Details

Time bar (total: 3.4min)

analyze893.0ms (0.4%)

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%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%99.9%0.1%8
0%96.7%3.3%9
16.4%74.9%8.7%10
17.6%71.8%10.7%11
26.3%59.5%14.2%12
30.7%45.7%23.5%13
31.7%43.5%24.7%14
Compiler

Compiled 30 to 25 computations (16.7% saved)

sample47.0ms (0%)

Algorithm
1×intervals
Results
17.0ms256×body128valid
12.0ms173×body128invalid
Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify149.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0499937
1499937

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
8.9b
Counts
2 → 2
Compiler

Compiled 25 to 20 computations (20% saved)

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

2.7b
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r))
0.6b
(/.f64 2 (*.f64 r r))
0.0b
(-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v)))
0.0b
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))) 9/2)
2.7b
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r))
5.2b
(*.f64 (*.f64 (*.f64 w w) r) r)
6.3b
(/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))
10.9b
(*.f64 (*.f64 w w) r)

rewrite73.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
92×add-exp-log_binary64 add-cbrt-cube_binary64
57×cbrt-unprod_binary64 prod-exp_binary64
50×pow1_binary64
33×pow-prod-down_binary64
15×add-sqr-sqrt_binary64
14×*-un-lft-identity_binary64
9×cbrt-undiv_binary64 div-exp_binary64
8×add-cube-cbrt_binary64
7×associate-*r*_binary64
6×associate-/r*_binary64 times-frac_binary64
4×add-log-exp_binary64 associate-*r/_binary64 difference-of-squares_binary64 associate-*l/_binary64
3×flip3--_binary64 associate-*l*_binary64 flip--_binary64 *-commutative_binary64
2×associate-/l/_binary64 associate-/r/_binary64 distribute-lft-out--_binary64
1×unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64
Counts
4 → 121
Calls

8 calls:

26.0ms
(/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))
13.0ms
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r))
8.0ms
(*.f64 (*.f64 w w) r)
7.0ms
(*.f64 (*.f64 (*.f64 w w) r) r)
0.0ms
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))) 9/2)

series742.0ms (0.4%)

Counts
4 → 39
Calls

4 calls:

312.0ms
(/.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) (-.f64 1 v))
280.0ms
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r))
81.0ms
(*.f64 (*.f64 w w) r)
70.0ms
(*.f64 (*.f64 (*.f64 w w) r) r)
Compiler

Compiled 2033 to 1790 computations (12% saved)

simplify69.0ms (0%)

Algorithm
1×egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049523344
149523344

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

4.3b
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))))
1.3b
(/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))
0.6b
(/.f64 2 (*.f64 r r))
0.0b
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w))))))
1.3b
(/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))
4.3b
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))))
5.9b
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w))))
10.9b
(*.f64 r (*.f64 w w))

rewrite75.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
109×times-frac_binary64
77×add-sqr-sqrt_binary64
71×*-un-lft-identity_binary64
52×add-exp-log_binary64 add-cbrt-cube_binary64
44×add-cube-cbrt_binary64
36×associate-*r*_binary64
18×difference-of-squares_binary64
17×cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64
11×associate-/r*_binary64 pow1_binary64
10×div-inv_binary64
9×associate-/l*_binary64 distribute-lft-out--_binary64
6×associate-*l*_binary64
4×pow-prod-down_binary64 add-log-exp_binary64
3×unswap-sqr_binary64
2×flip3-+_binary64 associate-/l/_binary64 associate-/r/_binary64 clear-num_binary64 frac-2neg_binary64 flip-+_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
1×flip3--_binary64 associate-*r/_binary64 div-sub_binary64 flip--_binary64
Counts
4 → 177
Calls

8 calls:

22.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))))
14.0ms
(/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))
12.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w))))
6.0ms
(*.f64 r (*.f64 w w))
0.0ms
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w))))))

series716.0ms (0.4%)

Counts
4 → 48
Calls

4 calls:

270.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))))
201.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w))))
188.0ms
(/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))
57.0ms
(*.f64 r (*.f64 w w))
Compiler

Compiled 2187 to 1856 computations (15.1% saved)

simplify112.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
225 → 225
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049514903
149514903

prune2.1s (1%)

