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)

sample25.0ms (0%)

Algorithm

1×

intervals

Results

10.0ms	73×	body	1024	valid
5.0ms	134×	body	128	valid
3.0ms	33×	body	512	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify102.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune6.0ms (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

19.2b

Counts

2 → 1

Compiler

Compiled 11 to 10 computations (9.1% saved)

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

3.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.3b	(/.f64 1 (sqrt.f64 x))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
3.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite77.0ms (0%)

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

8 calls:

37.0ms	(-.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))
4.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(sqrt.f64 (+.f64 x 1))

series77.0ms (0%)

Counts

4 → 18

Calls

4 calls:

26.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
20.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
18.0ms	(sqrt.f64 (+.f64 x 1))
12.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 370 to 323 computations (12.7% saved)

simplify94.0ms (0%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4860	3341
1	4860	3341

prune683.0ms (0.3%)

Pruning

70 alts after pruning (69 fresh and 1 done)

	Pruned	Kept	Total
New	138	69	207
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	138	70	208

Error

18.7b

Counts

208 → 70

Compiler

Compiled 2942 to 2363 computations (19.7% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

3.3b	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
3.3b	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))

rewrite156.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

257×	`add-sqr-sqrt_binary64_2146`
240×	`times-frac_binary64_2130`
202×	`*-un-lft-identity_binary64_2124`
143×	`sqrt-prod_binary64_2140`
140×	`cbrt-prod_binary64_2155`
102×	`add-cube-cbrt_binary64_2159`
49×	`difference-of-squares_binary64_2093`
48×	`cancel-sign-sub-inv_binary64_2090`
20×	`distribute-lft-out--_binary64_2076` `distribute-lft-out_binary64_2075`
13×	`associate-/r*_binary64_2068`
12×	`associate-/l*_binary64_2069`
8×	`add-exp-log_binary64_2162`
6×	`sqrt-div_binary64_2141` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
5×	`pow1_binary64_2185` `div-inv_binary64_2121`
4×	`associate-/r/_binary64_2070`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `div-exp_binary64_2175` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `frac-sub_binary64_2133`

Counts

4 → 274

Calls

8 calls:

94.0ms	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))
7.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))
0.0ms	(sqrt.f64 (+.f64 1 x))

series92.0ms (0%)

Counts

4 → 18

Calls

4 calls:

28.0ms	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))
25.0ms	(sqrt.f64 (+.f64 1 x))
24.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
15.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))

Compiler

Compiled 624 to 577 computations (7.5% saved)

simplify130.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4928	6993
1	4928	6993

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(/.f64 1 (sqrt.f64 x))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`times-frac_binary64_2130`
16×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
12×	`sqrt-prod_binary64_2140`
6×	`associate-/r*_binary64_2068`
5×	`add-exp-log_binary64_2162`
3×	`associate-/l*_binary64_2069` `pow1_binary64_2185` `pow-flip_binary64_2198` `add-cbrt-cube_binary64_2160`
2×	`div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `add-log-exp_binary64_2163` `pow1/2_binary64_2204` `1-exp_binary64_2168` `div-inv_binary64_2121` `inv-pow_binary64_2209` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`

Counts

1 → 45

Calls

2 calls:

5.0ms	(/.f64 1 (sqrt.f64 x))
0.0ms	(/.f64 1 (sqrt.f64 x))

series12.0ms (0%)

Counts

1 → 3

Calls

1 calls:

12.0ms

(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 44 to 42 computations (4.5% saved)

simplify100.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4427	490
1	4427	490

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

3.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.3b	(/.f64 1 (sqrt.f64 x))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
3.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite77.0ms (0%)

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

8 calls:

43.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))
0.0ms	(sqrt.f64 (+.f64 x 1))

series84.0ms (0%)

Counts

4 → 18

Calls

4 calls:

28.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
25.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
19.0ms	(sqrt.f64 (+.f64 x 1))
12.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 426 to 379 computations (11% saved)

simplify93.0ms (0%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4860	3341
1	4860	3341

