Details

Time bar (total: 2.0min)

analyze2.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%0%50%2
Compiler

Compiled 12 to 11 computations (8.3% saved)

sample36.0ms (0%)

Algorithm
1×intervals
Results
14.0ms76×body1024valid
7.0ms141×body128valid
3.0ms21×body512valid
2.0ms18×body256valid
Compiler

Compiled 26 to 26 computations (0% saved)

simplify102.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
3 → 3
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
07519
17519

prune3.0ms (0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New123
Fresh033
Picked000
Done000
Total156
Error
18.9b
Counts
6 → 3
Compiler

Compiled 13 to 12 computations (7.7% saved)

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

2.6b
(-.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))
2.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite71.0ms (0.1%)

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:

35.0ms
(-.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))
3.0ms
(sqrt.f64 (+.f64 x 1))
0.0ms
(sqrt.f64 (+.f64 x 1))

series79.0ms (0.1%)

Counts
4 → 18
Calls

4 calls:

26.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
22.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
18.0ms
(sqrt.f64 (+.f64 x 1))
13.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 370 to 323 computations (12.7% saved)

simplify104.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
048603341
148603341

prune1.0s (0.8%)

Pruning

71 alts after pruning (70 fresh and 1 done)

PrunedKeptTotal
New13968207
Fresh022
Picked000
Done011
Total13971210
Error
18.6b
Counts
210 → 71
Compiler

Compiled 2929 to 2349 computations (19.8% saved)

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (sqrt.f64 x) (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))))
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1 x))
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)))
2.6b
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite49.0ms (0%)

Algorithm
1×rewrite-expression-head
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×associate-/l*_binary64_2069 times-frac_binary64_2130
9×distribute-lft-out--_binary64_2076 pow1_binary64_2185
7×associate-*r*_binary64_2064
6×cancel-sign-sub-inv_binary64_2090 sqrt-div_binary64_2141 add-log-exp_binary64_2163 associate-*l*_binary64_2065
5×distribute-lft-out_binary64_2075
4×unswap-sqr_binary64_2092 associate-*r/_binary64_2066
3×pow-prod-down_binary64_2195 sqrt-pow1_binary64_2142 pow1/2_binary64_2204 flip3-+_binary64_2127 flip-+_binary64_2098
2×flip--_binary64_2099 flip3--_binary64_2128 cbrt-undiv_binary64_2158 associate-/r/_binary64_2070 prod-exp_binary64_2173 associate-/l/_binary64_2071 div-exp_binary64_2175 cbrt-unprod_binary64_2157
1×clear-num_binary64_2123 sqrt-unprod_binary64_2144 *-commutative_binary64_2055 associate-/r*_binary64_2068 diff-log_binary64_2216 rem-sqrt-square_binary64_2137 sub-neg_binary64_2117 div-sub_binary64_2129 div-inv_binary64_2121 frac-2neg_binary64_2135
Counts
4 → 113
Calls

8 calls:

17.0ms
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms
(sqrt.f64 (+.f64 1 x))
0.0ms
(sqrt.f64 (+.f64 1 x))

series143.0ms (0.1%)

Counts
4 → 18
Calls

4 calls:

62.0ms
(/.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))
27.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
19.0ms
(sqrt.f64 (+.f64 1 x))
Compiler

Compiled 528 to 419 computations (20.6% saved)

simplify76.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
052772138

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

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

rewrite7.0ms (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:

4.0ms
(/.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)

simplify110.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 0 (99.0ms)

IterNodesCost
04427490
14427490

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

9.5b
(-.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.4b
(/.f64 1 (pow.f64 x 3/2))
0.2b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b
(sqrt.f64 (+.f64 x 1))
0.2b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.4b
(/.f64 1 (pow.f64 x 3/2))
9.5b
(-.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
18.2b
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))