Pruning

160 alts after pruning (160 fresh and 0 done)

PrunedKeptTotal
New225160385
Fresh000
Picked000
Done202
Total227160387
Error
1.2b
Counts
387 → 160
Compiler

Compiled 12717 to 8220 computations (35.4% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

1.3b
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
0.6b
(/.f64 2 (*.f64 r r))
0.2b
(*.f64 (*.f64 r w) w)
0.0b
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))))
0.6b
(/.f64 2 (*.f64 r r))
1.3b
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
4.3b
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))
5.9b
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))

rewrite70.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
112×times-frac_binary64
77×add-sqr-sqrt_binary64
72×*-un-lft-identity_binary64
52×add-exp-log_binary64 add-cbrt-cube_binary64
45×add-cube-cbrt_binary64
35×associate-*r*_binary64
19×cbrt-undiv_binary64 div-exp_binary64
18×difference-of-squares_binary64
15×cbrt-unprod_binary64 prod-exp_binary64
12×associate-/r*_binary64 associate-/l*_binary64
11×div-inv_binary64
9×distribute-lft-out--_binary64
6×pow1_binary64
4×add-log-exp_binary64
3×associate-*l*_binary64 clear-num_binary64 frac-2neg_binary64
2×flip3-+_binary64 associate-/l/_binary64 associate-/r/_binary64 unswap-sqr_binary64 flip-+_binary64 frac-times_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 flip3--_binary64 associate-*r/_binary64 div-sub_binary64 flip--_binary64 *-commutative_binary64
Counts
4 → 179
Calls

8 calls:

21.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))
12.0ms
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
11.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))
4.0ms
(/.f64 2 (*.f64 r r))
0.0ms
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))))

series704.0ms (0.3%)

Counts
4 → 45
Calls

4 calls:

276.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))
207.0ms
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
194.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))
27.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 2037 to 1730 computations (15.1% saved)

simplify101.0ms (0%)

Algorithm
1×egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049495010
149495010

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

5.2b
(*.f64 r (*.f64 r (*.f64 w w)))
0.6b
(/.f64 2 (*.f64 r r))
0.0b
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (*.f64 r (*.f64 r (*.f64 w w))) 1/4))
0.0b
(*.f64 (*.f64 r (*.f64 r (*.f64 w w))) 1/4)
0.0b
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (*.f64 r (*.f64 r (*.f64 w w))) 1/4))
0.6b
(/.f64 2 (*.f64 r r))
5.2b
(*.f64 r (*.f64 r (*.f64 w w)))
10.9b
(*.f64 r (*.f64 w w))

rewrite35.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
23×add-exp-log_binary64 add-cbrt-cube_binary64
18×pow1_binary64
10×cbrt-unprod_binary64 prod-exp_binary64
9×pow-prod-down_binary64 add-log-exp_binary64 add-sqr-sqrt_binary64
8×*-un-lft-identity_binary64 add-cube-cbrt_binary64
6×associate-*l*_binary64
3×associate-/l*_binary64 times-frac_binary64
2×diff-log_binary64 associate-*r*_binary64 cbrt-undiv_binary64 div-exp_binary64 *-commutative_binary64
1×associate-/r*_binary64 sub-neg_binary64 flip3--_binary64 cancel-sign-sub-inv_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 flip--_binary64 associate--l+_binary64 sum-log_binary64
Counts
4 → 75
Calls

8 calls:

11.0ms
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (*.f64 r (*.f64 r (*.f64 w w))) 1/4))
8.0ms
(*.f64 r (*.f64 r (*.f64 w w)))
6.0ms
(*.f64 r (*.f64 w w))
4.0ms
(/.f64 2 (*.f64 r r))
0.0ms
(*.f64 (*.f64 r (*.f64 r (*.f64 w w))) 1/4)

series409.0ms (0.2%)

Counts
4 → 30
Calls

4 calls:

249.0ms
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (*.f64 r (*.f64 r (*.f64 w w))) 1/4))
74.0ms
(*.f64 r (*.f64 r (*.f64 w w)))
61.0ms
(*.f64 r (*.f64 w w))
24.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 821 to 785 computations (4.4% saved)

simplify50.0ms (0%)