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

9.8b	(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
0.3b	(/.f64 1 (sqrt.f64 x))
0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))))
0.0b	(+.f64 (*.f64 x x) (-.f64 1 x))
9.8b	(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
11.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))))
11.1b	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))
15.4b	(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))

rewrite259.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

452×	`times-frac_binary64_2130`
367×	`add-sqr-sqrt_binary64_2146`
277×	`*-un-lft-identity_binary64_2124`
256×	`sqrt-prod_binary64_2140`
168×	`add-cube-cbrt_binary64_2159`
149×	`cancel-sign-sub-inv_binary64_2090`
55×	`difference-of-squares_binary64_2093`
26×	`distribute-lft-out_binary64_2075`
14×	`sqrt-div_binary64_2141`
9×	`associate-/r/_binary64_2070` `div-inv_binary64_2121`
7×	`distribute-lft-out--_binary64_2076` `associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098`
6×	`pow1_binary64_2185` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `associate-/l/_binary64_2071`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `sqrt-undiv_binary64_2145` `diff-log_binary64_2216` `sub-neg_binary64_2117` `frac-sub_binary64_2133` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 326

Calls

8 calls:

165.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))))
17.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))
10.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))
6.0ms	(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
0.0ms	(+.f64 (*.f64 x x) (-.f64 1 x))

series122.0ms (0.1%)

Counts

4 → 23

Calls

4 calls:

36.0ms	(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))
30.0ms	(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
30.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))))
25.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))

Compiler

Compiled 580 to 498 computations (14.1% saved)

simplify185.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

349 → 349

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4973	15006
1	4973	15006

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

3.3b	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
3.3b	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))

rewrite147.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

257×	`add-sqr-sqrt_binary64_2146`
240×	`times-frac_binary64_2130`
202×	`*-un-lft-identity_binary64_2124`
143×	`sqrt-prod_binary64_2140`
140×	`cbrt-prod_binary64_2155`
102×	`add-cube-cbrt_binary64_2159`
49×	`difference-of-squares_binary64_2093`
48×	`cancel-sign-sub-inv_binary64_2090`
20×	`distribute-lft-out--_binary64_2076` `distribute-lft-out_binary64_2075`
13×	`associate-/r*_binary64_2068`
12×	`associate-/l*_binary64_2069`
8×	`add-exp-log_binary64_2162`
6×	`sqrt-div_binary64_2141` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
5×	`pow1_binary64_2185` `div-inv_binary64_2121`
4×	`associate-/r/_binary64_2070`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `div-exp_binary64_2175` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `frac-sub_binary64_2133`

Counts

4 → 274

Calls

8 calls:

93.0ms	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))
7.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
6.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))
0.0ms	(sqrt.f64 (+.f64 1 x))

series94.0ms (0%)

Counts

4 → 18

Calls

4 calls:

33.0ms	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))
24.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
21.0ms	(sqrt.f64 (+.f64 1 x))
16.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))

Compiler

Compiled 652 to 605 computations (7.2% saved)

simplify133.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4928	6993
1	4928	6993

prune18.2s (9.2%)

Pruning

412 alts after pruning (406 fresh and 6 done)

	Pruned	Kept	Total
New	845	343	1188
Fresh	1	63	64
Picked	0	0	0
Done	0	6	6
Total	846	412	1258

Error

18.7b

Counts

1258 → 412

Compiler

Compiled 25550 to 21116 computations (17.4% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

