Details

Time bar (total: 2.8min)

analyze183.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%74.9%25.1%4
0%74.9%25.1%5
0%62.4%37.6%6
12.5%43.7%43.8%7
12.5%43.7%43.8%8
25%28.1%47%9
28.1%20.3%51.6%10
28.1%20.3%51.6%11
34.3%13.3%52.4%12
35.9%9.8%54.4%13
35.9%9.8%54.4%14
Compiler

Compiled 13 to 12 computations (7.7% saved)

sample26.0ms (0%)

Algorithm
1×intervals
Results
16.0ms256×body128valid
1.0ms11×body128invalid
0.0ms5×body128nan
Compiler

Compiled 25 to 26 computations (-4% saved)

simplify454.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (362.0ms)

IterNodesCost
0488918
1488918

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.1b
Counts
2 → 1
Compiler

Compiled 12 to 11 computations (8.3% saved)

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

0.2b
(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
0.0b
(+.f64 (-.f64 1 z) (log.f64 z))
0.0b
(+.f64 (-.f64 1 z) (log.f64 z))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
0.2b
(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))

rewrite35.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
23×*-un-lft-identity_binary64_12013
9×add-sqr-sqrt_binary64_12035 pow1_binary64_12074
8×distribute-lft-out_binary64_11964 add-log-exp_binary64_12052
7×add-cube-cbrt_binary64_12048 associate-*r*_binary64_11953
5×add-cbrt-cube_binary64_12049 associate-+r+_binary64_11945 add-exp-log_binary64_12051
4×log-pow_binary64_12102 associate-+l+_binary64_11946 distribute-lft-out--_binary64_11965
3×sum-log_binary64_12104 cancel-sign-sub-inv_binary64_11979 flip3-+_binary64_12016 associate-*l*_binary64_11954 flip-+_binary64_11987 log-prod_binary64_12099
2×+-commutative_binary64_11943 distribute-lft-in_binary64_11962 distribute-rgt-in_binary64_11963 associate-*r/_binary64_11955
1×*-commutative_binary64_11944 associate-+l-_binary64_11948 unswap-sqr_binary64_11981 pow-prod-down_binary64_12084 diff-log_binary64_12105 cbrt-unprod_binary64_12046 prod-exp_binary64_12062 sub-neg_binary64_12006
Counts
3 → 63
Calls

6 calls:

12.0ms
(+.f64 (-.f64 1 z) (log.f64 z))
11.0ms
(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
7.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
0.0ms
(+.f64 (-.f64 1 z) (log.f64 z))
0.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))

series502.0ms (0.3%)

Counts
3 → 30
Calls

3 calls:

306.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))))
142.0ms
(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
54.0ms
(+.f64 (-.f64 1 z) (log.f64 z))
Compiler

Compiled 584 to 510 computations (12.7% saved)

simplify76.0ms (0%)

Algorithm
1×egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
053701270

prune284.0ms (0.2%)

Pruning

36 alts after pruning (35 fresh and 1 done)

PrunedKeptTotal
New583593
Fresh000
Picked000
Done011
Total583694
Error
0.0b
Counts
94 → 36
Compiler

Compiled 1612 to 1113 computations (31% saved)

localize11.0ms (0%)

Local error

Found 6 expressions with local error:

0.2b
(*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z)))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z))))
0.0b
(+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z))
0.0b
(+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z))))
0.2b
(*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z)))

rewrite48.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
52×*-un-lft-identity_binary64_12013
36×distribute-lft-out_binary64_11964
23×pow1_binary64_12074
18×log-pow_binary64_12102
13×associate-*r*_binary64_11953
9×add-log-exp_binary64_12052
8×add-sqr-sqrt_binary64_12035 distribute-lft-out--_binary64_11965
6×sum-log_binary64_12104 add-cube-cbrt_binary64_12048
5×add-cbrt-cube_binary64_12049 associate-+r+_binary64_11945 add-exp-log_binary64_12051
3×flip3-+_binary64_12016 associate-*l*_binary64_11954 flip-+_binary64_11987 log-prod_binary64_12099
2×+-commutative_binary64_11943 distribute-lft-in_binary64_11962 associate-+l-_binary64_11948 distribute-rgt-in_binary64_11963 associate-*r/_binary64_11955
1×*-commutative_binary64_11944 unswap-sqr_binary64_11981 pow-prod-down_binary64_12084 associate-+l+_binary64_11946 diff-log_binary64_12105 cbrt-unprod_binary64_12046 prod-exp_binary64_12062
Counts
3 → 73
Calls

6 calls:

16.0ms
(*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z)))
13.0ms
(+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z))
11.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z))))
0.0ms
(+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z))
0.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z))))

series495.0ms (0.3%)

Counts
3 → 30
Calls

3 calls:

298.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z))))
139.0ms
(*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z)))
58.0ms
(+.f64 (+.f64 (-.f64 1 z) (log.f64 1)) (log.f64 z))
Compiler

Compiled 584 to 510 computations (12.7% saved)

simplify135.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (113.0ms)

IterNodesCost
055401313

localize2.0ms (0%)

rewrite0.0ms (0%)

