Details

analyze95.0ms (1.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Symmetry

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample26.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	65×	body	1024	valid
4.0ms	142×	body	128	valid
2.0ms	34×	body	512	valid
1.0ms	13×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0%)

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

28.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite65.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

27.7b

Rules

15×	`sqrt-prod_binary64_2140`
14×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
6×	`cancel-sign-sub-inv_binary64_2090`
5×	`add-cube-cbrt_binary64_2159`
4×	`add-log-exp_binary64_2163` `difference-of-squares_binary64_2093`
3×	`pow1_binary64_2185` `distribute-lft-out--_binary64_2076`
2×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `distribute-lft-out_binary64_2075` `sqrt-div_binary64_2141`
1×	`diff-log_binary64_2216` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `flip3-+_binary64_2127` `flip-+_binary64_2098` `rem-sqrt-square_binary64_2137`

Counts

2 → 40

Calls

2 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 571 to 370 computations (35.2% saved)

series50.0ms (0.7%)

Error

27.5b

Counts

2 → 9

Calls

2 calls:

29.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 245 to 193 computations (21.2% saved)

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4932	589
1	4932	589

prune47.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	7	50

Error

0.1b

Counts

50 → 7

Compiler

Compiled 636 to 424 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite113.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

52×	`*-un-lft-identity_binary64_2124`
24×	`sqrt-prod_binary64_2140`
21×	`distribute-lft-out_binary64_2075`
18×	`times-frac_binary64_2130`
16×	`add-sqr-sqrt_binary64_2146`
15×	`add-cube-cbrt_binary64_2159`
7×	`add-exp-log_binary64_2162`
6×	`associate-/r*_binary64_2068`
5×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l*_binary64_2069`
2×	`div-exp_binary64_2175` `associate-/r/_binary64_2070` `sqrt-div_binary64_2141`
1×	`inv-pow_binary64_2209` `pow-flip_binary64_2198` `1-exp_binary64_2168` `rec-exp_binary64_2174` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

3 → 75

Calls

3 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 1268 to 926 computations (27% saved)

series53.0ms (0.7%)

Error

0.1b

Counts

3 → 12

Calls

3 calls:

17.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(sqrt.f64 (+.f64 1 x))
14.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 268 to 232 computations (13.4% saved)

simplify93.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4859	1227
1	4859	1227

prune88.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	5	0	5
Picked	0	1	1
Done	1	0	1
Total	87	7	94

Error

0.0b

Counts

94 → 7

Compiler

Compiled 1304 to 951 computations (27.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite813.0ms (10.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

310×	`*-un-lft-identity_binary64_2124`
290×	`sqrt-prod_binary64_2140`
172×	`times-frac_binary64_2130`
144×	`add-sqr-sqrt_binary64_2146`
116×	`distribute-lft-out_binary64_2075`
88×	`add-cube-cbrt_binary64_2159`
43×	`swap-sqr_binary64_2091`
31×	`pow1_binary64_2185`
27×	`sqrt-pow1_binary64_2142` `associate-l_binary64_2065` `associate-r_binary64_2064`
16×	`unswap-sqr_binary64_2092`
14×	`add-exp-log_binary64_2162` `associate-/r/_binary64_2070`
12×	`associate-/r*_binary64_2068`
11×	`inv-pow_binary64_2209` `pow-flip_binary64_2198`
10×	`add-cbrt-cube_binary64_2160`
9×	`pow1/2_binary64_2204` `pow-prod-up_binary64_2194` `rem-sqrt-square_binary64_2137` `div-inv_binary64_2121`
7×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
6×	`associate-/l*_binary64_2069`
5×	`pow-prod-down_binary64_2195` `sqrt-div_binary64_2141` `pow-sqr_binary64_2097`
4×	`add-log-exp_binary64_2163` `div-exp_binary64_2175`
3×	`sqr-abs_binary64_2139`
2×	`1-exp_binary64_2168` `rec-exp_binary64_2174` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123`
1×	`pow2_binary64_2205` `pow-plus_binary64_2187` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `sqrt-unprod_binary64_2144` `rem-square-sqrt_binary64_2136` `frac-times_binary64_2134` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `*-commutative_binary64_2055`