3.3b	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
3.3b	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64_2124`
78×	`times-frac_binary64_2130`
64×	`add-sqr-sqrt_binary64_2146`
63×	`add-cube-cbrt_binary64_2159`
53×	`sqrt-prod_binary64_2140`
45×	`cbrt-prod_binary64_2155`
13×	`associate-/r*_binary64_2068`
12×	`associate-/l*_binary64_2069`
9×	`distribute-lft-out_binary64_2075`
8×	`add-exp-log_binary64_2162`
6×	`add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
5×	`pow1_binary64_2185`
4×	`sqrt-div_binary64_2141`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `div-exp_binary64_2175` `frac-2neg_binary64_2135`
1×	`unsub-neg_binary64_2118` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `distribute-neg-frac_binary64_2088` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `associate-*r/_binary64_2066` `distribute-rgt-neg-out_binary64_2084` `frac-add_binary64_2132`

Counts

4 → 159

Calls

8 calls:

13.0ms	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))
8.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))
0.0ms	(sqrt.f64 (+.f64 1 x))

series108.0ms (0.1%)

Counts

4 → 18

Calls

4 calls:

34.0ms	(sqrt.f64 (+.f64 1 x))
28.0ms	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))
26.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
20.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))

Compiler

Compiled 712 to 665 computations (6.6% saved)

simplify98.0ms (0%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4842	3134
1	4842	3134

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))
0.3b	(/.f64 1 (sqrt.f64 x))
17.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))

rewrite830.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

1795×	`sqrt-prod_binary64_2140`
1689×	`times-frac_binary64_2130`
1096×	`add-sqr-sqrt_binary64_2146`
1068×	`*-un-lft-identity_binary64_2124`
682×	`add-cube-cbrt_binary64_2159`
366×	`cancel-sign-sub-inv_binary64_2090`
140×	`distribute-lft-out_binary64_2075`
110×	`difference-of-squares_binary64_2093`
96×	`sqrt-div_binary64_2141`
48×	`associate-/r/_binary64_2070`
42×	`associate-/l*_binary64_2069`
28×	`div-inv_binary64_2121`
26×	`associate-/r*_binary64_2068`
24×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
21×	`add-exp-log_binary64_2162`
13×	`add-cbrt-cube_binary64_2160`
10×	`div-exp_binary64_2175`
9×	`pow1_binary64_2185`
8×	`pow-flip_binary64_2198`
6×	`distribute-lft-out--_binary64_2076` `add-log-exp_binary64_2163`
5×	`cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142`
3×	`clear-num_binary64_2123` `pow1/2_binary64_2204` `1-exp_binary64_2168` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
2×	`inv-pow_binary64_2209`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `diff-log_binary64_2216` `sub-neg_binary64_2117` `frac-sub_binary64_2133` `associate-/l/_binary64_2071`

Counts

4 → 1000

Calls

8 calls:

363.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
26.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))
8.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
4.0ms	(/.f64 1 (sqrt.f64 x))
0.0ms	(sqrt.f64 (+.f64 1 x))

series120.0ms (0.1%)

Counts

4 → 21

Calls

4 calls:

48.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
29.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))
28.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
14.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 557 to 488 computations (12.4% saved)

simplify385.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1021 → 1021

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5058	31256

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

3.3b	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (cbrt.f64 1) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
3.3b	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (cbrt.f64 1) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))))

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64_2124`
78×	`times-frac_binary64_2130`
64×	`add-sqr-sqrt_binary64_2146`
63×	`add-cube-cbrt_binary64_2159`
53×	`sqrt-prod_binary64_2140`
45×	`cbrt-prod_binary64_2155`
13×	`associate-/r*_binary64_2068`
12×	`associate-/l*_binary64_2069`
8×	`distribute-lft-out_binary64_2075` `add-exp-log_binary64_2162`
6×	`add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
5×	`pow1_binary64_2185`
4×	`sqrt-div_binary64_2141`
3×	`div-inv_binary64_2121`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-exp_binary64_2175` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `distribute-lft-out--_binary64_2076` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `associate-*r/_binary64_2066` `frac-sub_binary64_2133`

Counts

4 → 159

Calls

8 calls:

15.0ms	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (cbrt.f64 1) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))))
7.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))
0.0ms	(sqrt.f64 (+.f64 1 x))

series97.0ms (0%)