Algorithm
1×egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
050181387

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

2.7b
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r))
0.6b
(/.f64 2 (*.f64 r r))
0.0b
(-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (pow.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) 1) (-.f64 1 v)))
0.0b
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (pow.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) 1) (-.f64 1 v))) 9/2)
2.7b
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r))
5.2b
(*.f64 (*.f64 (*.f64 w w) r) r)
6.3b
(/.f64 (pow.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) 1) (-.f64 1 v))
10.9b
(*.f64 (*.f64 w w) r)

rewrite62.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
95×add-exp-log_binary64
57×prod-exp_binary64
52×add-cbrt-cube_binary64
50×pow1_binary64
38×add-sqr-sqrt_binary64
37×*-un-lft-identity_binary64
33×pow-prod-down_binary64 cbrt-unprod_binary64
30×times-frac_binary64
19×add-cube-cbrt_binary64
12×difference-of-squares_binary64
11×div-exp_binary64
9×pow-exp_binary64
7×associate-*r*_binary64 sqr-pow_binary64 unpow-prod-down_binary64
6×associate-/r*_binary64 distribute-lft-out--_binary64
5×associate-/l*_binary64
4×add-log-exp_binary64
3×associate-*l*_binary64 *-commutative_binary64
2×flip3--_binary64 associate-*r/_binary64 associate-/r/_binary64 flip--_binary64 associate-*l/_binary64
1×pow-to-exp_binary64 cbrt-undiv_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64
Counts
4 → 141
Calls

8 calls:

15.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) 1) (-.f64 1 v))
14.0ms
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r))
8.0ms
(*.f64 (*.f64 (*.f64 w w) r) r)
6.0ms
(*.f64 (*.f64 w w) r)
0.0ms
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (/.f64 (pow.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) 1) (-.f64 1 v))) 9/2)

series753.0ms (0.4%)

Counts
4 → 39
Calls

4 calls:

326.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r)) 1) (-.f64 1 v))
288.0ms
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 (*.f64 w w) r) r))
72.0ms
(*.f64 (*.f64 (*.f64 w w) r) r)
67.0ms
(*.f64 (*.f64 w w) r)
Compiler

Compiled 2123 to 1880 computations (11.4% saved)

simplify76.0ms (0%)

Algorithm
1×egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
052164678

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v)))))
0.0b
(sqrt.f64 (-.f64 1 v))
0.0b
(sqrt.f64 (-.f64 1 v))
0.0b
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v))))) 9/2)
0.1b
(/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v)))
0.6b
(/.f64 2 (*.f64 r r))
0.9b
(*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v))))
20.7b
(*.f64 (*.f64 w w) (*.f64 r r))

rewrite83.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
119×add-exp-log_binary64 add-cbrt-cube_binary64
58×cbrt-unprod_binary64 prod-exp_binary64
34×pow1_binary64
31×cbrt-undiv_binary64 div-exp_binary64
30×add-sqr-sqrt_binary64 times-frac_binary64
28×*-un-lft-identity_binary64
24×sqrt-prod_binary64
16×associate-*r*_binary64 add-cube-cbrt_binary64 associate-*l*_binary64
15×pow-prod-down_binary64
10×associate-/r*_binary64
8×difference-of-squares_binary64
6×associate-/r/_binary64 sqrt-div_binary64
4×add-log-exp_binary64 flip3--_binary64 pow-prod-up_binary64 pow-plus_binary64 associate-/l*_binary64 distribute-lft-out--_binary64 div-inv_binary64 flip--_binary64
3×associate-*r/_binary64
2×associate-/l/_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 pow-sqr_binary64 pow2_binary64 *-commutative_binary64
1×frac-times_binary64 associate-*l/_binary64
Counts
4 → 166
Calls

8 calls:

33.0ms
(*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v))))
11.0ms
(/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v)))
9.0ms
(*.f64 (*.f64 w w) (*.f64 r r))
4.0ms
(/.f64 2 (*.f64 r r))
0.0ms
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v))))) 9/2)

series479.0ms (0.2%)

Counts
4 → 28
Calls

4 calls:

328.0ms
(*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v))))
87.0ms
(*.f64 (*.f64 w w) (*.f64 r r))
34.0ms
(/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v)))
29.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 1554 to 1345 computations (13.4% saved)

simplify92.0ms (0%)

