localize11.0ms (0.1%)

rewrite1.8s (13.9%)

series388.0ms (2.9%)

simplify202.0ms (1.5%)

prune1.6s (11.8%)

localize13.0ms (0.1%)

rewrite1.3s (9.7%)

series324.0ms (2.5%)

simplify164.0ms (1.2%)

prune771.0ms (5.8%)

regimes509.0ms (3.9%)

bsearch52.0ms (0.4%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample3.5s (26.2%)

Profiling