Counts

4 → 18

Calls

4 calls:

28.0ms	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (cbrt.f64 1) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))))
25.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
22.0ms	(sqrt.f64 (+.f64 1 x))
21.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))

Compiler

Compiled 718 to 671 computations (6.5% saved)

simplify92.0ms (0%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4898	3167
1	4898	3167

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (neg.f64 (/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 (+.f64 1 x))))) (/.f64 (cbrt.f64 1) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))))
0.2b	(/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 (+.f64 1 x))))
0.1b	(/.f64 (cbrt.f64 1) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.1b	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))
17.0b	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (neg.f64 (/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 (+.f64 1 x))))) (/.f64 (cbrt.f64 1) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64_2124`
36×	`times-frac_binary64_2130`
34×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
29×	`cbrt-prod_binary64_2155`
21×	`sqrt-prod_binary64_2140`
6×	`associate-/l_binary64_2069` `associate-/r_binary64_2068` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162`
5×	`add-cbrt-cube_binary64_2160`
4×	`cbrt-div_binary64_2156` `pow1_binary64_2185`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `frac-add_binary64_2132`
2×	`distribute-neg-frac_binary64_2088` `distribute-lft-out_binary64_2075` `pow1/3_binary64_2206`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `distribute-lft-neg-out_binary64_2083` `unsub-neg_binary64_2118` `sum-log_binary64_2215` `associate-l/_binary64_2067` `+-commutative_binary64_2054` `associate-r/_binary64_2066` `frac-times_binary64_2134` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 103

Calls

8 calls:

13.0ms	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (neg.f64 (/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 (+.f64 1 x))))) (/.f64 (cbrt.f64 1) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))))
5.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))
0.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))

series194.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

66.0ms	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (*.f64 (neg.f64 (/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 (+.f64 1 x))))) (/.f64 (cbrt.f64 1) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))))
58.0ms	(cbrt.f64 (+.f64 1 x))
52.0ms	(cbrt.f64 (+.f64 1 x))
18.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))

Compiler

Compiled 1274 to 1184 computations (7.1% saved)

simplify95.0ms (0%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4907	2392
1	4907	2392

prune36.3s (18.3%)

Pruning

665 alts after pruning (655 fresh and 10 done)

	Pruned	Kept	Total
New	1208	294	1502
Fresh	40	361	401
Picked	0	0	0
Done	1	10	11
Total	1249	665	1914

Error

18.7b

Counts

1914 → 665

Compiler

Compiled 37230 to 32042 computations (13.9% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

3.3b	(+.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 x) (cbrt.f64 (cbrt.f64 1)))) (.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))
0.3b	(/.f64 (cbrt.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 x) (cbrt.f64 (cbrt.f64 1))))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (cbrt.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 x) (cbrt.f64 (cbrt.f64 1))))
3.3b	(+.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 x) (cbrt.f64 (cbrt.f64 1)))) (.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))

rewrite174.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

544×	`times-frac_binary64_2130`
353×	`cbrt-prod_binary64_2155`
295×	`*-un-lft-identity_binary64_2124`
280×	`add-sqr-sqrt_binary64_2146`
279×	`add-cube-cbrt_binary64_2159`
167×	`sqrt-prod_binary64_2140`
65×	`associate-/r*_binary64_2068`
11×	`add-exp-log_binary64_2162`
10×	`associate-/l*_binary64_2069`
8×	`distribute-lft-out_binary64_2075`
7×	`div-inv_binary64_2121` `add-cbrt-cube_binary64_2160`
6×	`add-log-exp_binary64_2163`
5×	`pow1_binary64_2185`
4×	`cbrt-undiv_binary64_2158` `sqrt-div_binary64_2141` `div-exp_binary64_2175`
3×	`associate-/r/_binary64_2070` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`clear-num_binary64_2123` `frac-2neg_binary64_2135`
1×	`unsub-neg_binary64_2118` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `distribute-neg-frac_binary64_2088` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `associate-*r/_binary64_2066` `distribute-rgt-neg-out_binary64_2084` `frac-add_binary64_2132`