rewrite85.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
165×add-sqr-sqrt_binary64_2146
146×times-frac_binary64_2130
112×*-un-lft-identity_binary64_2124
64×add-cube-cbrt_binary64_2159
60×cbrt-prod_binary64_2155
44×sqrt-prod_binary64_2140
40×difference-of-squares_binary64_2093
31×unpow-prod-down_binary64_2203
27×cancel-sign-sub-inv_binary64_2090
17×sqr-pow_binary64_2096 add-exp-log_binary64_2162
14×associate-/r*_binary64_2068
8×add-cbrt-cube_binary64_2160 div-exp_binary64_2175
7×distribute-lft-out_binary64_2075
6×associate-/l*_binary64_2069 pow1_binary64_2185 add-log-exp_binary64_2163
5×div-inv_binary64_2121
4×associate-/r/_binary64_2070 sqrt-div_binary64_2141 pow-flip_binary64_2198 1-exp_binary64_2168 rec-exp_binary64_2174
3×pow-exp_binary64_2192 pow-to-exp_binary64_2193
2×cbrt-div_binary64_2156 clear-num_binary64_2123 cbrt-undiv_binary64_2158 distribute-lft-out--_binary64_2076 flip3-+_binary64_2127 flip-+_binary64_2098 inv-pow_binary64_2209 frac-2neg_binary64_2135
1×flip--_binary64_2099 flip3--_binary64_2128 sqrt-pow1_binary64_2142 diff-log_binary64_2216 pow1/3_binary64_2206 pow1/2_binary64_2204 sub-neg_binary64_2117 frac-sub_binary64_2133
Counts
4 → 219
Calls

8 calls:

46.0ms
(-.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms
(/.f64 1 (pow.f64 x 3/2))
4.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
0.0ms
(sqrt.f64 (+.f64 x 1))

series106.0ms (0.1%)

Counts
4 → 15
Calls

4 calls:

36.0ms
(-.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
28.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
23.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
17.0ms
(/.f64 1 (pow.f64 x 3/2))
Compiler

Compiled 438 to 382 computations (12.8% saved)

simplify129.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
234 → 234
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
048644716
148644716

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

7.4b
(-.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))))))
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))
7.4b
(-.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))))))
9.7b
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))
11.2b
(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
15.2b
(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))

rewrite253.0ms (0.2%)

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:

163.0ms
(-.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))))))
16.0ms
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))
7.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))
5.0ms
(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
0.0ms
(+.f64 (*.f64 x x) (-.f64 1 x))

series124.0ms (0.1%)

Counts
4 → 23
Calls

4 calls:

32.0ms
(-.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))))))
32.0ms
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))
30.0ms
(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
29.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))
Compiler

Compiled 580 to 498 computations (14.1% saved)

simplify196.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
349 → 349
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
0497315006
1497315006

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
0.1b
(sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1 x))
0.3b
(/.f64 1 (sqrt.f64 x))
0.3b
(*.f64 (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
2.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
2.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))

rewrite301.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
861×add-sqr-sqrt_binary64_2146
690×sqrt-prod_binary64_2140
640×times-frac_binary64_2130
555×*-un-lft-identity_binary64_2124
262×difference-of-squares_binary64_2093
128×swap-sqr_binary64_2091
122×distribute-lft-out--_binary64_2076
99×add-cube-cbrt_binary64_2159
59×div-inv_binary64_2121
54×cancel-sign-sub-inv_binary64_2090
44×associate-*l*_binary64_2065 associate-*r*_binary64_2064
30×distribute-lft-out_binary64_2075
28×sqrt-div_binary64_2141
21×pow1_binary64_2185
10×flip--_binary64_2099 flip3--_binary64_2128 frac-sub_binary64_2133 add-exp-log_binary64_2162
9×sqrt-pow1_binary64_2142 pow1/2_binary64_2204 frac-times_binary64_2134
8×add-log-exp_binary64_2163 add-cbrt-cube_binary64_2160
6×associate-/r*_binary64_2068
5×pow-prod-up_binary64_2194
4×associate-/r/_binary64_2070 unswap-sqr_binary64_2092
3×pow-prod-down_binary64_2195 associate-/l*_binary64_2069 associate-*l/_binary64_2067 pow-flip_binary64_2198 associate-*r/_binary64_2066 pow-sqr_binary64_2097
2×diff-log_binary64_2216 rem-sqrt-square_binary64_2137 sub-neg_binary64_2117 flip3-+_binary64_2127 flip-+_binary64_2098 div-exp_binary64_2175
1×clear-num_binary64_2123 sqrt-unprod_binary64_2144 cbrt-undiv_binary64_2158 *-commutative_binary64_2055 prod-exp_binary64_2173 pow-plus_binary64_2187 rem-square-sqrt_binary64_2136 pow2_binary64_2205 sqr-abs_binary64_2139 1-exp_binary64_2168 inv-pow_binary64_2209 cbrt-unprod_binary64_2157 frac-2neg_binary64_2135 rec-exp_binary64_2174
Counts
4 → 460
Calls

