Details

Time bar (total: 2.1s)

analyze1.0ms (0.1%)

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

Compiled 8 to 6 computations (25% saved)

sample10.0ms (0.5%)

Algorithm
1×intervals
Results
6.0ms256×body128valid
Compiler

Compiled 15 to 12 computations (20% saved)

simplify162.0ms (7.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0810
1810

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.2b

Counts
2 → 1
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

15.2b
(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite9.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
9×times-frac_binary64_1117 *-un-lft-identity_binary64_1111 add-sqr-sqrt_binary64_1133 add-cube-cbrt_binary64_1146
3×add-cbrt-cube_binary64_1147 associate-/r*_binary64_1055 associate-/l*_binary64_1056 add-exp-log_binary64_1149
2×associate-/r/_binary64_1057
1×div-inv_binary64_1108 flip-+_binary64_1085 frac-2neg_binary64_1122 flip3-+_binary64_1114 div-exp_binary64_1162 cbrt-undiv_binary64_1145 add-log-exp_binary64_1150 pow1_binary64_1172 clear-num_binary64_1110
Counts
1 → 29
Calls

1 calls:

6.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))

series50.0ms (2.3%)

Counts
1 → 3
Calls

1 calls:

50.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))

simplify60.0ms (2.8%)

Algorithm
1×egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
05174550

prune81.0ms (3.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New29332
Fresh000
Picked101
Done000
Total30333

Merged error: 0b

Counts
33 → 3
Compiler

Compiled 1201 to 752 computations (37.4% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b
(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
15.2b
(sqrt.f64 (+.f64 (*.f64 x x) 1))
15.2b
(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite80.0ms (3.7%)

Algorithm
1×rewrite-expression-head
Rules
288×times-frac_binary64_1117
164×add-sqr-sqrt_binary64_1133
162×*-un-lft-identity_binary64_1111 add-cube-cbrt_binary64_1146
156×sqrt-prod_binary64_1127
27×associate-/l*_binary64_1056
22×sqrt-div_binary64_1128
18×associate-/r/_binary64_1057
12×associate-/r*_binary64_1055
11×add-cbrt-cube_binary64_1147 flip-+_binary64_1085 flip3-+_binary64_1114 add-exp-log_binary64_1149
9×div-inv_binary64_1108
6×pow1_binary64_1172
4×div-exp_binary64_1162 cbrt-undiv_binary64_1145 add-log-exp_binary64_1150
2×pow1/2_binary64_1191 rem-sqrt-square_binary64_1124 frac-2neg_binary64_1122 sqrt-pow1_binary64_1129 clear-num_binary64_1110
1×associate-/l/_binary64_1058
Counts
4 → 262
Calls

4 calls:

19.0ms
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
8.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
5.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))

series197.0ms (9.2%)

Counts
4 → 12
Calls

4 calls:

68.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
55.0ms
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
39.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
34.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify162.0ms (7.6%)

Algorithm
1×egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
048998543
148998543

prune363.0ms (17%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2740274
Fresh022
Picked011
Done000
Total2743277

Merged error: 0b

Counts
277 → 3
Compiler

Compiled 6881 to 3970 computations (42.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.1b
(/.f64 1 (/.f64 (+.f64 (*.f64 x x) 1) x))
15.2b
(/.f64 (+.f64 (*.f64 x x) 1) x)

rewrite29.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Rules
84×times-frac_binary64_1117
52×*-un-lft-identity_binary64_1111 add-sqr-sqrt_binary64_1133 add-cube-cbrt_binary64_1146
16×associate-/r*_binary64_1055
15×add-exp-log_binary64_1149
9×add-cbrt-cube_binary64_1147
8×div-exp_binary64_1162
6×div-inv_binary64_1108 associate-/l*_binary64_1056
4×cbrt-undiv_binary64_1145
3×pow1_binary64_1172
2×frac-2neg_binary64_1122 associate-/l/_binary64_1058 1-exp_binary64_1155 rec-exp_binary64_1161 add-log-exp_binary64_1150 clear-num_binary64_1110
1×flip-+_binary64_1085 pow-flip_binary64_1185 flip3-+_binary64_1114 inv-pow_binary64_1196 associate-/r/_binary64_1057
Counts
2 → 105
Calls

2 calls:

9.0ms
(/.f64 (+.f64 (*.f64 x x) 1) x)
9.0ms
(/.f64 1 (/.f64 (+.f64 (*.f64 x x) 1) x))

series147.0ms (6.9%)

Counts
2 → 6
Calls

2 calls:

99.0ms
(/.f64 (+.f64 (*.f64 x x) 1) x)
48.0ms
(/.f64 1 (/.f64 (+.f64 (*.f64 x x) 1) x))

simplify101.0ms (4.7%)

Algorithm
1×egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
058722232

prune95.0ms (4.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1101111
Fresh011
Picked101
Done011
Total1113114

Merged error: 0b

Counts
114 → 3
Compiler

Compiled 1918 to 1112 computations (42% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite13.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
24×*-un-lft-identity_binary64_1111
18×times-frac_binary64_1117
13×add-exp-log_binary64_1149
12×add-sqr-sqrt_binary64_1133 add-cube-cbrt_binary64_1146
8×distribute-lft-out_binary64_1062
6×associate-/r*_binary64_1055
5×div-inv_binary64_1108 rec-exp_binary64_1161
4×2cosh-undef_binary64_1307
3×add-cbrt-cube_binary64_1147 associate-/l*_binary64_1056
2×div-exp_binary64_1162 pow1_binary64_1172 associate-/r/_binary64_1057
1×flip-+_binary64_1085 pow-flip_binary64_1185 frac-2neg_binary64_1122 flip3-+_binary64_1114 1-exp_binary64_1155 cbrt-undiv_binary64_1145 add-log-exp_binary64_1150 clear-num_binary64_1110 inv-pow_binary64_1196
Counts
1 → 45
Calls

1 calls:

9.0ms
(/.f64 1 (+.f64 x (/.f64 1 x)))

series37.0ms (1.7%)

Counts
1 → 3
Calls

1 calls:

37.0ms
(/.f64 1 (+.f64 x (/.f64 1 x)))

simplify83.0ms (3.9%)

Algorithm
1×egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
04885672
14885672

prune38.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New48048
Fresh011
Picked011
Done011
Total48351

Merged error: 0b

Counts
51 → 3
Compiler

Compiled 627 to 479 computations (23.6% saved)

regimes11.0ms (0.5%)

Compiler

Compiled 39 to 31 computations (20.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0810
1810

end0.0ms (0%)

sample385.0ms (18%)

Algorithm
1×intervals
Results
187.0ms8000×body128valid
Compiler

Compiled 59 to 48 computations (18.6% saved)

Profiling

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