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

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))
0.2b
(*.f64 z (exp.f64 (-.f64 1 z)))
0.2b
(*.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z)))))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))))
0.2b
(*.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z)))))
0.2b
(*.f64 z (exp.f64 (-.f64 1 z)))
0.2b
(log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))

rewrite38.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
14×pow1_binary64_12074
13×add-sqr-sqrt_binary64_12035
12×associate-*r*_binary64_11953
9×add-cube-cbrt_binary64_12048 add-exp-log_binary64_12051 *-un-lft-identity_binary64_12013
8×add-cbrt-cube_binary64_12049
6×add-log-exp_binary64_12052 associate-*l*_binary64_11954
5×log-prod_binary64_12099
4×exp-sum_binary64_12059 log-pow_binary64_12102 pow-prod-down_binary64_12084
3×cancel-sign-sub-inv_binary64_11979 prod-exp_binary64_12062
2×distribute-lft-in_binary64_11962 rem-log-exp_binary64_12054 associate-+r+_binary64_11945 exp-diff_binary64_12061 *-commutative_binary64_11944 unswap-sqr_binary64_11981 cbrt-unprod_binary64_12046 distribute-rgt-in_binary64_11963 associate-*r/_binary64_11955
1×+-commutative_binary64_11943 sum-log_binary64_12104 flip3-+_binary64_12016 flip-+_binary64_11987 log-div_binary64_12100 sub-neg_binary64_12006
Counts
4 → 71
Calls

8 calls:

11.0ms
(*.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z)))))
9.0ms
(*.f64 z (exp.f64 (-.f64 1 z)))
7.0ms
(log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))
5.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))))
0.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))))

series831.0ms (0.5%)

Counts
4 → 33
Calls

4 calls:

446.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))))
242.0ms
(*.f64 y (log.f64 (*.f64 z (exp.f64 (-.f64 1 z)))))
111.0ms
(log.f64 (*.f64 z (exp.f64 (-.f64 1 z))))
33.0ms
(*.f64 z (exp.f64 (-.f64 1 z)))
Compiler

Compiled 726 to 667 computations (8.1% saved)

simplify64.0ms (0%)

Algorithm
1×egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049791424
149791424

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (*.f64 x 1/2) (/.f64 (*.f64 y (-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z))))
0.0b
(*.f64 (-.f64 1 z) (-.f64 1 z))
0.0b
(-.f64 (-.f64 1 z) (log.f64 z))
0.0b
(-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z)))
0.0b
(+.f64 (*.f64 x 1/2) (/.f64 (*.f64 y (-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z))))
0.5b
(*.f64 (log.f64 z) (log.f64 z))
4.6b
(*.f64 y (-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z))))
8.0b
(/.f64 (*.f64 y (-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z)))

rewrite77.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
36×*-un-lft-identity_binary64_12013
26×add-sqr-sqrt_binary64_12035
23×pow1_binary64_12074
21×distribute-lft-in_binary64_11962 distribute-rgt-in_binary64_11963
18×add-cube-cbrt_binary64_12048
16×associate--l+_binary64_11950
14×cancel-sign-sub-inv_binary64_11979
13×add-cbrt-cube_binary64_12049 add-exp-log_binary64_12051
12×distribute-lft-out--_binary64_11965
10×log-pow_binary64_12102
8×times-frac_binary64_12019 associate-/r*_binary64_11957 associate-*r*_binary64_11953
7×associate-*l*_binary64_11954
6×add-log-exp_binary64_12052 swap-sqr_binary64_11980 log-prod_binary64_12099 sub-neg_binary64_12006
4×associate-*r/_binary64_11955
3×flip3--_binary64_12017 difference-of-squares_binary64_11982 flip--_binary64_11988 cbrt-unprod_binary64_12046 prod-exp_binary64_12062
2×associate-/r/_binary64_11959 *-commutative_binary64_11944 div-exp_binary64_12064 unswap-sqr_binary64_11981 pow-prod-down_binary64_12084 cbrt-undiv_binary64_12047 associate-/l/_binary64_11960
1×+-commutative_binary64_11943 pow-prod-up_binary64_12083 sum-log_binary64_12104 flip3-+_binary64_12016 pow-plus_binary64_12076 clear-num_binary64_12012 div-inv_binary64_12010 flip-+_binary64_11987 pow-sqr_binary64_11986 frac-2neg_binary64_12024 associate-/l*_binary64_11958 pow2_binary64_12094
Counts
4 → 123
Calls

8 calls:

25.0ms
(/.f64 (*.f64 y (-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z)))
17.0ms
(*.f64 y (-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z))))
13.0ms
(+.f64 (*.f64 x 1/2) (/.f64 (*.f64 y (-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z))))
5.0ms
(*.f64 (log.f64 z) (log.f64 z))
0.0ms
(-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z)))

series2.6s (1.5%)

Counts
4 → 39
Calls

4 calls:

1.9s
(+.f64 (*.f64 x 1/2) (/.f64 (*.f64 y (-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z))))
385.0ms
(/.f64 (*.f64 y (-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z)))) (-.f64 (-.f64 1 z) (log.f64 z)))
260.0ms
(*.f64 y (-.f64 (*.f64 (-.f64 1 z) (-.f64 1 z)) (*.f64 (log.f64 z) (log.f64 z))))
71.0ms
(*.f64 (log.f64 z) (log.f64 z))
Compiler

Compiled 2086 to 1511 computations (27.6% saved)

simplify131.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
049334026
149334026