8 calls:

113.0ms
(*.f64 (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
41.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
36.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
4.0ms
(/.f64 1 (sqrt.f64 x))
0.0ms
(sqrt.f64 (+.f64 1 x))

series116.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

36.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
31.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
31.0ms
(*.f64 (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
17.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 524 to 459 computations (12.4% saved)

simplify203.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
472 → 472
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
0486213020
1486213020

prune14.5s (11.9%)

Pruning

368 alts after pruning (363 fresh and 5 done)

PrunedKeptTotal
New9313031234
Fresh56065
Picked000
Done156
Total9373681305
Error
0.2b
Counts
1305 → 368
Compiler

Compiled 21906 to 17061 computations (22.1% saved)

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite69.0ms (0.1%)

Algorithm
1×rewrite-expression-head
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×cbrt-undiv_binary64_2158 associate-/r*_binary64_2068 associate-*r*_binary64_2064
6×add-log-exp_binary64_2163 associate-*l*_binary64_2065 flip3-+_binary64_2127 flip-+_binary64_2098
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 1-exp_binary64_2168 cbrt-unprod_binary64_2157 rec-exp_binary64_2174
2×clear-num_binary64_2123 sqrt-pow1_binary64_2142 pow1/2_binary64_2204 frac-2neg_binary64_2135
1×sqrt-unprod_binary64_2144 sum-log_binary64_2215 *-commutative_binary64_2055 +-commutative_binary64_2054 pow-flip_binary64_2198 associate-/l/_binary64_2071 inv-pow_binary64_2209
Counts
4 → 166
Calls

8 calls:

20.0ms
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
10.0ms
(/.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))
0.0ms
(sqrt.f64 (+.f64 1 x))

series115.0ms (0.1%)

Counts
4 → 15
Calls

4 calls:

47.0ms
(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
27.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
20.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
20.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
Compiler

Compiled 386 to 331 computations (14.2% saved)

simplify116.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
049653678
149653678

localize6.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(/.f64 1 (sqrt.f64 x))
0.2b
(/.f64 1 (*.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))))
0.0b
(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x))))
0.0b
(+.f64 (*.f64 x x) (-.f64 1 x))
9.7b
(*.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))))
10.2b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (*.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))))))
11.2b
(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
15.2b
(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))

rewrite78.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
61×add-sqr-sqrt_binary64_2146
37×*-un-lft-identity_binary64_2124
33×times-frac_binary64_2130
31×sqrt-prod_binary64_2140
24×associate-*r*_binary64_2064
23×add-cube-cbrt_binary64_2159
14×sqrt-div_binary64_2141
13×cancel-sign-sub-inv_binary64_2090 add-exp-log_binary64_2162
10×unswap-sqr_binary64_2092
9×add-cbrt-cube_binary64_2160
8×associate-/r/_binary64_2070 pow1_binary64_2185
7×associate-*l*_binary64_2065 flip3-+_binary64_2127 flip-+_binary64_2098
6×add-log-exp_binary64_2163 div-inv_binary64_2121
5×difference-of-squares_binary64_2093
4×distribute-lft-out--_binary64_2076 associate-*l/_binary64_2067 prod-exp_binary64_2173 frac-times_binary64_2134
2×un-div-inv_binary64_2122 sqrt-pow1_binary64_2142 distribute-lft-out_binary64_2075 rem-sqrt-square_binary64_2137 pow1/2_binary64_2204 associate-*r/_binary64_2066 div-exp_binary64_2175 cbrt-unprod_binary64_2157
1×flip--_binary64_2099 pow-prod-down_binary64_2195 flip3--_binary64_2128 cbrt-undiv_binary64_2158 *-commutative_binary64_2055 diff-log_binary64_2216 sub-neg_binary64_2117 frac-sub_binary64_2133 1-exp_binary64_2168 rec-exp_binary64_2174
Counts
4 → 127
Calls

8 calls:

25.0ms
(*.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))))
22.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (*.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))))))
8.0ms
(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
7.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))
0.0ms
(+.f64 (*.f64 x x) (-.f64 1 x))

series121.0ms (0.1%)

Counts
4 → 23
Calls

4 calls:

35.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))
31.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (*.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))))))
29.0ms
(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
26.0ms
(*.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 1 x)))))
Compiler

Compiled 616 to 534 computations (13.3% saved)

simplify114.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
050113863

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.1b
(sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))))
0.1b
(sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))))
0.0b
(sqrt.f64 (+.f64 x 1))
0.5b
(*.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))) (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))))
16.7b
(-.f64 (*.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))) (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
18.2b
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
18.2b
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))

rewrite140.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
319×add-sqr-sqrt_binary64_2146
294×cbrt-prod_binary64_2155
276×sqrt-prod_binary64_2140
271×times-frac_binary64_2130
180×*-un-lft-identity_binary64_2124
110×add-cube-cbrt_binary64_2159
94×unpow-prod-down_binary64_2203
81×unswap-sqr_binary64_2092
58×sqr-pow_binary64_2096
35×swap-sqr_binary64_2091
31×associate-*l*_binary64_2065 associate-*r*_binary64_2064
27×cancel-sign-sub-inv_binary64_2090
19×pow1_binary64_2185
16×rem-sqrt-square_binary64_2137
14×sqrt-pow1_binary64_2142
10×cbrt-div_binary64_2156 sqrt-div_binary64_2141
9×div-inv_binary64_2121
8×pow1/3_binary64_2206 pow1/2_binary64_2204 sqr-abs_binary64_2139
6×pow-prod-up_binary64_2194 add-log-exp_binary64_2163 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
5×difference-of-squares_binary64_2093
4×pow-prod-down_binary64_2195 pow-sqr_binary64_2097
3×distribute-lft-out_binary64_2075 frac-sub_binary64_2133
2×associate-/r/_binary64_2070 associate-*l/_binary64_2067 associate-*r/_binary64_2066 frac-times_binary64_2134
1×flip--_binary64_2099 sqrt-unprod_binary64_2144 flip3--_binary64_2128 *-commutative_binary64_2055 diff-log_binary64_2216 prod-exp_binary64_2173 pow-plus_binary64_2187 rem-square-sqrt_binary64_2136 sub-neg_binary64_2117 pow2_binary64_2205 flip3-+_binary64_2127 flip-+_binary64_2098 cbrt-unprod_binary64_2157
Counts
4 → 331
Calls

8 calls:

37.0ms
(*.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))) (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))))
32.0ms
(-.f64 (*.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))) (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
4.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
0.0ms
(sqrt.f64 (+.f64 x 1))

series119.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

43.0ms
(-.f64 (*.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))) (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
26.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
25.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
25.0ms
(*.f64 (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))) (sqrt.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))))
Compiler

Compiled 538 to 473 computations (12.1% saved)

simplify179.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
343 → 343
Iterations

Useful iterations: 0 (91.0ms)

IterNodesCost
048668545
148668545

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
0.1b
(sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1 x))
0.3b
(*.f64 (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
0.5b
(*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))))
2.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
15.0b
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 1 x))))

rewrite267.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
443×add-sqr-sqrt_binary64_2146
411×sqrt-prod_binary64_2140
330×times-frac_binary64_2130
256×*-un-lft-identity_binary64_2124
108×add-cube-cbrt_binary64_2159
78×difference-of-squares_binary64_2093
69×associate-*l*_binary64_2065
66×sqrt-div_binary64_2141
54×cancel-sign-sub-inv_binary64_2090
50×sqrt-pow1_binary64_2142
44×swap-sqr_binary64_2091
40×unswap-sqr_binary64_2092
39×pow1_binary64_2185
36×associate-*r*_binary64_2064
26×distribute-lft-out--_binary64_2076
24×pow-flip_binary64_2198
22×frac-sub_binary64_2133
21×frac-times_binary64_2134
18×rem-sqrt-square_binary64_2137 pow1/2_binary64_2204
16×div-inv_binary64_2121
13×pow-prod-up_binary64_2194
12×flip--_binary64_2099 flip3--_binary64_2128 distribute-lft-out_binary64_2075
11×associate-*r/_binary64_2066
10×pow-prod-down_binary64_2195
9×associate-*l/_binary64_2067 sqr-abs_binary64_2139
8×add-log-exp_binary64_2163 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160 inv-pow_binary64_2209
7×pow-sqr_binary64_2097
4×associate-/r/_binary64_2070
2×sqrt-unprod_binary64_2144 *-commutative_binary64_2055 diff-log_binary64_2216 prod-exp_binary64_2173 sub-neg_binary64_2117 flip3-+_binary64_2127 flip-+_binary64_2098 cbrt-unprod_binary64_2157
1×pow-plus_binary64_2187 rem-square-sqrt_binary64_2136 pow2_binary64_2205
Counts
4 → 402
Calls

