Details

Time bar (total: 1.5s)

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)

sample14.0ms (1%)

Algorithm
1×intervals
Results
10.0ms256×body80valid
Compiler

Compiled 15 to 12 computations (20% saved)

simplify13.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0910
1910

prune3.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.6b

Counts
2 → 1
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

14.6b
(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite7.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
9×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 times-frac_binary64
3×associate-/r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 associate-/l*_binary64
2×associate-/r/_binary64
1×flip3-+_binary64 add-log-exp_binary64 pow1_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 flip-+_binary64
Counts
1 → 29
Calls

1 calls:

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

series5.0ms (0.3%)

Counts
1 → 3
Calls

1 calls:

5.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))

simplify77.0ms (5.1%)

Algorithm
1×egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
05053550

prune36.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New28432
Fresh000
Picked101
Done000
Total29433

Merged error: 0b

Counts
33 → 4
Compiler

Compiled 508 to 285 computations (43.9% saved)

localize6.0ms (0.4%)

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)))
14.5b
(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.5b
(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite51.0ms (3.4%)

Algorithm
1×rewrite-expression-head
Rules
288×times-frac_binary64
164×add-sqr-sqrt_binary64
162×*-un-lft-identity_binary64 add-cube-cbrt_binary64
156×sqrt-prod_binary64
27×associate-/l*_binary64
22×sqrt-div_binary64
18×associate-/r/_binary64
12×associate-/r*_binary64
11×flip3-+_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip-+_binary64
9×div-inv_binary64
6×pow1_binary64
4×add-log-exp_binary64 cbrt-undiv_binary64 div-exp_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64
1×associate-/l/_binary64
Counts
4 → 262
Calls

4 calls:

18.0ms
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
7.0ms
(/.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))

series19.0ms (1.2%)

Counts
4 → 12
Calls

4 calls:

6.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms
(/.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))) (sqrt.f64 (+.f64 (*.f64 x x) 1)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
3.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify176.0ms (11.6%)

Algorithm
1×egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 0 (95.0ms)

IterNodesCost
049178543
149178543

prune257.0ms (17%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2740274
Fresh033
Picked011
Done000
Total2744278

Merged error: 0b

Counts
278 → 4
Compiler

Compiled 6890 to 3977 computations (42.3% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.4b
(/.f64 1 (+.f64 (*.f64 x x) 1))
14.0b
(*.f64 x (/.f64 1 (+.f64 (*.f64 x x) 1)))

rewrite20.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×times-frac_binary64
19×*-un-lft-identity_binary64
18×add-cube-cbrt_binary64
15×associate-*r*_binary64 add-exp-log_binary64
9×add-cbrt-cube_binary64
5×pow1_binary64
4×associate-/r/_binary64 prod-exp_binary64 div-exp_binary64
3×associate-/r*_binary64 associate-*l*_binary64 unswap-sqr_binary64 associate-/l*_binary64
2×flip3-+_binary64 add-log-exp_binary64 cbrt-unprod_binary64 1-exp_binary64 cbrt-undiv_binary64 rec-exp_binary64 div-inv_binary64 flip-+_binary64
1×pow-prod-down_binary64 associate-*r/_binary64 clear-num_binary64 inv-pow_binary64 frac-2neg_binary64 un-div-inv_binary64 pow-flip_binary64 *-commutative_binary64
Counts
2 → 71
Calls

2 calls:

11.0ms
(*.f64 x (/.f64 1 (+.f64 (*.f64 x x) 1)))
6.0ms
(/.f64 1 (+.f64 (*.f64 x x) 1))

series8.0ms (0.5%)

Counts
2 → 6
Calls

2 calls:

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

simplify96.0ms (6.4%)

Algorithm
1×egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
050471121

prune46.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New77077
Fresh022
Picked011
Done011
Total77481

Merged error: 0b

Counts
81 → 4
Compiler

Compiled 1166 to 720 computations (38.3% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.1b
(/.f64 1 (/.f64 (+.f64 (*.f64 x x) 1) x))
14.5b
(/.f64 (+.f64 (*.f64 x x) 1) x)

rewrite22.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Rules
84×times-frac_binary64
52×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
16×associate-/r*_binary64
15×add-exp-log_binary64
9×add-cbrt-cube_binary64
8×div-exp_binary64
6×associate-/l*_binary64 div-inv_binary64
4×cbrt-undiv_binary64
3×pow1_binary64
2×associate-/l/_binary64 add-log-exp_binary64 1-exp_binary64 clear-num_binary64 frac-2neg_binary64 rec-exp_binary64
1×flip3-+_binary64 associate-/r/_binary64 inv-pow_binary64 pow-flip_binary64 flip-+_binary64
Counts
2 → 105
Calls

2 calls:

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

series12.0ms (0.8%)

Counts
2 → 6
Calls

2 calls:

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

simplify106.0ms (7%)

Algorithm
1×egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
050372232

prune65.0ms (4.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1101111
Fresh101
Picked101
Done022
Total1123115

Merged error: 0b

Counts
115 → 3
Compiler

Compiled 1850 to 1057 computations (42.9% saved)

regimes15.0ms (1%)

Compiler

Compiled 33 to 25 computations (24.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0910
1910

end0.0ms (0%)

sample438.0ms (29%)

Algorithm
1×intervals
Results
168.0ms8000×body80valid
Compiler

Compiled 53 to 42 computations (20.8% saved)

Profiling

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