Algorithm
1×egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049324277
149324277

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (cbrt.f64 (-.f64 1 v)))
0.1b
(/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))
0.0b
(-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (cbrt.f64 (-.f64 1 v)))))
0.0b
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (cbrt.f64 (-.f64 1 v))))) 9/2)
0.3b
(cbrt.f64 (-.f64 1 v))
0.6b
(/.f64 2 (*.f64 r r))
1.4b
(*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (cbrt.f64 (-.f64 1 v))))
20.7b
(*.f64 (*.f64 w w) (*.f64 r r))

rewrite88.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
194×add-exp-log_binary64
145×add-cbrt-cube_binary64
103×cbrt-unprod_binary64 prod-exp_binary64
51×cbrt-undiv_binary64 div-exp_binary64
34×pow1_binary64
19×add-sqr-sqrt_binary64
17×*-un-lft-identity_binary64
16×cbrt-div_binary64 associate-*r*_binary64
15×pow-prod-down_binary64
14×associate-*l*_binary64
13×times-frac_binary64
12×cbrt-prod_binary64
11×add-cube-cbrt_binary64
10×associate-/r/_binary64
8×flip3--_binary64 flip--_binary64
5×frac-times_binary64
4×add-log-exp_binary64 pow-prod-up_binary64 pow-plus_binary64 difference-of-squares_binary64
3×associate-*r/_binary64 associate-/l*_binary64 div-inv_binary64 associate-*l/_binary64
2×unswap-sqr_binary64 distribute-lft-out--_binary64 pow-sqr_binary64 pow2_binary64 *-commutative_binary64
1×associate-/r*_binary64 pow1/3_binary64 clear-num_binary64 frac-2neg_binary64
Counts
4 → 167
Calls

8 calls:

35.0ms
(*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (cbrt.f64 (-.f64 1 v))))
9.0ms
(*.f64 (*.f64 w w) (*.f64 r r))
4.0ms
(/.f64 2 (*.f64 r r))
3.0ms
(cbrt.f64 (-.f64 1 v))
0.0ms
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (cbrt.f64 (-.f64 1 v))))) 9/2)

series488.0ms (0.2%)

Counts
4 → 29
Calls

4 calls:

335.0ms
(*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (cbrt.f64 (-.f64 1 v))))
84.0ms
(*.f64 (*.f64 w w) (*.f64 r r))
40.0ms
(cbrt.f64 (-.f64 1 v))
28.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 1811 to 1561 computations (13.8% saved)

simplify106.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
050424581

prune13.4s (6.6%)

Pruning

411 alts after pruning (411 fresh and 0 done)

PrunedKeptTotal
New584315899
Fresh5996155
Picked000
Done505
Total6484111059
Error
0.0b
Counts
1059 → 411
Compiler

Compiled 32804 to 22332 computations (31.9% saved)

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(*.f64 (*.f64 w r) (*.f64 w r))
0.2b
(/.f64 (-.f64 1 v) (*.f64 (*.f64 w r) (*.f64 w r)))
0.0b
(-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (/.f64 1 (/.f64 (-.f64 1 v) (*.f64 (*.f64 w r) (*.f64 w r))))))
0.0b
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (/.f64 1 (/.f64 (-.f64 1 v) (*.f64 (*.f64 w r) (*.f64 w r)))))) 9/2)
0.4b
(*.f64 (*.f64 w r) (*.f64 w r))
0.6b
(/.f64 2 (*.f64 r r))
0.9b
(/.f64 1 (/.f64 (-.f64 1 v) (*.f64 (*.f64 w r) (*.f64 w r))))
4.3b
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (/.f64 1 (/.f64 (-.f64 1 v) (*.f64 (*.f64 w r) (*.f64 w r)))))