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2))
0.0b
(+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2))
0.0b
(+.f64 (-.f64 1 z) (log.f64 z))
0.0b
(+.f64 (-.f64 1 z) (log.f64 z))
0.0b
(sqrt.f64 (+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2)))
0.2b
(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
0.2b
(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
0.2b
(*.f64 (sqrt.f64 (+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2))) (sqrt.f64 (+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2))))

rewrite79.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
36×add-sqr-sqrt_binary64_12035
33×*-un-lft-identity_binary64_12013
28×pow1_binary64_12074
21×sqrt-prod_binary64_12029
20×associate-*r*_binary64_11953
17×add-cube-cbrt_binary64_12048
14×sqrt-div_binary64_12030
12×associate-*l*_binary64_11954
10×add-cbrt-cube_binary64_12049 add-exp-log_binary64_12051
9×pow1/2_binary64_12093 flip3-+_binary64_12016 flip-+_binary64_11987 sqrt-pow1_binary64_12031
8×distribute-lft-out_binary64_11964 swap-sqr_binary64_11980
6×unswap-sqr_binary64_11981 associate-*r/_binary64_11955
5×pow-prod-up_binary64_12083 pow-prod-down_binary64_12084
4×add-log-exp_binary64_12052 log-pow_binary64_12102 distribute-lft-out--_binary64_11965 frac-times_binary64_12023
3×*-commutative_binary64_11944 rem-sqrt-square_binary64_12026 pow-sqr_binary64_11986 cbrt-unprod_binary64_12046 prod-exp_binary64_12062
2×distribute-lft-in_binary64_11962 associate-*l/_binary64_11956 distribute-rgt-in_binary64_11963
1×rem-square-sqrt_binary64_12025 sqr-abs_binary64_12028 pow-plus_binary64_12076 sqrt-unprod_binary64_12033 pow2_binary64_12094
Counts
4 → 125
Calls

8 calls:

31.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2))) (sqrt.f64 (+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2))))
11.0ms
(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
11.0ms
(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
10.0ms
(sqrt.f64 (+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2)))
0.0ms
(+.f64 (-.f64 1 z) (log.f64 z))

series835.0ms (0.5%)

Counts
4 → 46
Calls

4 calls:

308.0ms
(*.f64 (sqrt.f64 (+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2))) (sqrt.f64 (+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2))))
223.0ms
(sqrt.f64 (+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2)))
155.0ms
(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
149.0ms
(*.f64 y (+.f64 (-.f64 1 z) (log.f64 z)))
Compiler

Compiled 2220 to 1688 computations (24% saved)

simplify100.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049383409
149383409

prune4.7s (2.7%)

Pruning

173 alts after pruning (167 fresh and 6 done)

PrunedKeptTotal
New395145540
Fresh82230
Picked000
Done066
Total403173576
Error
0b
Counts
576 → 173
Compiler

Compiled 12986 to 8706 computations (33% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))))
0.0b
(log.f64 (sqrt.f64 z))
0.0b
(log.f64 (sqrt.f64 z))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))))
0.0b
(+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))
0.0b
(+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z)))
0.2b
(*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z))))

rewrite66.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
65×*-un-lft-identity_binary64_12013
40×distribute-lft-out_binary64_11964
26×pow1_binary64_12074
20×log-pow_binary64_12102
14×associate-+r+_binary64_11945
13×add-log-exp_binary64_12052 add-sqr-sqrt_binary64_12035 associate-*r*_binary64_11953
12×log-prod_binary64_12099
11×add-cube-cbrt_binary64_12048
10×distribute-lft-out--_binary64_11965
8×sum-log_binary64_12104
6×add-cbrt-cube_binary64_12049 add-exp-log_binary64_12051 sqrt-prod_binary64_12029
5×associate-+l+_binary64_11946
4×flip3-+_binary64_12016 flip-+_binary64_11987
3×+-commutative_binary64_11943 cancel-sign-sub-inv_binary64_11979 associate-+l-_binary64_11948 associate-*l*_binary64_11954
2×distribute-lft-in_binary64_11962 diff-log_binary64_12105 distribute-rgt-in_binary64_11963 associate-*r/_binary64_11955
1×*-commutative_binary64_11944 unswap-sqr_binary64_11981 pow-prod-down_binary64_12084 cbrt-unprod_binary64_12046 prod-exp_binary64_12062 sub-neg_binary64_12006
Counts
4 → 103
Calls

8 calls:

20.0ms
(*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z))))
15.0ms
(+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))
11.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))))
10.0ms
(+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z)))
0.0ms
(log.f64 (sqrt.f64 z))

series471.0ms (0.3%)

Counts
4 → 27
Calls

4 calls:

302.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))))
133.0ms
(*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z))))
19.0ms
(+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))
17.0ms
(+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z)))
Compiler

Compiled 724 to 650 computations (10.2% saved)

simplify121.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (95.0ms)

IterNodesCost
048481762
148481762

localize4.0ms (0%)

rewrite0.0ms (0%)

