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)

sample31.0ms (0.4%)

Algorithm

1×

intervals

Results

18.0ms	90×	body	1024	valid
5.0ms	123×	body	128	valid
3.0ms	31×	body	512	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify101.0ms (1.3%)

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%)

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: 21.5b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

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))))

rewrite68.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64_2146`
118×	`times-frac_binary64_2130`
117×	`*-un-lft-identity_binary64_2124`
76×	`sqrt-prod_binary64_2140`
56×	`add-cube-cbrt_binary64_2159`
27×	`cancel-sign-sub-inv_binary64_2090`
25×	`difference-of-squares_binary64_2093`
13×	`distribute-lft-out--_binary64_2076` `associate-/r*_binary64_2068`
12×	`add-exp-log_binary64_2162`
11×	`distribute-lft-out_binary64_2075`
9×	`pow1_binary64_2185`
8×	`add-cbrt-cube_binary64_2160`
7×	`div-inv_binary64_2121`
6×	`associate-/l*_binary64_2069` `sqrt-div_binary64_2141` `add-log-exp_binary64_2163` `pow-flip_binary64_2198`
4×	`associate-/r/_binary64_2070` `div-exp_binary64_2175`
3×	`sqrt-pow1_binary64_2142` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `1-exp_binary64_2168` `inv-pow_binary64_2209` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `sub-neg_binary64_2117` `frac-sub_binary64_2133`

Counts

4 → 189

Calls

4 calls:

38.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series102.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
34.0ms	(/.f64 1 (sqrt.f64 x))
18.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify100.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4945	3696
1	4945	3696

prune237.0ms (3%)

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: 20.9b

Counts

202 → 10

Compiler

Compiled 3808 to 2803 computations (26.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite205.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

1332×	`*-un-lft-identity_binary64_2124`
1249×	`times-frac_binary64_2130`
725×	`add-sqr-sqrt_binary64_2146`
429×	`distribute-lft-out_binary64_2075`
304×	`sqrt-prod_binary64_2140`
293×	`add-cube-cbrt_binary64_2159`
180×	`distribute-lft-out--_binary64_2076`
168×	`div-inv_binary64_2121`
162×	`difference-of-squares_binary64_2093`
29×	`associate-/r*_binary64_2068`
28×	`associate-/l*_binary64_2069`
18×	`cancel-sign-sub-inv_binary64_2090`
14×	`add-exp-log_binary64_2162`
10×	`add-cbrt-cube_binary64_2160`
8×	`pow1_binary64_2185`
7×	`associate-/r/_binary64_2070`
6×	`add-log-exp_binary64_2163` `pow-flip_binary64_2198`
5×	`div-exp_binary64_2175`
3×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-pow1_binary64_2142` `sqrt-div_binary64_2141` `pow1/2_binary64_2204` `frac-sub_binary64_2133` `1-exp_binary64_2168` `inv-pow_binary64_2209` `rec-exp_binary64_2174`
1×	`diff-log_binary64_2216` `sub-neg_binary64_2117` `div-sub_binary64_2129` `frac-add_binary64_2132`

Counts

4 → 554

Calls

4 calls:

63.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
20.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

series126.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
35.0ms	(/.f64 1 (sqrt.f64 x))
17.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
14.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

simplify237.0ms (3%)

Algorithm

1×	egg-herbie

Counts

566 → 566

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5050	22210

prune1.9s (24.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	563	3	566
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	572	4	576

Merged error: 6.9b

Counts

576 → 4

Compiler

Compiled 17933 to 13985 computations (22% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 1 (sqrt.f64 x))
0.5b	(/.f64 1 (*.f64 x (+.f64 1 x)))
7.1b	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite111.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

417×	`times-frac_binary64_2130`
399×	`*-un-lft-identity_binary64_2124`
164×	`distribute-lft-out_binary64_2075`
148×	`sqrt-prod_binary64_2140`
141×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
61×	`div-inv_binary64_2121`
42×	`add-exp-log_binary64_2162`
41×	`associate-/r/_binary64_2070`
36×	`associate-*r/_binary64_2066`
30×	`associate-/r*_binary64_2068`
22×	`add-cbrt-cube_binary64_2160`
20×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
19×	`div-exp_binary64_2175`
18×	`associate-/l*_binary64_2069`
11×	`pow1_binary64_2185`
9×	`cbrt-undiv_binary64_2158`
8×	`pow-flip_binary64_2198`
6×	`prod-exp_binary64_2173` `1-exp_binary64_2168` `rec-exp_binary64_2174`
4×	`clear-num_binary64_2123` `add-log-exp_binary64_2163` `frac-2neg_binary64_2135`
3×	`inv-pow_binary64_2209`
2×	`sqrt-pow1_binary64_2142` `sqrt-div_binary64_2141` `pow1/2_binary64_2204` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `associate-/l/_binary64_2071` `frac-add_binary64_2132`