8 calls:

82.0ms
(*.f64 (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
36.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
34.0ms
(*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))))
31.0ms
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
0.0ms
(sqrt.f64 (+.f64 1 x))

series114.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

31.0ms
(-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
30.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
30.0ms
(*.f64 (sqrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
23.0ms
(*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))))
Compiler

Compiled 566 to 489 computations (13.6% saved)

simplify171.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
414 → 414
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
049379538
149379538

prune29.8s (24.4%)

Pruning

592 alts after pruning (582 fresh and 10 done)

PrunedKeptTotal
New8082801088
Fresh56302358
Picked000
Done01010
Total8645921456
Error
0.0b
Counts
1456 → 592
Compiler

Compiled 33276 to 26512 computations (20.3% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite63.0ms (0.1%)

Algorithm
1×rewrite-expression-head
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×cbrt-undiv_binary64_2158 unswap-sqr_binary64_2092 add-log-exp_binary64_2163
3×pow-prod-down_binary64_2195 sqrt-pow1_binary64_2142 pow1/2_binary64_2204
2×clear-num_binary64_2123 associate-*r/_binary64_2066 1-exp_binary64_2168 frac-2neg_binary64_2135 rec-exp_binary64_2174
1×sqrt-unprod_binary64_2144 *-commutative_binary64_2055 rem-sqrt-square_binary64_2137 prod-exp_binary64_2173 pow-flip_binary64_2198 associate-/l/_binary64_2071 inv-pow_binary64_2209 cbrt-unprod_binary64_2157
Counts
4 → 256
Calls

8 calls:

13.0ms
(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
9.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms
(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms
(sqrt.f64 (+.f64 1 x))
0.0ms
(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

series133.0ms (0.1%)

Counts
4 → 21
Calls

4 calls:

43.0ms
(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
43.0ms
(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
27.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
20.0ms
(sqrt.f64 (+.f64 1 x))
Compiler

Compiled 540 to 455 computations (15.7% saved)

simplify162.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
277 → 277
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
049759112
149759112

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)))

rewrite13.0ms (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)))

series13.0ms (0%)

Counts
1 → 3
Calls

1 calls:

13.0ms
(/.f64 -1 (neg.f64 (sqrt.f64 x)))
Compiler

Compiled 44 to 42 computations (4.5% saved)

simplify124.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (105.0ms)

IterNodesCost
047461212
147461212

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

9.3b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 1 1) (*.f64 x 1)))))
0.4b
(/.f64 1 (pow.f64 x 3/2))
0.3b
(/.f64 1 (sqrt.f64 (+.f64 1 (pow.f64 x 3))))
0.0b
(+.f64 (*.f64 x x) (-.f64 (*.f64 1 1) (*.f64 x 1)))
11.2b
(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
11.2b
(-.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 1 1) (*.f64 x 1))))))
15.2b
(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 1 1) (*.f64 x 1))))
18.2b
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))

rewrite52.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
25×cbrt-prod_binary64_2155
22×add-sqr-sqrt_binary64_2146 *-un-lft-identity_binary64_2124
21×times-frac_binary64_2130
20×add-cube-cbrt_binary64_2159
9×unpow-prod-down_binary64_2203
8×sqrt-div_binary64_2141
7×sqrt-prod_binary64_2140
6×cbrt-div_binary64_2156 pow1_binary64_2185 add-log-exp_binary64_2163
5×frac-sub_binary64_2133
4×flip3-+_binary64_2127 flip-+_binary64_2098 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
3×sqr-pow_binary64_2096
2×sqrt-pow1_binary64_2142 rem-sqrt-square_binary64_2137 pow1/2_binary64_2204 associate-*r/_binary64_2066 frac-times_binary64_2134
1×flip--_binary64_2099 flip3--_binary64_2128 cancel-sign-sub-inv_binary64_2090 distribute-lft-out_binary64_2075 diff-log_binary64_2216 associate-*l/_binary64_2067 pow1/3_binary64_2206 sub-neg_binary64_2117 div-inv_binary64_2121
Counts
4 → 82
Calls