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

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 (neg.f64 (pow.f64 (log.f64 z) 2)) (*.f64 z (-.f64 1 z)))
0.0b
(-.f64 (-.f64 1 z) (log.f64 z))
0.0b
(*.f64 z (-.f64 1 z))
0.0b
(*.f64 y (-.f64 1 z))
0.1b
(+.f64 (*.f64 y (-.f64 1 z)) (*.f64 y (-.f64 (neg.f64 (pow.f64 (log.f64 z) 2)) (*.f64 z (-.f64 1 z)))))
0.5b
(pow.f64 (log.f64 z) 2)
4.7b
(*.f64 y (-.f64 (neg.f64 (pow.f64 (log.f64 z) 2)) (*.f64 z (-.f64 1 z))))
8.0b
(/.f64 (+.f64 (*.f64 y (-.f64 1 z)) (*.f64 y (-.f64 (neg.f64 (pow.f64 (log.f64 z) 2)) (*.f64 z (-.f64 1 z))))) (-.f64 (-.f64 1 z) (log.f64 z)))

rewrite68.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
64×*-un-lft-identity_binary64_12013
36×add-sqr-sqrt_binary64_12035
32×times-frac_binary64_12019
30×distribute-lft-out--_binary64_11965
24×add-cube-cbrt_binary64_12048
18×pow1_binary64_12074 associate-*r/_binary64_11955
11×log-pow_binary64_12102
10×distribute-lft-out_binary64_11964 cancel-sign-sub-inv_binary64_11979 flip3--_binary64_12017 flip--_binary64_11988
9×add-exp-log_binary64_12051
8×add-cbrt-cube_binary64_12049 distribute-lft-in_binary64_11962 frac-add_binary64_12021 associate-/r*_binary64_11957 associate-+l+_binary64_11946 distribute-rgt-in_binary64_11963
6×add-log-exp_binary64_12052 associate-/l/_binary64_11960 sub-neg_binary64_12006
5×difference-of-squares_binary64_11982
4×associate-+r+_binary64_11945 unpow-prod-down_binary64_12092 associate-/l*_binary64_11958
3×associate-*l*_binary64_11954 pow-unpow_binary64_12090 associate-*r*_binary64_11953
2×associate-/r/_binary64_11959 flip3-+_binary64_12016 flip-+_binary64_11987
1×+-commutative_binary64_11943 sum-log_binary64_12104 *-commutative_binary64_11944 clear-num_binary64_12012 div-exp_binary64_12064 unswap-sqr_binary64_11981 sqr-pow_binary64_11985 unpow2_binary64_12078 div-inv_binary64_12010 pow-prod-down_binary64_12084 cbrt-undiv_binary64_12047 frac-2neg_binary64_12024 pow-to-exp_binary64_12082 cbrt-unprod_binary64_12046 pow-pow_binary64_12085 prod-exp_binary64_12062 pow-exp_binary64_12081
Counts
4 → 135
Calls

8 calls:

20.0ms
(/.f64 (+.f64 (*.f64 y (-.f64 1 z)) (*.f64 y (-.f64 (neg.f64 (pow.f64 (log.f64 z) 2)) (*.f64 z (-.f64 1 z))))) (-.f64 (-.f64 1 z) (log.f64 z)))
11.0ms
(+.f64 (*.f64 y (-.f64 1 z)) (*.f64 y (-.f64 (neg.f64 (pow.f64 (log.f64 z) 2)) (*.f64 z (-.f64 1 z)))))
10.0ms
(*.f64 y (-.f64 (neg.f64 (pow.f64 (log.f64 z) 2)) (*.f64 z (-.f64 1 z))))
2.0ms
(pow.f64 (log.f64 z) 2)
0.0ms
(*.f64 y (-.f64 1 z))

series923.0ms (0.5%)

Counts
4 → 30
Calls

4 calls:

371.0ms
(/.f64 (+.f64 (*.f64 y (-.f64 1 z)) (*.f64 y (-.f64 (neg.f64 (pow.f64 (log.f64 z) 2)) (*.f64 z (-.f64 1 z))))) (-.f64 (-.f64 1 z) (log.f64 z)))
295.0ms
(+.f64 (*.f64 y (-.f64 1 z)) (*.f64 y (-.f64 (neg.f64 (pow.f64 (log.f64 z) 2)) (*.f64 z (-.f64 1 z)))))
177.0ms
(*.f64 y (-.f64 (neg.f64 (pow.f64 (log.f64 z) 2)) (*.f64 z (-.f64 1 z))))
80.0ms
(pow.f64 (log.f64 z) 2)
Compiler

Compiled 1480 to 1156 computations (21.9% saved)

simplify89.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
050005538

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))) (*.f64 x 1/2))
0.0b
(pow.f64 (-.f64 1 z) 2)
0.0b
(-.f64 (-.f64 1 z) (log.f64 z))
0.0b
(-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))
0.2b
(/.f64 y (-.f64 (-.f64 1 z) (log.f64 z)))
0.5b
(pow.f64 (log.f64 z) 2)
3.3b
(log.f64 (exp.f64 (+.f64 (*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))) (*.f64 x 1/2))))
13.9b
(*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))

