Details

Time bar (total: 7.8s)

analyze10.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%25%75%0
0%25%75%1
0%12.5%87.5%2
0%6.3%93.7%3
0%3.1%96.9%4
0%1.6%98.4%5
0%0.8%99.2%6
0%0.4%99.6%7
0%0.2%99.8%8
0.1%0.1%99.8%9
0.1%0%99.9%10
0.1%0%99.9%11
0.1%0%99.9%12
0.1%0%99.9%13
0.1%0%99.9%14
Compiler

Compiled 106 to 71 computations (33% saved)

sample70.0ms (0.9%)

Algorithm
1×intervals
Results
54.0ms256×body128valid
3.0ms259×pre128true
1.0ms3×body128invalid
Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify165.0ms (2.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
0551247

prune8.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 2.4b

Counts
2 → 2
Compiler

Compiled 163 to 111 computations (31.9% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))
0.4b
(/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))
1.0b
(sqrt.f64 PI.f64)
2.4b
(exp.f64 (*.f64 x x))

rewrite84.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
129×times-frac_binary64_2130
84×add-sqr-sqrt_binary64_2146
79×*-un-lft-identity_binary64_2124
70×add-cube-cbrt_binary64_2159 associate-*l*_binary64_2065
31×sqrt-prod_binary64_2140
18×add-cbrt-cube_binary64_2160
17×add-exp-log_binary64_2162
7×pow1_binary64_2185
6×add-log-exp_binary64_2163
5×cbrt-undiv_binary64_2158 distribute-lft-out_binary64_2075 associate-*r*_binary64_2064 div-inv_binary64_2121 div-exp_binary64_2175
4×unswap-sqr_binary64_2092 associate-/l*_binary64_2069 prod-exp_binary64_2173 cbrt-unprod_binary64_2157
3×flip3-+_binary64_2127 flip-+_binary64_2098
2×associate-*r/_binary64_2066 frac-times_binary64_2134 associate-/l/_binary64_2071
1×pow-prod-down_binary64_2195 clear-num_binary64_2123 sqrt-pow1_binary64_2142 *-commutative_binary64_2055 exp-to-pow_binary64_2186 associate-/r*_binary64_2068 rem-sqrt-square_binary64_2137 associate-*l/_binary64_2067 rem-exp-log_binary64_2164 pow1/2_binary64_2204 distribute-rgt-in_binary64_2074 exp-prod_binary64_2176 distribute-lft-in_binary64_2073 frac-2neg_binary64_2135
Counts
4 → 149
Calls

4 calls:

46.0ms
(*.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))
9.0ms
(/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))
2.0ms
(exp.f64 (*.f64 x x))
1.0ms
(sqrt.f64 PI.f64)

series66.0ms (0.9%)

Counts
4 → 10
Calls

4 calls:

49.0ms
(*.f64 (/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x)))))
11.0ms
(/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))
6.0ms
(exp.f64 (*.f64 x x))
0.0ms
(sqrt.f64 PI.f64)

simplify92.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
051286210

prune346.0ms (4.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New13623159
Fresh101
Picked101
Done000
Total13823161

Merged error: 0.3b

Counts
161 → 23
Compiler

Compiled 7891 to 3653 computations (53.7% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b
(pow.f64 (exp.f64 x) x)
1.0b
(pow.f64 (exp.f64 x) x)
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)

rewrite16.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64_2146
12×add-cube-cbrt_binary64_2159 *-un-lft-identity_binary64_2124
8×pow-pow_binary64_2196 pow1_binary64_2185
6×pow-unpow_binary64_2201 unpow-prod-down_binary64_2203 sqrt-prod_binary64_2140 exp-prod_binary64_2176
4×add-log-exp_binary64_2163 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
2×sqrt-pow1_binary64_2142 pow-exp_binary64_2192 rem-sqrt-square_binary64_2137 sqr-pow_binary64_2096 pow1/2_binary64_2204 pow-to-exp_binary64_2193
Counts
4 → 66
Calls

4 calls:

3.0ms
(pow.f64 (exp.f64 x) x)
3.0ms
(pow.f64 (exp.f64 x) x)
1.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)

series26.0ms (0.3%)

