Details

Time bar (total: 3.2s)

analyze9.0ms (0.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
12.5%25%62.5%4
18.7%12.5%68.8%5
21.9%6.2%71.9%6
23.4%3.1%73.5%7
24.2%1.6%74.2%8
24.6%0.8%74.6%9
24.8%0.4%74.8%10
24.9%0.2%74.9%11
24.9%0.1%75%12
25%0%75%13
25%0%75%14
Compiler

Compiled 14 to 11 computations (21.4% saved)

sample32.0ms (1%)

Algorithm
1×intervals
Results
24.0ms256×body128valid
Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify445.0ms (13.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (175.0ms)

IterNodesCost
0557420

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1
Compiler

Compiled 26 to 20 computations (23.1% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite104.0ms (3.2%)

Algorithm
1×rewrite-expression-head
Rules
43×*-un-lft-identity_binary64_1101
26×times-frac_binary64_1107
19×add-sqr-sqrt_binary64_1123
16×distribute-lft-out_binary64_1052
15×log-prod_binary64_1187
12×add-cube-cbrt_binary64_1136 div-inv_binary64_1098
7×add-log-exp_binary64_1140
6×distribute-rgt-out_binary64_1054 sqrt-prod_binary64_1117
4×add-exp-log_binary64_1139 pow1_binary64_1162
3×add-cbrt-cube_binary64_1137 log-div_binary64_1188
2×difference-of-squares_binary64_1070 flip3-+_binary64_1104 flip-+_binary64_1075 frac-add_binary64_1109 distribute-rgt1-in_binary64_1057
1×diff-log_binary64_1193 sum-log_binary64_1192 sub-neg_binary64_1094 rem-log-exp_binary64_1142 flip--_binary64_1076 flip3--_binary64_1105 +-commutative_binary64_1031 log-pow_binary64_1190 cancel-sign-sub-inv_binary64_1067
Counts
3 → 65
Calls

3 calls:

46.0ms
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
39.0ms
(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
6.0ms
(-.f64 1 (*.f64 x x))

series300.0ms (9.3%)

Counts
3 → 9
Calls

3 calls:

151.0ms
(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
79.0ms
(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
69.0ms
(-.f64 1 (*.f64 x x))

simplify82.0ms (2.5%)

Algorithm
1×egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
048871554
148871554

prune108.0ms (3.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New73174
Fresh000
Picked011
Done000
Total73275

Merged error: 0b

Counts
75 → 2
Compiler

Compiled 1398 to 902 computations (35.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
0.3b
(/.f64 1 (sqrt.f64 x))
0.3b
(/.f64 1 (sqrt.f64 x))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))))

rewrite137.0ms (4.3%)

Algorithm
1×rewrite-expression-head
Rules
140×times-frac_binary64_1107
129×*-un-lft-identity_binary64_1101
123×add-sqr-sqrt_binary64_1123
122×sqrt-prod_binary64_1117
88×add-cube-cbrt_binary64_1136
26×associate-*r*_binary64_1041
23×add-exp-log_binary64_1139
22×associate-*l*_binary64_1042
18×distribute-lft-out_binary64_1052 associate-/r*_binary64_1045
15×add-cbrt-cube_binary64_1137
14×difference-of-squares_binary64_1070 associate-/l*_binary64_1046
11×div-inv_binary64_1098
10×pow1_binary64_1162
7×div-exp_binary64_1152
6×pow-flip_binary64_1175
5×unswap-sqr_binary64_1069
4×distribute-rgt-out_binary64_1054 add-log-exp_binary64_1140 prod-exp_binary64_1150 cbrt-undiv_binary64_1135
3×1-exp_binary64_1145 frac-times_binary64_1111 frac-2neg_binary64_1112 clear-num_binary64_1100 associate-*r/_binary64_1043 rec-exp_binary64_1151
2×inv-pow_binary64_1186 cbrt-unprod_binary64_1134 sqrt-pow1_binary64_1119 flip3-+_binary64_1104 associate-/l/_binary64_1048 sqrt-div_binary64_1118 flip-+_binary64_1075 frac-add_binary64_1109 pow1/2_binary64_1181
1×*-commutative_binary64_1032 sqrt-undiv_binary64_1122 distribute-lft-in_binary64_1050 flip--_binary64_1076 flip3--_binary64_1105 pow-prod-down_binary64_1172 associate-*l/_binary64_1044 distribute-rgt-in_binary64_1051 distribute-rgt1-in_binary64_1057
Counts
4 → 244
Calls

4 calls:

88.0ms
(*.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))))
8.0ms
(/.f64 1 (sqrt.f64 x))
8.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
5.0ms
(/.f64 1 (sqrt.f64 x))

series381.0ms (11.8%)

Counts
4 → 12
Calls

4 calls:

147.0ms
(*.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))))
101.0ms
(/.f64 1 (sqrt.f64 x))
68.0ms
(/.f64 1 (sqrt.f64 x))
65.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))

simplify158.0ms (4.9%)

Algorithm
1×egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
049404786
149404786

prune451.0ms (14%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New2560256
Fresh000
Picked011
Done011
Total2562258

Merged error: 0b

Counts
258 → 2
Compiler

Compiled 6588 to 3712 computations (43.7% saved)

regimes50.0ms (1.5%)

Compiler

Compiled 373 to 268 computations (28.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02920
12920

end0.0ms (0%)

sample944.0ms (29.3%)

Algorithm
1×intervals
Results
591.0ms8000×body128valid
0.0ms5×body128nan
Compiler

Compiled 134 to 98 computations (26.9% saved)

Profiling

Loading profile data...