Details

analyze345.0ms (2.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17
0	1	1
1	1	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)

sample48.0ms (0.4%)

Algorithm

1×

intervals

Results

20.0ms	78×	body	1024	valid
8.0ms	125×	body	128	valid
7.0ms	36×	body	512	valid
2.0ms	17×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune4.0ms (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

Error

21.8b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize14.0ms (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)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite465.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

21.2b

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×	`add-log-exp_binary64_2163` `sqrt-div_binary64_2141` `pow-flip_binary64_2198` `associate-/l*_binary64_2069`
4×	`associate-/r/_binary64_2070` `div-exp_binary64_2175`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `pow1/2_binary64_2204` `sqrt-pow1_binary64_2142`
2×	`inv-pow_binary64_2209` `1-exp_binary64_2168` `rec-exp_binary64_2174` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123`
1×	`diff-log_binary64_2216` `frac-sub_binary64_2133` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `rem-sqrt-square_binary64_2137`

Counts

4 → 189

Calls

4 calls:

46.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
6.0ms	(sqrt.f64 (+.f64 x 1))
5.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 3837 to 2945 computations (23.2% saved)

series113.0ms (0.9%)

Error

21.5b

Counts

4 → 18

Calls

4 calls:

34.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
22.0ms	(/.f64 1 (sqrt.f64 x))
20.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
19.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 561 to 462 computations (17.6% saved)

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4860	3341
1	4860	3341

prune299.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	197	10	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	198	10	208

Error

21.2b

Counts

208 → 10

Compiler

Compiled 3610 to 2689 computations (25.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.1b	(/.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)))
2.2b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite231.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

21.0b

Rules

46×	`add-sqr-sqrt_binary64_2146`
42×	`sqrt-prod_binary64_2140`
38×	`*-un-lft-identity_binary64_2124`
13×	`add-cube-cbrt_binary64_2159`
12×	`difference-of-squares_binary64_2093`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`times-frac_binary64_2130` `associate-/l*_binary64_2069`
9×	`pow1_binary64_2185` `distribute-lft-out--_binary64_2076`
7×	`associate-r_binary64_2064`
6×	`add-log-exp_binary64_2163` `cancel-sign-sub-inv_binary64_2090` `sqrt-div_binary64_2141` `associate-l_binary64_2065`
5×	`distribute-lft-out_binary64_2075`
4×	`unswap-sqr_binary64_2092` `associate-*r/_binary64_2066`
3×	`pow1/2_binary64_2204` `pow-prod-down_binary64_2195` `sqrt-pow1_binary64_2142` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`flip3--_binary64_2128` `flip--_binary64_2099` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `associate-/l/_binary64_2071` `associate-/r/_binary64_2070`
1×	`diff-log_binary64_2216` `sub-neg_binary64_2117` `sqrt-unprod_binary64_2144` `-commutative_binary64_2055` `frac-2neg_binary64_2135` `div-sub_binary64_2129` `clear-num_binary64_2123` `div-inv_binary64_2121` `associate-/r_binary64_2068` `rem-sqrt-square_binary64_2137`

Counts

4 → 113

Calls

4 calls:

21.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
17.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
17.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 2641 to 1665 computations (37% saved)

series171.0ms (1.4%)

Error

21.1b

Counts

4 → 18

Calls

4 calls:

63.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
35.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
26.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
20.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 782 to 587 computations (24.9% saved)

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5277	2138

prune170.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	7	2	9
Picked	0	1	1
Done	0	0	0
Total	135	6	141

Error

0.2b

Counts

141 → 6

Compiler

Compiled 2646 to 1697 computations (35.9% saved)

localize9.0ms (0.1%)

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)))
0.2b	(/.f64 (/.f64 1 (+.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)))