Counts

4 → 407

Calls

8 calls:

67.0ms	(+.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 x) (cbrt.f64 (cbrt.f64 1)))) (.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))
19.0ms	(/.f64 (cbrt.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 x) (cbrt.f64 (cbrt.f64 1))))
8.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (+.f64 1 x))
0.0ms	(sqrt.f64 (+.f64 1 x))

series109.0ms (0.1%)

Counts

4 → 18

Calls

4 calls:

38.0ms	(+.f64 (/.f64 (cbrt.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 x) (cbrt.f64 (cbrt.f64 1)))) (.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))
28.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
26.0ms	(sqrt.f64 (+.f64 1 x))
17.0ms	(/.f64 (cbrt.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 x) (cbrt.f64 (cbrt.f64 1))))

Compiler

Compiled 840 to 793 computations (5.6% saved)

simplify212.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4924	15459
1	4924	15459

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 -1 (neg.f64 (sqrt.f64 x)))
0.3b	(/.f64 -1 (neg.f64 (sqrt.f64 x)))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_2130`
38×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
24×	`distribute-lft-neg-in_binary64_2081` `sqrt-prod_binary64_2140` `distribute-rgt-neg-in_binary64_2082`
16×	`associate-/r*_binary64_2068`
4×	`neg-mul-1_binary64_2120`
3×	`associate-/l*_binary64_2069` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `pow1_binary64_2185` `add-log-exp_binary64_2163` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

1 → 79

Calls

2 calls:

6.0ms	(/.f64 -1 (neg.f64 (sqrt.f64 x)))
0.0ms	(/.f64 -1 (neg.f64 (sqrt.f64 x)))

series12.0ms (0%)

Counts

1 → 3

Calls

1 calls:

12.0ms

(/.f64 -1 (neg.f64 (sqrt.f64 x)))

Compiler

Compiled 44 to 42 computations (4.5% saved)

simplify115.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4746	1212
1	4746	1212

localize15.0ms (0%)

Local error

Found 6 expressions with local error:

0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
0.0b	(/.f64 (cbrt.f64 1) (+.f64 1 (*.f64 x 1/2)))
0.0b	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (+.f64 1 (.f64 x 1/2))))))
0.0b	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (+.f64 1 (.f64 x 1/2))))))
0.0b	(/.f64 (cbrt.f64 1) (+.f64 1 (*.f64 x 1/2)))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64_2130`
46×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
33×	`cbrt-prod_binary64_2155`
21×	`sqrt-prod_binary64_2140`
12×	`associate-/l*_binary64_2069`
9×	`associate-/r*_binary64_2068`
7×	`add-exp-log_binary64_2162`
5×	`add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
3×	`pow1_binary64_2185` `div-inv_binary64_2121`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-exp_binary64_2175` `frac-2neg_binary64_2135`
1×	`unsub-neg_binary64_2118` `sum-log_binary64_2215` `distribute-neg-frac_binary64_2088` `distribute-lft-out_binary64_2075` `+-commutative_binary64_2054` `associate-*r/_binary64_2066` `distribute-rgt-neg-out_binary64_2084` `frac-add_binary64_2132`

Counts

3 → 115

Calls

6 calls:

13.0ms	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (+.f64 1 (.f64 x 1/2))))))
6.0ms	(/.f64 (cbrt.f64 1) (+.f64 1 (*.f64 x 1/2)))
5.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
0.0ms	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (+.f64 1 (.f64 x 1/2))))))
0.0ms	(/.f64 (cbrt.f64 1) (+.f64 1 (*.f64 x 1/2)))

series70.0ms (0%)

Counts

3 → 13

Calls

3 calls:

30.0ms	(/.f64 (cbrt.f64 1) (+.f64 1 (*.f64 x 1/2)))
23.0ms	(+.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (+.f64 1 (.f64 x 1/2))))))
16.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))