rewrite107.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
104×*-un-lft-identity_binary64_12013
73×add-sqr-sqrt_binary64_12035
49×times-frac_binary64_12019 distribute-lft-out--_binary64_11965
38×add-cube-cbrt_binary64_12048
30×associate-*l*_binary64_11954
28×unpow-prod-down_binary64_12092
27×pow1_binary64_12074
24×associate-*r*_binary64_11953
23×log-pow_binary64_12102 difference-of-squares_binary64_11982
18×cancel-sign-sub-inv_binary64_11979
12×add-exp-log_binary64_12051
11×add-cbrt-cube_binary64_12049 sqr-pow_binary64_11985 unpow2_binary64_12078
10×distribute-lft-in_binary64_11962 distribute-rgt-in_binary64_11963
8×associate-/r*_binary64_11957
4×associate-/r/_binary64_11959 add-log-exp_binary64_12052 flip3--_binary64_12017 log-prod_binary64_12099 flip--_binary64_11988
3×associate-/l*_binary64_11958 exp-prod_binary64_12065 pow-unpow_binary64_12090
2×div-exp_binary64_12064 unswap-sqr_binary64_11981 div-inv_binary64_12010 cbrt-undiv_binary64_12047 cbrt-unprod_binary64_12046 prod-exp_binary64_12062 associate-*r/_binary64_11955 frac-times_binary64_12023 sub-neg_binary64_12006
1×rem-log-exp_binary64_12054 exp-sum_binary64_12059 *-commutative_binary64_11944 clear-num_binary64_12012 pow-prod-down_binary64_12084 associate-*l/_binary64_11956 frac-2neg_binary64_12024 pow-to-exp_binary64_12082 pow-pow_binary64_12085 pow-exp_binary64_12081
Counts
4 → 178
Calls

8 calls:

42.0ms
(*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
25.0ms
(log.f64 (exp.f64 (+.f64 (*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))) (*.f64 x 1/2))))
10.0ms
(/.f64 y (-.f64 (-.f64 1 z) (log.f64 z)))
2.0ms
(pow.f64 (log.f64 z) 2)
0.0ms
(-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))

series2.8s (1.6%)

Counts
4 → 34
Calls

4 calls:

2.1s
(log.f64 (exp.f64 (+.f64 (*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))) (*.f64 x 1/2))))
413.0ms
(*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
138.0ms
(/.f64 y (-.f64 (-.f64 1 z) (log.f64 z)))
75.0ms
(pow.f64 (log.f64 z) 2)
Compiler

Compiled 2552 to 1831 computations (28.3% saved)

simplify117.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
050386806

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (*.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (+.f64 (-.f64 1 z) (log.f64 z)) (cbrt.f64 y))) (*.f64 x 1/2))
0.0b
(+.f64 (*.f64 y (+.f64 (-.f64 1 z) (log.f64 z))) (*.f64 x 1/2))
0.0b
(+.f64 (-.f64 1 z) (log.f64 z))
0.0b
(+.f64 (-.f64 1 z) (log.f64 z))
0.5b
(*.f64 (cbrt.f64 y) (cbrt.f64 y))
0.6b
(cbrt.f64 y)
0.6b
(cbrt.f64 y)
0.6b
(cbrt.f64 y)

rewrite19.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
25×cbrt-prod_binary64_12044
23×add-sqr-sqrt_binary64_12035
15×add-cube-cbrt_binary64_12048 *-un-lft-identity_binary64_12013
11×pow1_binary64_12074
9×pow1/3_binary64_12095
6×swap-sqr_binary64_11980 associate-*l*_binary64_11954 add-exp-log_binary64_12051 associate-*r*_binary64_11953
4×add-cbrt-cube_binary64_12049 add-log-exp_binary64_12052 unswap-sqr_binary64_11981
2×pow-prod-up_binary64_12083 pow-prod-down_binary64_12084 pow-sqr_binary64_11986
1×*-commutative_binary64_11944 pow-plus_binary64_12076 cbrt-unprod_binary64_12046 prod-exp_binary64_12062 pow2_binary64_12094
Counts
4 → 73
Calls

8 calls:

6.0ms
(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
0.0ms
(+.f64 (-.f64 1 z) (log.f64 z))

series332.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

93.0ms
(*.f64 (cbrt.f64 y) (cbrt.f64 y))
83.0ms
(cbrt.f64 y)
82.0ms
(cbrt.f64 y)
74.0ms
(cbrt.f64 y)
Compiler

Compiled 874 to 670 computations (23.3% saved)

simplify77.0ms (0%)

Algorithm
1×egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
04873548
14873548

prune17.4s (10.2%)

Pruning

341 alts after pruning (330 fresh and 11 done)

PrunedKeptTotal
New417175592
Fresh7155162
Picked000
Done01111
Total424341765
Error
0b
Counts
765 → 341
Compiler

Compiled 25285 to 17146 computations (32.2% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 1 (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z))))))
0.0b
(log.f64 (sqrt.f64 z))
0.0b
(log.f64 (sqrt.f64 z))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 1 (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z))))))
0.0b
(+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))
0.0b
(+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z)))
0.2b
(*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z))))

rewrite65.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
65×*-un-lft-identity_binary64_12013
40×distribute-lft-out_binary64_11964
26×pow1_binary64_12074
20×log-pow_binary64_12102
16×associate-+r+_binary64_11945
13×add-log-exp_binary64_12052 add-sqr-sqrt_binary64_12035 associate-*r*_binary64_11953
12×log-prod_binary64_12099
11×add-cube-cbrt_binary64_12048
10×distribute-lft-out--_binary64_11965
8×sum-log_binary64_12104
6×add-cbrt-cube_binary64_12049 add-exp-log_binary64_12051 sqrt-prod_binary64_12029
5×distribute-lft-in_binary64_11962 associate-+l+_binary64_11946 distribute-rgt-in_binary64_11963
4×flip3-+_binary64_12016 flip-+_binary64_11987
3×+-commutative_binary64_11943 cancel-sign-sub-inv_binary64_11979 associate-+l-_binary64_11948 associate-*l*_binary64_11954
2×diff-log_binary64_12105 associate-*r/_binary64_11955
1×*-commutative_binary64_11944 unswap-sqr_binary64_11981 pow-prod-down_binary64_12084 cbrt-unprod_binary64_12046 prod-exp_binary64_12062 sub-neg_binary64_12006
Counts
4 → 105
Calls