8 calls:

16.0ms
(-.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 1 1) (*.f64 x 1))))))
12.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 1 1) (*.f64 x 1))))
9.0ms
(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
4.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
0.0ms
(+.f64 (*.f64 x x) (-.f64 (*.f64 1 1) (*.f64 x 1)))

series137.0ms (0.1%)

Counts
4 → 20
Calls

4 calls:

46.0ms
(-.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 1 1) (*.f64 x 1))))))
34.0ms
(sqrt.f64 (+.f64 1 (pow.f64 x 3)))
31.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (-.f64 (*.f64 1 1) (*.f64 x 1))))
27.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
Compiler

Compiled 770 to 664 computations (13.8% saved)

simplify113.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (86.0ms)

IterNodesCost
048972262
148972262

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(/.f64 1 (pow.f64 x 3/2))
0.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))) (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))))
0.2b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b
(sqrt.f64 (+.f64 x 1))
18.2b
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
18.2b
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
18.2b
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
18.2b
(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))) (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))))

rewrite48.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
76×cbrt-prod_binary64_2155
63×times-frac_binary64_2130
46×add-cube-cbrt_binary64_2159 add-sqr-sqrt_binary64_2146 *-un-lft-identity_binary64_2124
27×unpow-prod-down_binary64_2203
22×cbrt-div_binary64_2156
9×sqr-pow_binary64_2096
5×associate-*l/_binary64_2067 frac-times_binary64_2134
4×pow1_binary64_2185 add-log-exp_binary64_2163 pow1/3_binary64_2206 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
3×associate-*r/_binary64_2066 div-inv_binary64_2121
1×rem-cbrt-cube_binary64_2148 pow3_binary64_2207
Counts
4 → 119
Calls

8 calls:

19.0ms
(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))) (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))))
5.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
4.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
4.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
0.0ms
(sqrt.f64 (+.f64 x 1))

series114.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

34.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
27.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
27.0ms
(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 3/2))) (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))) (cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))))
26.0ms
(cbrt.f64 (/.f64 1 (pow.f64 x 3/2)))
Compiler

Compiled 706 to 618 computations (12.5% saved)

simplify137.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 0 (102.0ms)

IterNodesCost
049012084
149012084

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (cbrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1 x))
0.3b
(cbrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
2.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
2.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
2.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))

rewrite210.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
351×add-sqr-sqrt_binary64_2146
295×times-frac_binary64_2130
269×*-un-lft-identity_binary64_2124
164×sqrt-prod_binary64_2140
100×difference-of-squares_binary64_2093
81×cancel-sign-sub-inv_binary64_2090
71×add-cube-cbrt_binary64_2159
52×distribute-lft-out--_binary64_2076
41×cbrt-prod_binary64_2155
21×distribute-lft-out_binary64_2075
19×div-inv_binary64_2121
10×add-log-exp_binary64_2163
6×associate-/r/_binary64_2070 sqrt-div_binary64_2141
4×flip--_binary64_2099 flip3--_binary64_2128 pow1_binary64_2185 frac-sub_binary64_2133 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
3×cbrt-div_binary64_2156 diff-log_binary64_2216 sub-neg_binary64_2117 flip3-+_binary64_2127 flip-+_binary64_2098
1×pow1/3_binary64_2206
Counts
4 → 283
Calls

8 calls:

41.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
40.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
36.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
33.0ms
(cbrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
0.0ms
(sqrt.f64 (+.f64 1 x))

series158.0ms (0.1%)

Counts
4 → 12
Calls

4 calls:

53.0ms
(cbrt.f64 (-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
38.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
34.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
32.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
Compiler

Compiled 1038 to 877 computations (15.5% saved)

simplify159.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
295 → 295
Iterations

Useful iterations: 0 (86.0ms)

