Details

analyze180.0ms (1%)

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)

sample56.0ms (0.3%)

Algorithm

1×

intervals

Results

22.0ms	74×	body	1024	valid
10.0ms	132×	body	128	valid
8.0ms	37×	body	512	valid
2.0ms	13×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

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

20.5b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize15.0ms (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))
1.8b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite619.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

20.0b

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:

74.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(/.f64 1 (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 3837 to 2945 computations (23.2% saved)

series153.0ms (0.9%)

Error

20.2b

Counts

4 → 18

Calls

4 calls:

39.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
34.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
33.0ms	(sqrt.f64 (+.f64 x 1))
19.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 561 to 462 computations (17.6% saved)

simplify166.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4860	3341
1	4860	3341

prune434.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	195	12	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	196	12	208

Error

20.0b

Counts

208 → 12

Compiler

Compiled 3631 to 2709 computations (25.4% saved)

localize16.0ms (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)))
1.7b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite351.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

19.7b

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:

34.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
22.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
18.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
6.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 2641 to 1665 computations (37% saved)

series270.0ms (1.5%)

Error

19.8b

Counts

4 → 18

Calls

4 calls:

93.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
57.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
49.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
33.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 782 to 587 computations (24.9% saved)

simplify118.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5277	2138

prune269.0ms (1.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	141	2	143

Error

0.3b

Counts

143 → 2

Compiler

Compiled 2569 to 1638 computations (36.2% saved)

localize19.0ms (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)))

rewrite604.0ms (3.4%)

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:

38.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
21.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
16.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 4418 to 3053 computations (30.9% saved)

series220.0ms (1.2%)

Error

0.1b

Counts

4 → 15

Calls

4 calls:

88.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
52.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
32.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
27.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 561 to 452 computations (19.4% saved)

simplify183.0ms (1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4965	3678
1	4965	3678

prune444.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	176	5	181
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	177	6	183

Error

0.0b

Counts

183 → 6

Compiler

Compiled 4102 to 2821 computations (31.2% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite1.0s (5.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

234×	`times-frac_binary64_2130`
162×	`*-un-lft-identity_binary64_2124`
157×	`add-sqr-sqrt_binary64_2146`
120×	`add-cube-cbrt_binary64_2159`
91×	`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×	`pow1_binary64_2185` `div-inv_binary64_2121`
8×	`div-exp_binary64_2175`
7×	`associate-r_binary64_2064`
6×	`sqrt-div_binary64_2141` `associate-l_binary64_2065`
4×	`add-log-exp_binary64_2163` `unswap-sqr_binary64_2092` `cbrt-undiv_binary64_2158`
3×	`pow1/2_binary64_2204` `pow-prod-down_binary64_2195` `sqrt-pow1_binary64_2142`
2×	`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` `inv-pow_binary64_2209` `pow-flip_binary64_2198` `associate-/l/_binary64_2071` `rem-sqrt-square_binary64_2137`

Counts

4 → 256

Calls

4 calls:

27.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
19.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
10.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
6.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 8030 to 5819 computations (27.5% saved)

series238.0ms (1.3%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

71.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
53.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
48.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
31.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 865 to 704 computations (18.6% saved)

simplify270.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4975	9112
1	4975	9112

prune755.0ms (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	275	2	277
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	276	7	283

Error

0.0b

Counts

283 → 7

Compiler

Compiled 7378 to 5263 computations (28.7% saved)

regimes1.7s (9.5%)

Accuracy

Total 0.3b remaining (99.1%)

Threshold costs 0.3b (99.1%)

Compiler

Compiled 9081 to 7243 computations (20.2% 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%)

sample9.5s (53.7%)

Algorithm

1×

intervals

Results

674.0ms	2210×	body	1024	valid
328.0ms	4283×	body	128	valid
226.0ms	994×	body	512	valid
74.0ms	513×	body	256	valid

Compiler

Compiled 4499 to 3586 computations (20.3% saved)

Details

analyze180.0ms (1%)

sample56.0ms (0.3%)

simplify19.0ms (0.1%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite619.0ms (3.5%)

series153.0ms (0.9%)

simplify166.0ms (0.9%)

prune434.0ms (2.5%)

localize16.0ms (0.1%)

rewrite351.0ms (2%)

series270.0ms (1.5%)

simplify118.0ms (0.7%)

prune269.0ms (1.5%)

localize19.0ms (0.1%)

rewrite604.0ms (3.4%)

series220.0ms (1.2%)

simplify183.0ms (1%)

prune444.0ms (2.5%)

localize22.0ms (0.1%)

rewrite1.0s (5.9%)

series238.0ms (1.3%)

simplify270.0ms (1.5%)

prune755.0ms (4.3%)

regimes1.7s (9.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample9.5s (53.7%)

Profiling