Counts

4 → 281

Calls

4 calls:

49.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
12.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 9177 to 6931 computations (24.5% saved)

series90.0ms (1.2%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
20.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
18.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 545 to 477 computations (12.5% saved)

simplify121.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5824	5963

prune662.0ms (8.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	290	3	293
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	292	8	300

Error

Counts

300 → 8

Compiler

Compiled 6988 to 5160 computations (26.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (/.f64 1 (+.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 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

rewrite1.2s (16.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

702×	`sqrt-prod_binary64_2140`
655×	`*-un-lft-identity_binary64_2124`
461×	`times-frac_binary64_2130`
264×	`distribute-lft-out_binary64_2075`
197×	`add-sqr-sqrt_binary64_2146`
192×	`add-cube-cbrt_binary64_2159`
30×	`associate-/l*_binary64_2069`
26×	`associate-/r/_binary64_2070`
15×	`associate-/r*_binary64_2068`
14×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
13×	`div-inv_binary64_2121`
12×	`pow1_binary64_2185`
10×	`sqrt-pow1_binary64_2142` `add-exp-log_binary64_2162`
8×	`add-cbrt-cube_binary64_2160`
6×	`sqrt-div_binary64_2141`
4×	`pow1/2_binary64_2204` `inv-pow_binary64_2209` `pow-div_binary64_2199` `pow-flip_binary64_2198` `add-log-exp_binary64_2163` `rem-sqrt-square_binary64_2137`
3×	`div-exp_binary64_2175`
2×	`cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123`
1×	`sqrt-undiv_binary64_2145` `associate-/l/_binary64_2071` `1-exp_binary64_2168` `rec-exp_binary64_2174`

Counts

4 → 401

Calls

4 calls:

33.0ms	(/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 14370 to 10613 computations (26.1% saved)

series99.0ms (1.3%)

Error

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
25.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
20.0ms	(/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 518 to 447 computations (13.7% saved)

simplify243.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

413 → 413

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4855	16587
1	4855	16587

prune1.1s (14.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	413	0	413
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	413	8	421

Error

Counts

421 → 8

Compiler

Compiled 12310 to 8845 computations (28.1% saved)

regimes284.0ms (3.8%)

Accuracy

Total 0.2b remaining (97.7%)

Threshold costs 0.2b (97.7%)

Compiler

Compiled 3538 to 2809 computations (20.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

Removed

()

end0.0ms (0%)

sample2.2s (29.3%)

Algorithm

1×

intervals

Results

192.0ms	2016×	body	1024	valid
124.0ms	4293×	body	128	valid
74.0ms	984×	body	512	valid
27.0ms	497×	body	256	valid
26.0ms	210×	body	2048	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 1738 to 1383 computations (20.4% saved)

Details

analyze95.0ms (1.3%)

sample26.0ms (0.3%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite65.0ms (0.9%)

series50.0ms (0.7%)

simplify40.0ms (0.5%)

prune47.0ms (0.6%)

localize9.0ms (0.1%)

rewrite113.0ms (1.5%)

series53.0ms (0.7%)

simplify93.0ms (1.2%)

prune88.0ms (1.2%)

localize10.0ms (0.1%)

rewrite813.0ms (10.8%)

series90.0ms (1.2%)

simplify121.0ms (1.6%)

prune662.0ms (8.8%)

localize10.0ms (0.1%)

rewrite1.2s (16.4%)

series99.0ms (1.3%)

simplify243.0ms (3.2%)

prune1.1s (14.2%)

regimes284.0ms (3.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (29.3%)

Profiling