Details

analyze2.0ms (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)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	75×	body	1024	valid
6.0ms	140×	body	128	valid
3.0ms	27×	body	512	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify176.0ms (3.6%)

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: 18.7b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (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))
1.2b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite79.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64_2165`
118×	`times-frac_binary64_2149`
117×	`*-un-lft-identity_binary64_2143`
76×	`sqrt-prod_binary64_2159`
56×	`add-cube-cbrt_binary64_2178`
27×	`cancel-sign-sub-inv_binary64_2109`
25×	`difference-of-squares_binary64_2112`
13×	`associate-/r*_binary64_2087` `distribute-lft-out--_binary64_2095`
12×	`add-exp-log_binary64_2181`
11×	`distribute-lft-out_binary64_2094`
9×	`pow1_binary64_2204`
8×	`add-cbrt-cube_binary64_2179`
7×	`div-inv_binary64_2140`
6×	`sqrt-div_binary64_2160` `add-log-exp_binary64_2182` `associate-/l*_binary64_2088` `pow-flip_binary64_2217`
4×	`associate-/r/_binary64_2089` `div-exp_binary64_2194`
3×	`pow1/2_binary64_2223` `flip3-+_binary64_2146` `sqrt-pow1_binary64_2161` `flip-+_binary64_2117`
2×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `1-exp_binary64_2187` `rec-exp_binary64_2193` `inv-pow_binary64_2228` `frac-2neg_binary64_2154`
1×	`rem-sqrt-square_binary64_2156` `diff-log_binary64_2235` `flip--_binary64_2118` `sub-neg_binary64_2136` `flip3--_binary64_2147` `frac-sub_binary64_2152`

Counts

4 → 189

Calls

4 calls:

44.0ms	(-.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))
4.0ms	(sqrt.f64 (+.f64 x 1))

series181.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
51.0ms	(/.f64 1 (sqrt.f64 x))
33.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4913	3696
1	4913	3696

prune473.0ms (9.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	193	8	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	194	8	202

Merged error: 18.2b

Counts

202 → 8

Compiler

Compiled 7804 to 6138 computations (21.3% saved)

localize8.0ms (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)))
1.2b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite56.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_2165`
42×	`sqrt-prod_binary64_2159`
38×	`*-un-lft-identity_binary64_2143`
13×	`add-cube-cbrt_binary64_2178`
12×	`difference-of-squares_binary64_2112`
11×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
10×	`associate-/l*_binary64_2088` `times-frac_binary64_2149`
9×	`pow1_binary64_2204` `distribute-lft-out--_binary64_2095`
7×	`associate-r_binary64_2083`
6×	`sqrt-div_binary64_2160` `add-log-exp_binary64_2182` `associate-l_binary64_2084` `cancel-sign-sub-inv_binary64_2109`
5×	`distribute-lft-out_binary64_2094`
4×	`associate-*r/_binary64_2085` `unswap-sqr_binary64_2111`
3×	`pow1/2_binary64_2223` `pow-prod-down_binary64_2214` `flip3-+_binary64_2146` `sqrt-pow1_binary64_2161` `flip-+_binary64_2117`
2×	`cbrt-undiv_binary64_2177` `flip--_binary64_2118` `associate-/r/_binary64_2089` `cbrt-unprod_binary64_2176` `flip3--_binary64_2147` `prod-exp_binary64_2192` `div-exp_binary64_2194` `associate-/l/_binary64_2090`
1×	`rem-sqrt-square_binary64_2156` `diff-log_binary64_2235` `clear-num_binary64_2142` `associate-/r_binary64_2087` `sub-neg_binary64_2136` `sqrt-unprod_binary64_2163` `div-inv_binary64_2140` `-commutative_binary64_2074` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 113

Calls

4 calls:

20.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 1 x))

series314.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
76.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
52.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
26.0ms	(sqrt.f64 (+.f64 1 x))

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5009	2693

prune194.0ms (4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	130	3	133

Merged error: 0.3b

Counts

133 → 3

Compiler

Compiled 3565 to 2430 computations (31.8% saved)

localize11.0ms (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)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))

