Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	73×	body	1024	valid
5.0ms	138×	body	128	valid
3.0ms	30×	body	512	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify172.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 19.8b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
3.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite76.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`add-sqr-sqrt_binary64_1783`
97×	`times-frac_binary64_1768` `*-un-lft-identity_binary64_1762`
64×	`sqrt-prod_binary64_1777`
42×	`add-cube-cbrt_binary64_1794`
25×	`difference-of-squares_binary64_1731`
13×	`associate-/r*_binary64_1708` `distribute-lft-out--_binary64_1716`
12×	`add-exp-log_binary64_1797`
9×	`pow1_binary64_1820`
8×	`distribute-lft-out_binary64_1715` `add-cbrt-cube_binary64_1795`
6×	`div-inv_binary64_1759` `pow-flip_binary64_1833` `add-log-exp_binary64_1798` `associate-/l*_binary64_1709`
4×	`div-exp_binary64_1810` `sqrt-div_binary64_1778`
3×	`sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`
2×	`associate-/r/_binary64_1710` `frac-2neg_binary64_1773` `inv-pow_binary64_1844` `flip3-+_binary64_1765` `clear-num_binary64_1761` `flip-+_binary64_1736` `cbrt-undiv_binary64_1793` `1-exp_binary64_1803` `rec-exp_binary64_1809`
1×	`flip3--_binary64_1766` `rem-sqrt-square_binary64_1775` `diff-log_binary64_1851` `frac-sub_binary64_1771` `flip--_binary64_1737` `sub-neg_binary64_1755`

Counts

4 → 162

Calls

4 calls:

42.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series178.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
54.0ms	(/.f64 1 (sqrt.f64 x))
34.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
25.0ms	(sqrt.f64 (+.f64 x 1))

simplify73.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4950	3382
1	4950	3382

prune230.0ms (5.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	163	11	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	11	175

Merged error: 19.1b

Counts

175 → 11

Compiler

Compiled 3483 to 2575 computations (26.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.4b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite55.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_1783`
39×	`sqrt-prod_binary64_1777`
36×	`*-un-lft-identity_binary64_1762`
12×	`difference-of-squares_binary64_1731`
11×	`add-cube-cbrt_binary64_1794` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
10×	`times-frac_binary64_1768` `associate-/l*_binary64_1709`
9×	`distribute-lft-out--_binary64_1716` `pow1_binary64_1820`
7×	`associate-r_binary64_1704`
6×	`add-log-exp_binary64_1798` `sqrt-div_binary64_1778` `associate-l_binary64_1705`
5×	`distribute-lft-out_binary64_1715`
4×	`unswap-sqr_binary64_1730` `associate-*r/_binary64_1706`
3×	`pow-prod-down_binary64_1830` `flip3-+_binary64_1765` `flip-+_binary64_1736` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`
2×	`associate-/r/_binary64_1710` `flip3--_binary64_1766` `associate-/l/_binary64_1711` `prod-exp_binary64_1808` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `cbrt-unprod_binary64_1792` `flip--_binary64_1737`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `diff-log_binary64_1851` `div-sub_binary64_1767` `clear-num_binary64_1761` `associate-/r_binary64_1708` `div-inv_binary64_1759` `sqrt-unprod_binary64_1781` `sub-neg_binary64_1755` `-commutative_binary64_1695`

Counts

4 → 107

Calls

4 calls:

19.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (+.f64 1 x))

series318.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
68.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
51.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
26.0ms	(sqrt.f64 (+.f64 1 x))