Counts
4 → 8
Calls

4 calls:

14.0ms
(pow.f64 (exp.f64 x) x)
12.0ms
(pow.f64 (exp.f64 x) x)
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)

simplify69.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
04932642
14932642

prune171.0ms (2.2%)

Pruning

29 alts after pruning (29 fresh and 0 done)

PrunedKeptTotal
New641074
Fresh31922
Picked101
Done000
Total682997

Merged error: 0.2b

Counts
97 → 29
Compiler

Compiled 4570 to 1989 computations (56.5% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b
(pow.f64 (exp.f64 x) x)
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)
2.4b
(exp.f64 (*.f64 x x))

rewrite16.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64_2146
9×add-cube-cbrt_binary64_2159 *-un-lft-identity_binary64_2124
7×pow1_binary64_2185
6×sqrt-prod_binary64_2140 add-log-exp_binary64_2163
4×pow-pow_binary64_2196 exp-prod_binary64_2176 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
3×pow-unpow_binary64_2201 unpow-prod-down_binary64_2203
2×sqrt-pow1_binary64_2142 rem-sqrt-square_binary64_2137 pow1/2_binary64_2204
1×pow-exp_binary64_2192 exp-to-pow_binary64_2186 rem-exp-log_binary64_2164 sqr-pow_binary64_2096 pow-to-exp_binary64_2193
Counts
4 → 56
Calls

4 calls:

3.0ms
(pow.f64 (exp.f64 x) x)
3.0ms
(sqrt.f64 PI.f64)
2.0ms
(exp.f64 (*.f64 x x))
1.0ms
(sqrt.f64 PI.f64)

series18.0ms (0.2%)

Counts
4 → 8
Calls

4 calls:

12.0ms
(pow.f64 (exp.f64 x) x)
6.0ms
(exp.f64 (*.f64 x x))
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)

simplify80.0ms (1%)

Algorithm
1×egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
04925530
14925530

prune151.0ms (1.9%)

Pruning

29 alts after pruning (28 fresh and 1 done)

PrunedKeptTotal
New63164
Fresh12728
Picked011
Done000
Total642993

Merged error: 0.2b

Counts
93 → 29
Compiler

Compiled 4086 to 1825 computations (55.3% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b
(pow.f64 (exp.f64 x) (*.f64 1/2 x))
1.0b
(pow.f64 (exp.f64 x) x)
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)

rewrite19.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64_2146
11×add-cube-cbrt_binary64_2159 *-un-lft-identity_binary64_2124
8×pow-pow_binary64_2196 pow1_binary64_2185
6×unpow-prod-down_binary64_2203 sqrt-prod_binary64_2140 exp-prod_binary64_2176
4×pow-unpow_binary64_2201 add-log-exp_binary64_2163 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
2×sqrt-pow1_binary64_2142 pow-exp_binary64_2192 rem-sqrt-square_binary64_2137 sqr-pow_binary64_2096 pow1/2_binary64_2204 pow-to-exp_binary64_2193
Counts
4 → 64
Calls

4 calls:

4.0ms
(pow.f64 (exp.f64 x) (*.f64 1/2 x))
3.0ms
(pow.f64 (exp.f64 x) x)
2.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)

series25.0ms (0.3%)

Counts
4 → 8
Calls

4 calls:

13.0ms
(pow.f64 (exp.f64 x) (*.f64 1/2 x))
12.0ms
(pow.f64 (exp.f64 x) x)
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)

simplify37.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
04975675
14975675

prune153.0ms (2%)

Pruning

31 alts after pruning (31 fresh and 0 done)

PrunedKeptTotal
New64872
Fresh42327
Picked101
Done101
Total7031101

Merged error: 0.2b

Counts
101 → 31
Compiler

Compiled 3647 to 1650 computations (54.8% saved)

regimes936.0ms (12%)

Compiler

Compiled 14735 to 9402 computations (36.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02963
12963

end0.0ms (0%)

sample5.1s (65.7%)

Algorithm
1×intervals
Results
1.6s8000×body128valid
102.0ms8120×pre128true
23.0ms120×body128invalid
Compiler

Compiled 4986 to 3182 computations (36.2% saved)

Profiling

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