rewrite402.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

118×	`*-un-lft-identity_binary64_2124`
78×	`times-frac_binary64_2130`
55×	`sqrt-prod_binary64_2140`
47×	`add-sqr-sqrt_binary64_2146`
45×	`distribute-lft-out_binary64_2075`
39×	`add-cube-cbrt_binary64_2159`
32×	`add-exp-log_binary64_2162`
27×	`associate-/l*_binary64_2069`
20×	`add-cbrt-cube_binary64_2160`
14×	`div-exp_binary64_2175`
9×	`pow1_binary64_2185`
8×	`associate-/r/_binary64_2070`
7×	`associate-r_binary64_2064` `cbrt-undiv_binary64_2158` `associate-/r*_binary64_2068`
6×	`add-log-exp_binary64_2163` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-l_binary64_2065`
5×	`prod-exp_binary64_2173`
4×	`unswap-sqr_binary64_2092` `sqrt-div_binary64_2141` `associate-*r/_binary64_2066` `div-inv_binary64_2121`
3×	`pow-prod-down_binary64_2195` `cbrt-unprod_binary64_2157` `1-exp_binary64_2168` `rec-exp_binary64_2174`
2×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `frac-2neg_binary64_2135` `clear-num_binary64_2123`
1×	`sqrt-unprod_binary64_2144` `*-commutative_binary64_2055` `associate-/l/_binary64_2071` `inv-pow_binary64_2209` `pow-flip_binary64_2198` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 166

Calls

4 calls:

29.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 4418 to 3053 computations (30.9% saved)

series168.0ms (1.4%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

71.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
51.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
17.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
14.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 561 to 452 computations (19.4% saved)

simplify128.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4965	3678
1	4965	3678

prune305.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	1	3	4
Picked	1	0	1
Done	1	0	1
Total	175	12	187

Error

Counts

187 → 12

Compiler

Compiled 4264 to 2949 computations (30.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.2b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite642.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

234×	`times-frac_binary64_2130`
159×	`*-un-lft-identity_binary64_2124`
156×	`add-sqr-sqrt_binary64_2146`
119×	`add-cube-cbrt_binary64_2159`
87×	`sqrt-prod_binary64_2140`
49×	`distribute-lft-out_binary64_2075`
21×	`associate-/l*_binary64_2069`
20×	`associate-/r/_binary64_2070`
19×	`add-exp-log_binary64_2162`
13×	`add-cbrt-cube_binary64_2160`
12×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
11×	`associate-/r*_binary64_2068`
10×	`div-inv_binary64_2121`
9×	`pow1_binary64_2185`
8×	`div-exp_binary64_2175`
7×	`associate-r_binary64_2064`
6×	`add-log-exp_binary64_2163` `associate-l_binary64_2065`
4×	`unswap-sqr_binary64_2092` `sqrt-div_binary64_2141` `cbrt-undiv_binary64_2158`
3×	`pow-prod-down_binary64_2195`
2×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `associate-*r/_binary64_2066` `1-exp_binary64_2168` `rec-exp_binary64_2174` `frac-2neg_binary64_2135` `clear-num_binary64_2123`
1×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `sqrt-unprod_binary64_2144` `*-commutative_binary64_2055` `associate-/l/_binary64_2071` `inv-pow_binary64_2209` `pow-flip_binary64_2198` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 252

Calls

4 calls:

15.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
14.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 7993 to 5774 computations (27.8% saved)

series201.0ms (1.7%)

Error

Counts

4 → 21

Calls

4 calls:

66.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
45.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
34.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
25.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 813 to 681 computations (16.2% saved)

simplify221.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4896	9188
1	4896	9188

prune564.0ms (4.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	274	11	285

Error

Counts

285 → 11

Compiler

Compiled 7292 to 5200 computations (28.7% saved)

regimes897.0ms (7.4%)

Accuracy

Total 0.3b remaining (99.3%)

Threshold costs 0.3b (99.3%)

Compiler

Compiled 9713 to 7699 computations (20.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample6.5s (53.8%)

Algorithm

1×

intervals

Results

422.0ms	2214×	body	1024	valid
212.0ms	4259×	body	128	valid
145.0ms	1015×	body	512	valid
51.0ms	512×	body	256	valid

Compiler

Compiled 4815 to 3814 computations (20.8% saved)

Details

analyze345.0ms (2.8%)

sample48.0ms (0.4%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize14.0ms (0.1%)

rewrite465.0ms (3.8%)

series113.0ms (0.9%)

simplify94.0ms (0.8%)

prune299.0ms (2.5%)

localize13.0ms (0.1%)

rewrite231.0ms (1.9%)

series171.0ms (1.4%)

simplify77.0ms (0.6%)

prune170.0ms (1.4%)

localize9.0ms (0.1%)

rewrite402.0ms (3.3%)

series168.0ms (1.4%)

simplify128.0ms (1.1%)

prune305.0ms (2.5%)

localize13.0ms (0.1%)

rewrite642.0ms (5.3%)

series201.0ms (1.7%)

simplify221.0ms (1.8%)

prune564.0ms (4.6%)

regimes897.0ms (7.4%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.5s (53.8%)

Profiling