simplify73.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5224	2642

prune150.0ms (3.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	125	5	130

Merged error: 0.2b

Counts

130 → 5

Compiler

Compiled 2823 to 1833 computations (35.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite75.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_1762`
78×	`times-frac_binary64_1768`
55×	`sqrt-prod_binary64_1777`
47×	`add-sqr-sqrt_binary64_1783`
45×	`distribute-lft-out_binary64_1715`
39×	`add-cube-cbrt_binary64_1794`
32×	`add-exp-log_binary64_1797`
27×	`associate-/l*_binary64_1709`
20×	`add-cbrt-cube_binary64_1795`
14×	`div-exp_binary64_1810`
9×	`pow1_binary64_1820`
8×	`associate-/r/_binary64_1710`
7×	`associate-/r_binary64_1708` `cbrt-undiv_binary64_1793` `associate-r*_binary64_1704`
6×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `add-log-exp_binary64_1798` `associate-l_binary64_1705`
5×	`prod-exp_binary64_1808`
4×	`div-inv_binary64_1759` `unswap-sqr_binary64_1730` `associate-*r/_binary64_1706` `sqrt-div_binary64_1778`
3×	`pow-prod-down_binary64_1830` `cbrt-unprod_binary64_1792` `1-exp_binary64_1803` `rec-exp_binary64_1809`
2×	`frac-2neg_binary64_1773` `clear-num_binary64_1761` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`
1×	`inv-pow_binary64_1844` `associate-/l/_binary64_1711` `+-commutative_binary64_1694` `pow-flip_binary64_1833` `sqrt-unprod_binary64_1781` `*-commutative_binary64_1695` `sum-log_binary64_1850`

Counts

4 → 166

Calls

4 calls:

25.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series308.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

155.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
58.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
51.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
42.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify69.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5084	4167

prune269.0ms (6.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	168	10	178
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	172	11	183

Merged error: 0b

Counts

183 → 11

Compiler

Compiled 4494 to 3079 computations (31.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))

rewrite73.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64_1768`
159×	`*-un-lft-identity_binary64_1762`
156×	`add-sqr-sqrt_binary64_1783`
119×	`add-cube-cbrt_binary64_1794`
87×	`sqrt-prod_binary64_1777`
49×	`distribute-lft-out_binary64_1715`
21×	`associate-/l*_binary64_1709`
20×	`associate-/r/_binary64_1710`
19×	`add-exp-log_binary64_1797`
13×	`add-cbrt-cube_binary64_1795`
12×	`flip3-+_binary64_1765` `flip-+_binary64_1736`
11×	`associate-/r*_binary64_1708`
10×	`div-inv_binary64_1759`
9×	`pow1_binary64_1820`
8×	`div-exp_binary64_1810`
7×	`associate-r_binary64_1704`
6×	`add-log-exp_binary64_1798` `associate-l_binary64_1705`
4×	`unswap-sqr_binary64_1730` `cbrt-undiv_binary64_1793` `sqrt-div_binary64_1778`
3×	`pow-prod-down_binary64_1830`
2×	`frac-2neg_binary64_1773` `clear-num_binary64_1761` `associate-*r/_binary64_1706` `sqrt-pow1_binary64_1779` `1-exp_binary64_1803` `rec-exp_binary64_1809` `pow1/2_binary64_1839`
1×	`inv-pow_binary64_1844` `associate-/l/_binary64_1711` `prod-exp_binary64_1808` `+-commutative_binary64_1694` `pow-flip_binary64_1833` `sqrt-unprod_binary64_1781` `cbrt-unprod_binary64_1792` `*-commutative_binary64_1695` `sum-log_binary64_1850`

Counts

4 → 252

Calls

4 calls:

15.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

series329.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
83.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
45.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
43.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

simplify132.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4952	9729
1	4952	9729

prune487.0ms (11.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	260	4	264
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	266	9	275

Merged error: 0b

Counts

275 → 9

Compiler

Compiled 7549 to 5390 computations (28.6% saved)

regimes24.0ms (0.6%)

Compiler: Compiled 213 to 168 computations (21.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	37
1	19	37

end0.0ms (0%)

sample1.0s (24.3%)

Algorithm

1×

intervals

Results

322.0ms	2252×	body	1024	valid
167.0ms	4251×	body	128	valid
111.0ms	990×	body	512	valid
35.0ms	507×	body	256	valid

Compiler

Compiled 261 to 209 computations (19.9% saved)

Details

analyze1.0ms (0%)

sample24.0ms (0.6%)

simplify172.0ms (4.1%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite76.0ms (1.8%)

series178.0ms (4.3%)

simplify73.0ms (1.8%)

prune230.0ms (5.5%)

localize7.0ms (0.2%)

rewrite55.0ms (1.3%)

series318.0ms (7.6%)

simplify73.0ms (1.8%)

prune150.0ms (3.6%)

localize8.0ms (0.2%)

rewrite75.0ms (1.8%)

series308.0ms (7.4%)

simplify69.0ms (1.7%)

prune269.0ms (6.5%)

localize11.0ms (0.3%)

rewrite73.0ms (1.8%)

series329.0ms (7.9%)

simplify132.0ms (3.2%)

prune487.0ms (11.7%)

regimes24.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (24.3%)

Profiling