Compiler

Compiled 556 to 524 computations (5.8% saved)

simplify94.0ms (0%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4896	2432
1	4896	2432

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 x)))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.1b	(sqrt.f64 (cbrt.f64 x))
0.0b	(sqrt.f64 (+.f64 1 x))
0.3b	(/.f64 (/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
15.8b	(-.f64 (/.f64 (/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))

rewrite482.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

657×	`times-frac_binary64_2130`
592×	`add-sqr-sqrt_binary64_2146`
316×	`*-un-lft-identity_binary64_2124`
311×	`cbrt-prod_binary64_2155`
265×	`sqrt-prod_binary64_2140`
232×	`add-cube-cbrt_binary64_2159`
91×	`difference-of-squares_binary64_2093`
48×	`cancel-sign-sub-inv_binary64_2090`
22×	`associate-/l*_binary64_2069`
15×	`div-inv_binary64_2121`
9×	`associate-/r*_binary64_2068` `add-exp-log_binary64_2162`
8×	`distribute-lft-out_binary64_2075` `add-cbrt-cube_binary64_2160`
7×	`distribute-lft-out--_binary64_2076`
6×	`add-log-exp_binary64_2163`
4×	`pow1_binary64_2185`
3×	`cbrt-undiv_binary64_2158` `div-exp_binary64_2175`
2×	`associate-/r/_binary64_2070` `sqrt-div_binary64_2141` `pow1/3_binary64_2206`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `diff-log_binary64_2216` `sub-neg_binary64_2117` `frac-sub_binary64_2133` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135`

Counts

4 → 424

Calls

8 calls:

381.0ms	(-.f64 (/.f64 (/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))
13.0ms	(/.f64 (/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(sqrt.f64 (+.f64 1 x))

series382.0ms (0.2%)

Counts

4 → 15

Calls

4 calls:

142.0ms	(/.f64 (/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))
84.0ms	(cbrt.f64 x)
78.0ms	(-.f64 (/.f64 (/.f64 (cbrt.f64 1) (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))
77.0ms	(cbrt.f64 x)

Compiler

Compiled 788 to 736 computations (6.6% saved)

simplify224.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

439 → 439

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4949	18114
1	4949	18114

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (cbrt.f64 1) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))))
0.2b	(/.f64 (cbrt.f64 1) (cbrt.f64 (sqrt.f64 x)))
0.2b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.0b	(sqrt.f64 (+.f64 1 x))
0.6b	(cbrt.f64 (sqrt.f64 x))
0.6b	(cbrt.f64 (sqrt.f64 x))
0.6b	(cbrt.f64 (sqrt.f64 x))
22.3b	(+.f64 (.f64 (/.f64 (cbrt.f64 1) (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (/.f64 (cbrt.f64 1) (cbrt.f64 (sqrt.f64 x)))) (*.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))

rewrite44.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64_2155`
10×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
9×	`sqrt-prod_binary64_2140`
6×	`add-log-exp_binary64_2163`
4×	`pow1_binary64_2185` `associate-*r/_binary64_2066` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`distribute-neg-frac_binary64_2088` `pow1/3_binary64_2206` `frac-add_binary64_2132`
1×	`unsub-neg_binary64_2118` `sum-log_binary64_2215` `associate-*l/_binary64_2067` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `frac-times_binary64_2134` `distribute-rgt-neg-out_binary64_2084` `flip-+_binary64_2098`

Counts

4 → 57

Calls

8 calls:

30.0ms	(+.f64 (.f64 (/.f64 (cbrt.f64 1) (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (/.f64 (cbrt.f64 1) (cbrt.f64 (sqrt.f64 x)))) (*.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))
2.0ms	(cbrt.f64 (sqrt.f64 x))
2.0ms	(cbrt.f64 (sqrt.f64 x))
2.0ms	(cbrt.f64 (sqrt.f64 x))
0.0ms	(sqrt.f64 (+.f64 1 x))

series388.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

241.0ms	(cbrt.f64 (sqrt.f64 x))
59.0ms	(cbrt.f64 (sqrt.f64 x))
55.0ms	(cbrt.f64 (sqrt.f64 x))
33.0ms	(+.f64 (.f64 (/.f64 (cbrt.f64 1) (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (/.f64 (cbrt.f64 1) (cbrt.f64 (sqrt.f64 x)))) (*.f64 (cbrt.f64 1) (neg.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))))

Compiler

Compiled 816 to 719 computations (11.9% saved)

simplify79.0ms (0%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5106	978

prune1.1min (34.1%)

Pruning

1075 alts after pruning (1060 fresh and 15 done)

	Pruned	Kept	Total
New	700	443	1143
Fresh	33	617	650
Picked	0	0	0
Done	0	15	15
Total	733	1075	1808

Error

18.7b

Counts

1808 → 1075

Compiler

Compiled 27821 to 21775 computations (21.7% saved)

simplify1.6s (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5512	96046

regimes8.9s (4.5%)

Compiler: Compiled 104390 to 92028 computations (11.8% saved)

bsearch0.0ms (0%)

regimes45.0ms (0%)

Compiler: Compiled 194 to 182 computations (6.2% saved)

bsearch20.0ms (0%)

Steps

Iters	Range		Point
7	6.653005123369202e+90	9.391780611362517e+92	2.3678566194252168e+91

Compiler

Compiled 1 to 1 computations (0% saved)

regimes45.0ms (0%)

Compiler: Compiled 184 to 173 computations (6% saved)

bsearch18.0ms (0%)

Steps

Iters	Range		Point
8	8.393568525486575e+57	2.8527866112307675e+60	9.117725950103936e+57

Compiler

Compiled 1 to 1 computations (0% saved)

regimes41.0ms (0%)

Compiler: Compiled 174 to 164 computations (5.7% saved)

bsearch26.0ms (0%)

Steps

Iters	Range		Point
9	1.9630761091106349e+118	2.0566658036332655e+123	8.423173255108411e+122

Compiler

Compiled 1 to 1 computations (0% saved)

regimes28.0ms (0%)

Compiler: Compiled 84 to 83 computations (1.2% saved)

bsearch25.0ms (0%)

Steps

Iters	Range		Point
9	1.9630761091106349e+118	2.0566658036332655e+123	8.423173255108411e+122

Compiler

Compiled 1 to 1 computations (0% saved)

regimes24.0ms (0%)

Compiler: Compiled 58 to 60 computations (-3.4% saved)

bsearch23.0ms (0%)

Steps

Iters	Range		Point
8	5.73703793150327e+76	3.167201405442088e+80	8.059265398421139e+76

Compiler

Compiled 1 to 1 computations (0% saved)

regimes23.0ms (0%)

Compiler: Compiled 48 to 51 computations (-6.3% saved)

bsearch13.0ms (0%)

Steps

Iters	Range		Point
8	0.0195769410811402	98.34028342914021	0.9934451274417744

Compiler

Compiled 1 to 1 computations (0% saved)

regimes11.0ms (0%)

Accuracy

Total 0.5b remaining (2.3%)

Threshold costs 0.5b (2.3%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch30.0ms (0%)

Steps

Iters	Range		Point
8	6.284420973036512e+100	1.7128680911466219e+103	2.6904587650047774e+102

Compiler

Compiled 112 to 100 computations (10.7% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	216	162
1	216	162

end0.0ms (0%)

sample57.6s (29.1%)

Algorithm

1×

intervals

Results

309.0ms	2211×	body	1024	valid
159.0ms	4213×	body	128	valid
112.0ms	1054×	body	512	valid
36.0ms	522×	body	256	valid

Compiler

Compiled 52497 to 46280 computations (11.8% saved)

Pareto

0.5673838248201274