rewrite72.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_2143`
78×	`times-frac_binary64_2149`
55×	`sqrt-prod_binary64_2159`
47×	`add-sqr-sqrt_binary64_2165`
45×	`distribute-lft-out_binary64_2094`
39×	`add-cube-cbrt_binary64_2178`
32×	`add-exp-log_binary64_2181`
27×	`associate-/l*_binary64_2088`
20×	`add-cbrt-cube_binary64_2179`
14×	`div-exp_binary64_2194`
9×	`pow1_binary64_2204`
8×	`associate-/r/_binary64_2089`
7×	`cbrt-undiv_binary64_2177` `associate-/r_binary64_2087` `associate-r*_binary64_2083`
6×	`add-log-exp_binary64_2182` `associate-l_binary64_2084` `flip3-+_binary64_2146` `flip-+_binary64_2117`
5×	`prod-exp_binary64_2192`
4×	`sqrt-div_binary64_2160` `div-inv_binary64_2140` `associate-*r/_binary64_2085` `unswap-sqr_binary64_2111`
3×	`1-exp_binary64_2187` `cbrt-unprod_binary64_2176` `rec-exp_binary64_2193` `pow-prod-down_binary64_2214`
2×	`pow1/2_binary64_2223` `clear-num_binary64_2142` `sqrt-pow1_binary64_2161` `frac-2neg_binary64_2154`
1×	`+-commutative_binary64_2073` `sqrt-unprod_binary64_2163` `sum-log_binary64_2234` `pow-flip_binary64_2217` `*-commutative_binary64_2074` `inv-pow_binary64_2228` `associate-/l/_binary64_2090`

Counts

4 → 166

Calls

4 calls:

22.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series311.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
62.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
46.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
38.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify86.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4944	4177
1	4944	4177

prune734.0ms (15.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	168	10	178
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	169	12	181

Merged error: 0.0b

Counts

181 → 12

Compiler

Compiled 13362 to 9906 computations (25.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite80.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-sqr-sqrt_binary64_2165`
82×	`times-frac_binary64_2149`
66×	`*-un-lft-identity_binary64_2143`
54×	`add-exp-log_binary64_2181`
53×	`add-cube-cbrt_binary64_2178`
38×	`sqrt-prod_binary64_2159`
29×	`associate-l_binary64_2084`
28×	`associate-r_binary64_2083`
22×	`add-cbrt-cube_binary64_2179`
20×	`div-exp_binary64_2194`
19×	`unswap-sqr_binary64_2111`
17×	`prod-exp_binary64_2192`
15×	`pow1_binary64_2204`
12×	`associate-/r/_binary64_2089`
11×	`associate-*l/_binary64_2086` `flip3-+_binary64_2146` `flip-+_binary64_2117`
10×	`sqrt-div_binary64_2160` `associate-/r*_binary64_2087` `1-exp_binary64_2187` `rec-exp_binary64_2193`
8×	`distribute-lft-out_binary64_2094` `frac-add_binary64_2151`
6×	`cbrt-undiv_binary64_2177` `associate-/l*_binary64_2088` `pow-prod-down_binary64_2214` `pow-flip_binary64_2217`
5×	`cbrt-unprod_binary64_2176`
4×	`add-log-exp_binary64_2182` `div-inv_binary64_2140` `inv-pow_binary64_2228`
3×	`pow1/2_binary64_2223` `sqrt-pow1_binary64_2161`
2×	`clear-num_binary64_2142` `*-commutative_binary64_2074` `frac-2neg_binary64_2154`
1×	`sqrt-unprod_binary64_2163` `frac-times_binary64_2153` `associate-*r/_binary64_2085` `un-div-inv_binary64_2141`

Counts

4 → 213

Calls

4 calls:

30.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
10.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
10.0ms	(/.f64 1 (+.f64 (+.f64 1 x) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
5.0ms	(/.f64 1 (sqrt.f64 x))

series275.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (+.f64 (+.f64 1 x) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
52.0ms	(/.f64 1 (+.f64 (+.f64 1 x) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
52.0ms	(/.f64 1 (sqrt.f64 x))
48.0ms	(*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify98.0ms (2%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4930	5472
1	4930	5472

prune513.0ms (10.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	6	4	10
Picked	1	0	1
Done	1	0	1
Total	230	7	237

Merged error: 0b

Counts

237 → 7

Compiler

Compiled 9115 to 6354 computations (30.3% saved)

regimes23.0ms (0.5%)

Compiler: Compiled 185 to 138 computations (25.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	26
1	17	26

end0.0ms (0%)

sample988.0ms (20.2%)

Algorithm

1×

intervals

Results

345.0ms	2246×	body	1024	valid
173.0ms	4280×	body	128	valid
110.0ms	993×	body	512	valid
38.0ms	481×	body	256	valid

Compiler

Compiled 227 to 174 computations (23.3% saved)

Details

analyze2.0ms (0%)

sample26.0ms (0.5%)

simplify176.0ms (3.6%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite79.0ms (1.6%)

series181.0ms (3.7%)

simplify82.0ms (1.7%)

prune473.0ms (9.7%)

localize8.0ms (0.2%)

rewrite56.0ms (1.1%)

series314.0ms (6.4%)

simplify73.0ms (1.5%)

prune194.0ms (4%)

localize11.0ms (0.2%)

rewrite72.0ms (1.5%)

series311.0ms (6.4%)

simplify86.0ms (1.8%)

prune734.0ms (15.1%)

localize10.0ms (0.2%)

rewrite80.0ms (1.6%)

series275.0ms (5.6%)

simplify98.0ms (2%)

prune513.0ms (10.5%)

regimes23.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample988.0ms (20.2%)

Profiling