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 (0.4%)

Algorithm

1×

intervals

Results

12.0ms	79×	body	1024	valid
5.0ms	140×	body	128	valid
3.0ms	24×	body	512	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify175.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune5.0ms (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: 18.3b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 1 (sqrt.f64 x))
2.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite83.0ms (1.2%)

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:

43.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series184.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
54.0ms	(/.f64 1 (sqrt.f64 x))
33.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4913	3696
1	4913	3696

prune690.0ms (9.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	191	10	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	192	10	202

Merged error: 17.7b

Counts

202 → 10

Compiler

Compiled 11159 to 8958 computations (19.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (sqrt.f64 x))
0.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
2.7b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite245.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

1332×	`*-un-lft-identity_binary64_2143`
1249×	`times-frac_binary64_2149`
725×	`add-sqr-sqrt_binary64_2165`
429×	`distribute-lft-out_binary64_2094`
304×	`sqrt-prod_binary64_2159`
293×	`add-cube-cbrt_binary64_2178`
180×	`distribute-lft-out--_binary64_2095`
168×	`div-inv_binary64_2140`
162×	`difference-of-squares_binary64_2112`
29×	`associate-/r*_binary64_2087`
28×	`associate-/l*_binary64_2088`
18×	`cancel-sign-sub-inv_binary64_2109`
14×	`add-exp-log_binary64_2181`
10×	`add-cbrt-cube_binary64_2179`
8×	`pow1_binary64_2204`
7×	`associate-/r/_binary64_2089`
6×	`add-log-exp_binary64_2182` `pow-flip_binary64_2217`
5×	`div-exp_binary64_2194`
3×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `flip3-+_binary64_2146` `flip-+_binary64_2117` `frac-2neg_binary64_2154` `associate-/l/_binary64_2090`
2×	`pow1/2_binary64_2223` `sqrt-div_binary64_2160` `flip--_binary64_2118` `1-exp_binary64_2187` `rec-exp_binary64_2193` `flip3--_binary64_2147` `frac-sub_binary64_2152` `sqrt-pow1_binary64_2161` `inv-pow_binary64_2228`
1×	`diff-log_binary64_2235` `sub-neg_binary64_2136` `div-sub_binary64_2148` `frac-add_binary64_2151`

Counts

4 → 554

Calls

4 calls:

79.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
24.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))

series248.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
56.0ms	(/.f64 1 (sqrt.f64 x))
38.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
34.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

simplify248.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

566 → 566

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4952	22251
1	4952	22251

prune1.6s (22.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	564	2	566
Fresh	8	1	9
Picked	0	1	1
Done	0	0	0
Total	572	4	576

Merged error: 5.0b

Counts

576 → 4

Compiler

Compiled 18766 to 14682 computations (21.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (sqrt.f64 x))
0.5b	(/.f64 1 (*.f64 x (+.f64 1 x)))
5.2b	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite129.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

417×	`times-frac_binary64_2149`
399×	`*-un-lft-identity_binary64_2143`
164×	`distribute-lft-out_binary64_2094`
148×	`sqrt-prod_binary64_2159`
141×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178`
61×	`div-inv_binary64_2140`
42×	`add-exp-log_binary64_2181`
41×	`associate-/r/_binary64_2089`
36×	`associate-*r/_binary64_2085`
30×	`associate-/r*_binary64_2087`
22×	`add-cbrt-cube_binary64_2179`
20×	`flip3-+_binary64_2146` `flip-+_binary64_2117`
19×	`div-exp_binary64_2194`
18×	`associate-/l*_binary64_2088`
11×	`pow1_binary64_2204`
9×	`cbrt-undiv_binary64_2177`
8×	`pow-flip_binary64_2217`
6×	`1-exp_binary64_2187` `rec-exp_binary64_2193` `prod-exp_binary64_2192`
4×	`clear-num_binary64_2142` `add-log-exp_binary64_2182` `frac-2neg_binary64_2154`
3×	`inv-pow_binary64_2228`
2×	`pow1/2_binary64_2223` `sqrt-div_binary64_2160` `cbrt-unprod_binary64_2176` `sqrt-pow1_binary64_2161`
1×	`pow-prod-down_binary64_2214` `associate-/l/_binary64_2090` `frac-add_binary64_2151`