8 calls:

18.0ms
(*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z))))
15.0ms
(+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))
11.0ms
(+.f64 (*.f64 x 1/2) (*.f64 1 (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z))))))
10.0ms
(+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z)))
0.0ms
(log.f64 (sqrt.f64 z))

series486.0ms (0.3%)

Counts
4 → 27
Calls

4 calls:

305.0ms
(+.f64 (*.f64 x 1/2) (*.f64 1 (*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z))))))
142.0ms
(*.f64 y (+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z))))
23.0ms
(+.f64 (+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z))) (log.f64 (sqrt.f64 z)))
17.0ms
(+.f64 (-.f64 1 z) (log.f64 (sqrt.f64 z)))
Compiler

Compiled 772 to 698 computations (9.6% saved)

simplify105.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
048611802
148611802

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (*.f64 x 1/2) (*.f64 y (neg.f64 z)))
0.0b
(+.f64 (*.f64 x 1/2) (*.f64 y (neg.f64 z)))

rewrite5.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
3×add-log-exp_binary64_12052
1×add-cbrt-cube_binary64_12049 +-commutative_binary64_11943 sum-log_binary64_12104 flip3-+_binary64_12016 add-sqr-sqrt_binary64_12035 add-cube-cbrt_binary64_12048 add-exp-log_binary64_12051 unsub-neg_binary64_12007 flip-+_binary64_11987 pow1_binary64_12074 distribute-rgt-neg-out_binary64_11973 *-un-lft-identity_binary64_12013
Counts
1 → 12
Calls

2 calls:

4.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (neg.f64 z)))
0.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (neg.f64 z)))

series120.0ms (0.1%)

Counts
1 → 18
Calls

1 calls:

120.0ms
(+.f64 (*.f64 x 1/2) (*.f64 y (neg.f64 z)))
Compiler

Compiled 163 to 176 computations (-8% saved)

simplify84.0ms (0%)

Algorithm
1×egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
05679317

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 (-.f64 1 z) (log.f64 z))
0.0b
(-.f64 (*.f64 z (+.f64 -1 z)) (pow.f64 (log.f64 z) 2))
0.0b
(*.f64 y (-.f64 1 z))
0.0b
(*.f64 z (+.f64 -1 z))
0.1b
(+.f64 (*.f64 y (-.f64 1 z)) (pow.f64 (*.f64 y (-.f64 (*.f64 z (+.f64 -1 z)) (pow.f64 (log.f64 z) 2))) 1))
0.5b
(pow.f64 (log.f64 z) 2)
4.7b
(*.f64 y (-.f64 (*.f64 z (+.f64 -1 z)) (pow.f64 (log.f64 z) 2)))
8.0b
(/.f64 (+.f64 (*.f64 y (-.f64 1 z)) (pow.f64 (*.f64 y (-.f64 (*.f64 z (+.f64 -1 z)) (pow.f64 (log.f64 z) 2))) 1)) (-.f64 (-.f64 1 z) (log.f64 z)))

rewrite66.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
59×*-un-lft-identity_binary64_12013
37×add-sqr-sqrt_binary64_12035
27×add-cube-cbrt_binary64_12048
24×times-frac_binary64_12019 cancel-sign-sub-inv_binary64_11979 distribute-lft-out--_binary64_11965
18×distribute-lft-in_binary64_11962 pow1_binary64_12074 distribute-rgt-in_binary64_11963
12×unpow-prod-down_binary64_12092
11×log-pow_binary64_12102
9×add-exp-log_binary64_12051
8×add-cbrt-cube_binary64_12049 associate-/r*_binary64_11957 associate-+l+_binary64_11946
6×add-log-exp_binary64_12052
4×associate--l+_binary64_11950 difference-of-squares_binary64_11982 sub-neg_binary64_12006
3×sqr-pow_binary64_11985 associate-*l*_binary64_11954 unpow2_binary64_12078 associate-/l*_binary64_11958 pow-unpow_binary64_12090 associate-*r*_binary64_11953
2×associate-/r/_binary64_11959 flip3-+_binary64_12016 flip3--_binary64_12017 flip-+_binary64_11987 flip--_binary64_11988 associate-*r/_binary64_11955 associate-/l/_binary64_11960
1×+-commutative_binary64_11943 sum-log_binary64_12104 *-commutative_binary64_11944 clear-num_binary64_12012 div-exp_binary64_12064 unswap-sqr_binary64_11981 div-inv_binary64_12010 pow-prod-down_binary64_12084 cbrt-undiv_binary64_12047 frac-2neg_binary64_12024 pow-to-exp_binary64_12082 cbrt-unprod_binary64_12046 pow-pow_binary64_12085 prod-exp_binary64_12062 pow-exp_binary64_12081
Counts
4 → 133
Calls

8 calls:

19.0ms
(/.f64 (+.f64 (*.f64 y (-.f64 1 z)) (pow.f64 (*.f64 y (-.f64 (*.f64 z (+.f64 -1 z)) (pow.f64 (log.f64 z) 2))) 1)) (-.f64 (-.f64 1 z) (log.f64 z)))
15.0ms
(*.f64 y (-.f64 (*.f64 z (+.f64 -1 z)) (pow.f64 (log.f64 z) 2)))
11.0ms
(+.f64 (*.f64 y (-.f64 1 z)) (pow.f64 (*.f64 y (-.f64 (*.f64 z (+.f64 -1 z)) (pow.f64 (log.f64 z) 2))) 1))
2.0ms
(pow.f64 (log.f64 z) 2)
0.0ms
(*.f64 z (+.f64 -1 z))

series948.0ms (0.6%)

Counts
4 → 30
Calls

4 calls:

397.0ms
(/.f64 (+.f64 (*.f64 y (-.f64 1 z)) (pow.f64 (*.f64 y (-.f64 (*.f64 z (+.f64 -1 z)) (pow.f64 (log.f64 z) 2))) 1)) (-.f64 (-.f64 1 z) (log.f64 z)))
285.0ms
(+.f64 (*.f64 y (-.f64 1 z)) (pow.f64 (*.f64 y (-.f64 (*.f64 z (+.f64 -1 z)) (pow.f64 (log.f64 z) 2))) 1))
182.0ms
(*.f64 y (-.f64 (*.f64 z (+.f64 -1 z)) (pow.f64 (log.f64 z) 2)))
84.0ms
(pow.f64 (log.f64 z) 2)
Compiler

Compiled 1514 to 1190 computations (21.4% saved)

simplify97.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
052304857

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(pow.f64 (-.f64 1 z) 2)
0.0b
(-.f64 (-.f64 1 z) (log.f64 z))
0.0b
(/.f64 (log.f64 (pow.f64 (exp.f64 y) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))) (-.f64 (-.f64 1 z) (log.f64 z)))
0.0b
(-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))
0.0b
(pow.f64 (-.f64 1 z) 2)
0.1b
(pow.f64 (exp.f64 y) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
0.5b
(pow.f64 (log.f64 z) 2)
1.3b
(log.f64 (pow.f64 (exp.f64 y) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))))

rewrite46.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
40×unpow-prod-down_binary64_12092
36×add-sqr-sqrt_binary64_12035
30×pow-unpow_binary64_12090 *-un-lft-identity_binary64_12013
20×unpow-prod-up_binary64_12091
18×cancel-sign-sub-inv_binary64_11979 difference-of-squares_binary64_11982
17×add-cube-cbrt_binary64_12048 log-prod_binary64_12099
14×sqr-pow_binary64_11985
12×unpow2_binary64_12078 pow1_binary64_12074
8×distribute-lft-out--_binary64_11965
7×add-exp-log_binary64_12051
6×log-pow_binary64_12102 pow-pow_binary64_12085
4×add-cbrt-cube_binary64_12049 add-log-exp_binary64_12052 pow-to-exp_binary64_12082 pow-exp_binary64_12081
3×rem-log-exp_binary64_12054 exp-prod_binary64_12065
2×sub-neg_binary64_12006 pow-sub_binary64_12089
1×log-div_binary64_12100
Counts
4 → 121
Calls

8 calls:

17.0ms
(pow.f64 (exp.f64 y) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
8.0ms
(log.f64 (pow.f64 (exp.f64 y) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))))
5.0ms
(pow.f64 (-.f64 1 z) 2)
2.0ms
(pow.f64 (log.f64 z) 2)
0.0ms
(-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))

series823.0ms (0.5%)

Counts
4 → 21
Calls

4 calls:

400.0ms
(log.f64 (pow.f64 (exp.f64 y) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))))
336.0ms
(pow.f64 (exp.f64 y) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
73.0ms
(pow.f64 (log.f64 z) 2)
13.0ms
(pow.f64 (-.f64 1 z) 2)
Compiler

Compiled 1571 to 1256 computations (20.1% saved)

simplify92.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
051293063

localize33.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 z (log.f64 z))
0.0b
(-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))
0.0b
(-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))
0.0b
(-.f64 (*.f64 x 1/2) (*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))))
4.6b
(*.f64 y (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
5.1b
(/.f64 (*.f64 y (*.f64 y (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))) (-.f64 (-.f64 1 z) (log.f64 z)))
13.9b
(*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
29.2b
(/.f64 (-.f64 (*.f64 x (*.f64 1/4 x)) (*.f64 (/.f64 (*.f64 y (*.f64 y (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))) (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 1 (/.f64 (-.f64 z (log.f64 z)) 1)))) (-.f64 (*.f64 x 1/2) (*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))))

