Details

analyze5.0ms (0.1%)

Algorithm

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample48.0ms (0.8%)

Algorithm

1×

intervals

Results

21.0ms	71×	body	1024	valid
7.0ms	142×	body	128	valid
4.0ms	29×	body	512	valid
1.0ms	4×	body	2048	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify111.0ms (1.8%)

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

28.7b

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))
2.2b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite73.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

28.1b

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:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 571 to 370 computations (35.2% saved)

series56.0ms (0.9%)

Error

28.0b

Counts

2 → 9

Calls

2 calls:

33.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
15.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 245 to 193 computations (21.2% saved)

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4932	589
1	4932	589

prune57.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Error

0.1b

Counts

50 → 6

Compiler

Compiled 618 to 412 computations (33.3% saved)

localize7.0ms (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))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite119.0ms (1.9%)

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:

10.0ms	(/.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)

series74.0ms (1.2%)

Error

0.1b

Counts

3 → 12

Calls

3 calls:

23.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
20.0ms	(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)

simplify106.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4859	1227
1	4859	1227

prune100.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	5	0	5
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Error

0.0b

Counts

93 → 8

Compiler

Compiled 1313 to 960 computations (26.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite357.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

110×	`sqrt-prod_binary64_2140`
70×	`add-sqr-sqrt_binary64_2146`
46×	`*-un-lft-identity_binary64_2124`
40×	`sqrt-pow1_binary64_2142`
32×	`pow1_binary64_2185` `sqrt-div_binary64_2141`
28×	`add-cube-cbrt_binary64_2159`
20×	`pow1/2_binary64_2204`
18×	`swap-sqr_binary64_2091`
12×	`rem-sqrt-square_binary64_2137`
10×	`add-exp-log_binary64_2162` `associate-l_binary64_2065` `associate-r_binary64_2064`
9×	`pow-prod-up_binary64_2194` `flip3-+_binary64_2127` `flip-+_binary64_2098` `unswap-sqr_binary64_2092` `times-frac_binary64_2130`
8×	`add-cbrt-cube_binary64_2160` `distribute-lft-out_binary64_2075`
5×	`pow-prod-down_binary64_2195` `pow-sqr_binary64_2097`
4×	`add-log-exp_binary64_2163` `sqr-abs_binary64_2139` `frac-times_binary64_2134`
3×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`associate-l/_binary64_2067` `associate-r/_binary64_2066` `div-exp_binary64_2175` `associate-/r/_binary64_2070`
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` `*-commutative_binary64_2055` `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`

Counts

4 → 169

Calls

4 calls:

27.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
17.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

Compiler

Compiled 4294 to 3383 computations (21.2% saved)

series161.0ms (2.6%)

Error

0.0b

Counts

4 → 23

Calls

4 calls:

48.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
45.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
25.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
21.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))

Compiler

Compiled 901 to 755 computations (16.2% saved)

simplify115.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4888	2270
1	4888	2270

prune250.0ms (4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	192	8	200

Error

0.0b

Counts

200 → 8

Compiler

Compiled 3428 to 2581 computations (24.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite920.0ms (14.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

47.0ms	(*.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)))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 9177 to 6931 computations (24.5% saved)

series101.0ms (1.6%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
26.0ms	(/.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)))))
19.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 545 to 477 computations (12.5% saved)

simplify153.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5824	5963

prune530.0ms (8.4%)

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	1	1	2
Total	293	8	301

Error

0.0b

Counts

301 → 8

Compiler

Compiled 6834 to 5038 computations (26.3% saved)

regimes326.0ms (5.2%)

Accuracy

Total 0.2b remaining (96.1%)

Threshold costs 0.2b (96.1%)

Compiler

Compiled 3157 to 2527 computations (20% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample2.5s (40.4%)

Algorithm

1×

intervals

Results

236.0ms	1977×	body	1024	valid
140.0ms	4352×	body	128	valid
93.0ms	994×	body	512	valid
30.0ms	213×	body	2048	valid
26.0ms	464×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 1543 to 1238 computations (19.8% saved)

Details

analyze5.0ms (0.1%)

sample48.0ms (0.8%)

simplify111.0ms (1.8%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite73.0ms (1.2%)

series56.0ms (0.9%)

simplify45.0ms (0.7%)

prune57.0ms (0.9%)

localize7.0ms (0.1%)

rewrite119.0ms (1.9%)

series74.0ms (1.2%)

simplify106.0ms (1.7%)

prune100.0ms (1.6%)

localize14.0ms (0.2%)

rewrite357.0ms (5.7%)

series161.0ms (2.6%)

simplify115.0ms (1.8%)

prune250.0ms (4%)

localize15.0ms (0.2%)

rewrite920.0ms (14.6%)

series101.0ms (1.6%)

simplify153.0ms (2.4%)

prune530.0ms (8.4%)

regimes326.0ms (5.2%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.5s (40.4%)

Profiling