IterNodesCost
048677581
148677581

prune33.9s (27.8%)

Pruning

812 alts after pruning (798 fresh and 14 done)

PrunedKeptTotal
New637250887
Fresh29548577
Picked000
Done11415
Total6678121479
Error
0.0b
Counts
1479 → 812
Compiler

Compiled 13950 to 10605 computations (24% saved)

simplify826.0ms (0.7%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0529861823

regimes5.3s (4.4%)

Compiler

Compiled 60385 to 49548 computations (17.9% saved)

bsearch0.0ms (0%)

regimes246.0ms (0.2%)

Compiler

Compiled 2233 to 1916 computations (14.2% saved)

bsearch0.0ms (0%)

regimes138.0ms (0.1%)

Compiler

Compiled 869 to 766 computations (11.9% saved)

bsearch1.0ms (0%)

Compiler

Compiled 11 to 10 computations (9.1% saved)

regimes54.0ms (0%)

Compiler

Compiled 256 to 225 computations (12.1% saved)

bsearch16.0ms (0%)

Steps
ItersRangePoint
8
40.575275526118034
105906.85642316272
3608.7123357395576
Compiler

Compiled 1 to 1 computations (0% saved)

regimes52.0ms (0%)

Compiler

Compiled 246 to 216 computations (12.2% saved)

bsearch18.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.7497539621235764
Compiler

Compiled 1 to 1 computations (0% saved)

regimes41.0ms (0%)

Compiler

Compiled 183 to 162 computations (11.5% saved)

bsearch17.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.7932895805080596
Compiler

Compiled 1 to 1 computations (0% saved)

regimes37.0ms (0%)

Compiler

Compiled 165 to 147 computations (10.9% saved)

bsearch17.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.7932895805080596
Compiler

Compiled 1 to 1 computations (0% saved)

regimes33.0ms (0%)

Compiler

Compiled 133 to 120 computations (9.8% saved)

bsearch18.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.8585930080847847
Compiler

Compiled 1 to 1 computations (0% saved)

regimes32.0ms (0%)

Compiler

Compiled 117 to 106 computations (9.4% saved)

bsearch16.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.5756114885856433
Compiler

Compiled 1 to 1 computations (0% saved)

regimes28.0ms (0%)

Compiler

Compiled 89 to 83 computations (6.7% saved)

bsearch15.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.6844505345468515
Compiler

Compiled 1 to 1 computations (0% saved)

regimes27.0ms (0%)

Compiler

Compiled 77 to 73 computations (5.2% saved)

bsearch15.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
1.152542200014402
Compiler

Compiled 1 to 1 computations (0% saved)

regimes25.0ms (0%)

Compiler

Compiled 65 to 62 computations (4.6% saved)

bsearch14.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.7062183437390931
Compiler

Compiled 1 to 1 computations (0% saved)

regimes22.0ms (0%)

Compiler

Compiled 45 to 45 computations (0% saved)

bsearch14.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.4833862213122175
Compiler

Compiled 1 to 1 computations (0% saved)

regimes18.0ms (0%)

Compiler

Compiled 37 to 38 computations (-2.7% saved)

bsearch13.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.771521771315818
Compiler

Compiled 1 to 1 computations (0% saved)

regimes18.0ms (0%)

Compiler

Compiled 29 to 31 computations (-6.9% saved)

bsearch12.0ms (0%)

Steps
ItersRangePoint
8
0.017544672715054173
40.575275526118034
0.9891998632382345
Compiler

Compiled 1 to 1 computations (0% saved)

regimes12.0ms (0%)

Accuracy

Total 0.2b remaining (99.3%)

Threshold costs 0.2b (99.3%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch45.0ms (0%)

Steps
ItersRangePoint
10
3.092475084471501e+95
1.7678056399472296e+110
2.703773030902455e+102
Compiler

Compiled 407 to 331 computations (18.7% saved)

simplify26.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0592608
1592608

end0.0ms (0%)

sample29.8s (24.4%)

Algorithm
1×intervals
Results
304.0ms2191×body1024valid
159.0ms4321×body128valid
105.0ms965×body512valid
35.0ms523×body256valid
Compiler

Compiled 31002 to 25430 computations (18% saved)

Pareto

0.6303787495677683

Profiling

Loading profile data...