rewrite411.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
97×*-un-lft-identity_binary64_12013
86×add-sqr-sqrt_binary64_12035
48×unpow-prod-down_binary64_12092 associate-*r*_binary64_11953
44×distribute-lft-out--_binary64_11965
42×times-frac_binary64_12019
37×add-cube-cbrt_binary64_12048 difference-of-squares_binary64_11982
36×cancel-sign-sub-inv_binary64_11979
33×associate-*l*_binary64_11954
26×pow1_binary64_12074
22×add-cbrt-cube_binary64_12049 add-exp-log_binary64_12051
20×distribute-lft-in_binary64_11962 sqr-pow_binary64_11985 unpow2_binary64_12078 distribute-rgt-in_binary64_11963
18×log-pow_binary64_12102
11×associate-/r*_binary64_11957
8×flip3--_binary64_12017 flip--_binary64_11988 associate-*r/_binary64_11955
6×associate-/r/_binary64_11959 cbrt-unprod_binary64_12046 prod-exp_binary64_12062
5×div-exp_binary64_12064 cbrt-undiv_binary64_12047
4×add-log-exp_binary64_12052 associate-/l*_binary64_11958 associate-/l/_binary64_11960 sub-neg_binary64_12006
3×unswap-sqr_binary64_11981 div-inv_binary64_12010
2×*-commutative_binary64_11944 clear-num_binary64_12012 pow-prod-down_binary64_12084 frac-2neg_binary64_12024 frac-times_binary64_12023
1×div-sub_binary64_12018 associate-*l/_binary64_11956
Counts
4 → 224
Calls

8 calls:

288.0ms
(*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
30.0ms
(/.f64 (*.f64 y (*.f64 y (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))) (-.f64 (-.f64 1 z) (log.f64 z)))
28.0ms
(*.f64 y (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
15.0ms
(/.f64 (-.f64 (*.f64 x (*.f64 1/4 x)) (*.f64 (/.f64 (*.f64 y (*.f64 y (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))) (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 1 (/.f64 (-.f64 z (log.f64 z)) 1)))) (-.f64 (*.f64 x 1/2) (*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))))
0.0ms
(-.f64 (*.f64 x 1/2) (*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2))))

series34.4s (20.3%)

Counts
4 → 45
Calls

4 calls:

33.3s
(/.f64 (-.f64 (*.f64 x (*.f64 1/4 x)) (*.f64 (/.f64 (*.f64 y (*.f64 y (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))) (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 1 (/.f64 (-.f64 z (log.f64 z)) 1)))) (-.f64 (*.f64 x 1/2) (*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))))
406.0ms
(*.f64 (/.f64 y (-.f64 (-.f64 1 z) (log.f64 z))) (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
384.0ms
(/.f64 (*.f64 y (*.f64 y (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))) (-.f64 (-.f64 1 z) (log.f64 z)))
289.0ms
(*.f64 y (-.f64 (pow.f64 (-.f64 1 z) 2) (pow.f64 (log.f64 z) 2)))
Compiler

Compiled 27049 to 16921 computations (37.4% saved)

simplify201.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
269 → 269
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0513423450

prune32.1s (19%)

Pruning

579 alts after pruning (564 fresh and 15 done)

PrunedKeptTotal
New467269736
Fresh30295325
Picked000
Done11516
Total4985791077
Error
0b
Counts
1077 → 579
Compiler

Compiled 28964 to 17761 computations (38.7% saved)

simplify1.1s (0.6%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
0510174335

regimes23.2s (13.7%)

Compiler

Compiled 311295 to 220876 computations (29% saved)

bsearch0.0ms (0%)

regimes730.0ms (0.4%)

Compiler

Compiled 1068 to 1122 computations (-5.1% saved)

bsearch1.0ms (0%)

Compiler

Compiled 6 to 7 computations (-16.7% saved)

regimes398.0ms (0.2%)

Compiler

Compiled 828 to 894 computations (-8% saved)

bsearch1.0ms (0%)

Compiler

Compiled 6 to 7 computations (-16.7% saved)

regimes377.0ms (0.2%)

Compiler

Compiled 708 to 786 computations (-11% saved)

bsearch1.0ms (0%)

Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes171.0ms (0.1%)

Compiler

Compiled 388 to 428 computations (-10.3% saved)

bsearch1.0ms (0%)

Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes159.0ms (0.1%)

Compiler

Compiled 356 to 396 computations (-11.2% saved)

bsearch1.0ms (0%)

Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes76.0ms (0%)

Compiler

Compiled 324 to 368 computations (-13.6% saved)

bsearch0.0ms (0%)

regimes127.0ms (0.1%)

Compiler

Compiled 68 to 136 computations (-100% saved)

bsearch76.0ms (0%)

Steps
ItersRangePoint
7
1.9357795604821155e-138
3.946853944186567e-137
3.9099457876822657e-137
5
-2.696069074849004e-186
-7.015669702236174e-187
-2.640333964194819e-186
9
-1.4897182049507063e-87
-7.962383458231908e-97
-3.4403799285636905e-92
0
-3.050995196899053e-17
-3.019417234508112e-17
-3.0352062157035826e-17
Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes38.0ms (0%)

Compiler

Compiled 36 to 96 computations (-166.7% saved)

bsearch0.0ms (0%)

regimes26.0ms (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch0.0ms (0%)

regimes23.0ms (0%)

Accuracy

Total 0.1b remaining (100%)

Threshold costs 0.1b (100%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch11.0ms (0%)

Compiler

Compiled 219 to 176 computations (19.6% saved)

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0124289
1124289

end0.0ms (0%)

sample38.3s (22.6%)

Algorithm
1×intervals
Results
407.0ms8000×body128valid
14.0ms297×body128invalid
3.0ms63×body128nan
Compiler

Compiled 45058 to 32063 computations (28.8% saved)

Pareto

0.6265539928258911

Profiling

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