Counts

4 → 319

Calls

4 calls:

45.0ms	(/.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)))
6.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

series132.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
27.0ms	(/.f64 1 (sqrt.f64 x))
16.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
12.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))

simplify155.0ms (2%)

Algorithm

1×	egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4946	9572
1	4946	9572

prune687.0ms (8.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	323	8	331
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	326	9	335

Merged error: 0.0b

Counts

335 → 9

Compiler

Compiled 9075 to 6843 computations (24.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
0.4b	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

rewrite117.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`*-un-lft-identity_binary64_2124`
88×	`times-frac_binary64_2130`
59×	`add-sqr-sqrt_binary64_2146`
57×	`add-cube-cbrt_binary64_2159`
40×	`sqrt-prod_binary64_2140`
36×	`add-exp-log_binary64_2162`
22×	`add-cbrt-cube_binary64_2160`
21×	`distribute-lft-out_binary64_2075`
19×	`associate-/l*_binary64_2069`
16×	`associate-r_binary64_2064` `div-exp_binary64_2175`
15×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
14×	`associate-/r*_binary64_2068`
13×	`associate-/r/_binary64_2070`
12×	`frac-times_binary64_2134`
10×	`pow1_binary64_2185`
9×	`div-inv_binary64_2121`
8×	`cbrt-undiv_binary64_2158`
6×	`pow-flip_binary64_2198` `associate-*r/_binary64_2066` `frac-add_binary64_2132`
5×	`prod-exp_binary64_2173`
4×	`add-log-exp_binary64_2163` `associate-l_binary64_2065` `associate-*l/_binary64_2067` `1-exp_binary64_2168` `rec-exp_binary64_2174`
3×	`clear-num_binary64_2123` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`
2×	`sqrt-pow1_binary64_2142` `sqrt-div_binary64_2141` `pow1/2_binary64_2204` `inv-pow_binary64_2209`
1×	`pow-prod-down_binary64_2195` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `distribute-rgt-in_binary64_2074` `associate-/l/_binary64_2071` `distribute-lft-in_binary64_2073`

Counts

4 → 202

Calls

4 calls:

43.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
38.0ms	(*.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)))
4.0ms	(/.f64 1 (sqrt.f64 x))

series146.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))
31.0ms	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
25.0ms	(/.f64 1 (sqrt.f64 x))
16.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify134.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4966	4534
1	4966	4534

prune320.0ms (4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	217	6	223

Merged error: 0b

Counts

223 → 6

Compiler

Compiled 5511 to 3985 computations (27.7% saved)

regimes314.0ms (4%)

Compiler: Compiled 4246 to 3500 computations (17.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	39
1	16	39

end0.0ms (0%)

sample2.6s (33.4%)

Algorithm

1×

intervals

Results

322.0ms	2248×	body	1024	valid
166.0ms	4294×	body	128	valid
111.0ms	1002×	body	512	valid
32.0ms	456×	body	256	valid

Compiler

Compiled 2163 to 1782 computations (17.6% saved)

Details

analyze2.0ms (0%)

sample31.0ms (0.4%)

simplify101.0ms (1.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite68.0ms (0.9%)

series102.0ms (1.3%)

simplify100.0ms (1.3%)

prune237.0ms (3%)

localize12.0ms (0.2%)

rewrite205.0ms (2.6%)

series126.0ms (1.6%)

simplify237.0ms (3%)

prune1.9s (24.1%)

localize11.0ms (0.1%)

rewrite111.0ms (1.4%)

series132.0ms (1.7%)

simplify155.0ms (2%)

prune687.0ms (8.7%)

localize11.0ms (0.1%)

rewrite117.0ms (1.5%)

series146.0ms (1.8%)

simplify134.0ms (1.7%)

prune320.0ms (4%)

regimes314.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (33.4%)

Profiling