Counts

4 → 319

Calls

4 calls:

54.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
7.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))

series260.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
52.0ms	(/.f64 1 (sqrt.f64 x))
33.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
23.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))

simplify148.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4947	9579
1	4947	9579

prune995.0ms (14%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	325	6	331
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	328	7	335

Merged error: 0.0b

Counts

335 → 7

Compiler

Compiled 17299 to 13636 computations (21.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.2b	(/.f64 1 (sqrt.f64 x))
0.4b	(/.f64 (/.f64 (sqrt.f64 1) x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

rewrite136.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`times-frac_binary64_2149`
104×	`*-un-lft-identity_binary64_2143`
71×	`add-sqr-sqrt_binary64_2165`
69×	`add-cube-cbrt_binary64_2178`
58×	`sqrt-prod_binary64_2159`
28×	`associate-/l*_binary64_2088`
26×	`add-exp-log_binary64_2181`
22×	`add-cbrt-cube_binary64_2179`
21×	`distribute-lft-out_binary64_2094`
16×	`associate-r_binary64_2083`
15×	`flip3-+_binary64_2146` `flip-+_binary64_2117`
14×	`associate-/r*_binary64_2087`
13×	`associate-/r/_binary64_2089`
12×	`frac-times_binary64_2153`
10×	`pow1_binary64_2204` `div-exp_binary64_2194`
9×	`div-inv_binary64_2140`
8×	`cbrt-undiv_binary64_2177`
6×	`pow-flip_binary64_2217` `associate-*r/_binary64_2085` `frac-add_binary64_2151`
4×	`add-log-exp_binary64_2182` `associate-l_binary64_2084` `associate-*l/_binary64_2086`
3×	`clear-num_binary64_2142` `cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `frac-2neg_binary64_2154`
2×	`pow1/2_binary64_2223` `sqrt-div_binary64_2160` `1-exp_binary64_2187` `rec-exp_binary64_2193` `sqrt-pow1_binary64_2161` `inv-pow_binary64_2228`
1×	`distribute-rgt-in_binary64_2093` `pow-prod-down_binary64_2214` `unswap-sqr_binary64_2111` `*-commutative_binary64_2074` `distribute-lft-in_binary64_2092` `associate-/l/_binary64_2090`

Counts

4 → 216

Calls

4 calls:

49.0ms	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
49.0ms	(/.f64 (/.f64 (sqrt.f64 1) x) (*.f64 (+.f64 x 1) (+.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))

series293.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(/.f64 (/.f64 (sqrt.f64 1) x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
64.0ms	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
46.0ms	(/.f64 1 (sqrt.f64 x))
30.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5187	4942

prune509.0ms (7.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	225	3	228
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	229	6	235

Merged error: 0.0b

Counts

235 → 6

Compiler

Compiled 9135 to 6909 computations (24.4% saved)

regimes14.0ms (0.2%)

Compiler: Compiled 103 to 84 computations (18.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	23
1	30	23

end0.0ms (0%)

sample902.0ms (12.7%)

Algorithm

1×

intervals

Results

339.0ms	2270×	body	1024	valid
167.0ms	4315×	body	128	valid
101.0ms	934×	body	512	valid
35.0ms	481×	body	256	valid

Compiler

Compiled 143 to 118 computations (17.5% saved)

Details

analyze2.0ms (0%)

sample26.0ms (0.4%)

simplify175.0ms (2.5%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

rewrite83.0ms (1.2%)

series184.0ms (2.6%)

simplify84.0ms (1.2%)

prune690.0ms (9.7%)

localize15.0ms (0.2%)

rewrite245.0ms (3.5%)

series248.0ms (3.5%)

simplify248.0ms (3.5%)

prune1.6s (22.5%)

localize12.0ms (0.2%)

rewrite129.0ms (1.8%)

series260.0ms (3.7%)

simplify148.0ms (2.1%)

prune995.0ms (14%)

localize12.0ms (0.2%)

rewrite136.0ms (1.9%)

series293.0ms (4.1%)

simplify81.0ms (1.1%)

prune509.0ms (7.2%)

regimes14.0ms (0.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample902.0ms (12.7%)

Profiling