rewrite95.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
269×add-exp-log_binary64
138×prod-exp_binary64
119×add-cbrt-cube_binary64
105×times-frac_binary64
83×div-exp_binary64
63×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
54×cbrt-unprod_binary64
49×pow1_binary64
42×add-cube-cbrt_binary64
36×associate-*r*_binary64
35×cbrt-undiv_binary64
20×pow-prod-down_binary64
18×1-exp_binary64 rec-exp_binary64
14×difference-of-squares_binary64
11×associate-/r*_binary64
10×div-inv_binary64
7×distribute-lft-out--_binary64
6×associate-/l*_binary64
5×associate-*r/_binary64
4×add-log-exp_binary64 pow-prod-up_binary64 pow-sqr_binary64
2×flip3--_binary64 associate-/r/_binary64 associate-*l*_binary64 pow-plus_binary64 clear-num_binary64 frac-2neg_binary64 flip--_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
1×swap-sqr_binary64 inv-pow_binary64 un-div-inv_binary64 pow-flip_binary64 pow2_binary64
Counts
4 → 239
Calls

8 calls:

27.0ms
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (/.f64 1 (/.f64 (-.f64 1 v) (*.f64 (*.f64 w r) (*.f64 w r)))))
14.0ms
(/.f64 1 (/.f64 (-.f64 1 v) (*.f64 (*.f64 w r) (*.f64 w r))))
7.0ms
(*.f64 (*.f64 w r) (*.f64 w r))
4.0ms
(/.f64 2 (*.f64 r r))
0.0ms
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (/.f64 1 (/.f64 (-.f64 1 v) (*.f64 (*.f64 w r) (*.f64 w r)))))) 9/2)

series630.0ms (0.3%)

Counts
4 → 39
Calls

4 calls:

322.0ms
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (/.f64 1 (/.f64 (-.f64 1 v) (*.f64 (*.f64 w r) (*.f64 w r)))))
198.0ms
(/.f64 1 (/.f64 (-.f64 1 v) (*.f64 (*.f64 w r) (*.f64 w r))))
80.0ms
(*.f64 (*.f64 w r) (*.f64 w r))
29.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 2042 to 1788 computations (12.4% saved)

simplify111.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
278 → 278
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
051655958

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.6b
(/.f64 2 (*.f64 r r))
0.6b
(/.f64 2 (*.f64 r r))

rewrite6.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
6×add-exp-log_binary64 add-cbrt-cube_binary64
3×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 associate-/l*_binary64 times-frac_binary64
2×cbrt-undiv_binary64 div-exp_binary64
1×associate-/r*_binary64 add-log-exp_binary64 pow1_binary64 cbrt-unprod_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-inv_binary64
Counts
1 → 21
Calls

2 calls:

4.0ms
(/.f64 2 (*.f64 r r))
0.0ms
(/.f64 2 (*.f64 r r))

series24.0ms (0%)

Counts
1 → 3
Calls

1 calls:

24.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 30 to 42 computations (-40% saved)

simplify88.0ms (0%)

Algorithm
1×egg-herbie
Counts
24 → 24
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
04675212
14675212

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(/.f64 (sqrt.f64 2) r)
0.4b
(*.f64 (/.f64 (sqrt.f64 2) r) (/.f64 (sqrt.f64 2) r))
0.0b
(-.f64 (+.f64 (*.f64 (/.f64 (sqrt.f64 2) r) (/.f64 (sqrt.f64 2) r)) -3/2) (*.f64 (*.f64 r (*.f64 r (*.f64 w w))) 1/4))
0.0b
(*.f64 (*.f64 r (*.f64 r (*.f64 w w))) 1/4)
0.5b
(/.f64 (sqrt.f64 2) r)
0.5b
(/.f64 (sqrt.f64 2) r)
5.2b
(*.f64 r (*.f64 r (*.f64 w w)))
10.9b
(*.f64 r (*.f64 w w))

rewrite32.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
37×add-sqr-sqrt_binary64
36×*-un-lft-identity_binary64 add-cube-cbrt_binary64 times-frac_binary64
24×sqrt-prod_binary64
22×add-exp-log_binary64 add-cbrt-cube_binary64
18×pow1_binary64
12×associate-/l*_binary64
9×pow-prod-down_binary64 cbrt-unprod_binary64 prod-exp_binary64
6×associate-/r*_binary64 associate-*l*_binary64
4×add-log-exp_binary64
2×associate-*r*_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 *-commutative_binary64
1×unswap-sqr_binary64
Counts
4 → 118
Calls

8 calls:

7.0ms
(*.f64 r (*.f64 r (*.f64 w w)))
6.0ms
(*.f64 r (*.f64 w w))
4.0ms
(/.f64 (sqrt.f64 2) r)
4.0ms
(/.f64 (sqrt.f64 2) r)
0.0ms
(*.f64 (*.f64 r (*.f64 r (*.f64 w w))) 1/4)

series203.0ms (0.1%)

Counts
4 → 18
Calls

4 calls:

69.0ms
(*.f64 r (*.f64 r (*.f64 w w)))
65.0ms
(*.f64 r (*.f64 w w))
38.0ms
(/.f64 (sqrt.f64 2) r)
30.0ms
(/.f64 (sqrt.f64 2) r)
Compiler

Compiled 756 to 684 computations (9.5% saved)

simplify61.0ms (0%)

Algorithm
1×egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049451499
149451499

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(*.f64 (cbrt.f64 r) (cbrt.f64 r))
0.2b
(*.f64 (*.f64 r w) (*.f64 (cbrt.f64 r) (cbrt.f64 r)))
0.0b
(/.f64 (-.f64 1 v) w)
0.0b
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 r) (cbrt.f64 r))) (/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w)))))
0.6b
(/.f64 2 (*.f64 r r))
1.6b
(*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 r) (cbrt.f64 r))) (/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w)))
3.9b
(/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w))
4.3b
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 r) (cbrt.f64 r))) (/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w))))

rewrite179.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
501×times-frac_binary64
345×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
228×add-cube-cbrt_binary64
169×add-exp-log_binary64
138×associate-*r*_binary64
135×cbrt-prod_binary64
123×add-cbrt-cube_binary64
95×cbrt-unprod_binary64 prod-exp_binary64
78×difference-of-squares_binary64
47×pow1_binary64
39×distribute-lft-out--_binary64
35×cbrt-undiv_binary64 div-exp_binary64
32×pow-prod-down_binary64
23×associate-/r*_binary64
16×div-inv_binary64
9×associate-/l*_binary64
5×associate-*r/_binary64
4×add-log-exp_binary64 associate-*l*_binary64
2×flip3-+_binary64 associate-/r/_binary64 clear-num_binary64 frac-2neg_binary64 flip-+_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 433
Calls

8 calls:

41.0ms
(*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 r) (cbrt.f64 r))) (/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w)))
33.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 r) (cbrt.f64 r))) (/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w))))
11.0ms
(/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w))
10.0ms
(/.f64 2 (*.f64 r r))
0.0ms
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 r) (cbrt.f64 r))) (/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w)))))

series863.0ms (0.4%)

Counts
4 → 49
Calls

4 calls:

309.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 r) (cbrt.f64 r))) (/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w))))
297.0ms
(/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w))
226.0ms
(*.f64 (*.f64 (*.f64 r w) (*.f64 (cbrt.f64 r) (cbrt.f64 r))) (/.f64 (cbrt.f64 r) (/.f64 (-.f64 1 v) w)))
31.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 2445 to 1983 computations (18.9% saved)

simplify171.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
482 → 482
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
0497212364
1497212364

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (*.f64 (sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))) (sqrt.f64 (+.f64 3/8 (*.f64 v -1/4)))) (*.f64 (sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))) (sqrt.f64 (+.f64 3/8 (*.f64 v -1/4)))))
0.2b
(*.f64 w (*.f64 r w))
0.2b
(*.f64 w (*.f64 r w))
0.0b
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (*.f64 (sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))) (sqrt.f64 (+.f64 3/8 (*.f64 v -1/4)))) (*.f64 (sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))) (sqrt.f64 (+.f64 3/8 (*.f64 v -1/4))))))
5.9b
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))
5.9b
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))
17.3b
(sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w)))))
17.3b
(sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w)))))

rewrite88.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
206×times-frac_binary64
124×add-sqr-sqrt_binary64
118×*-un-lft-identity_binary64
76×add-cube-cbrt_binary64
70×sqrt-prod_binary64
32×add-exp-log_binary64 add-cbrt-cube_binary64
28×difference-of-squares_binary64
20×associate-/r*_binary64
18×div-inv_binary64
14×cbrt-undiv_binary64 distribute-lft-out--_binary64 div-exp_binary64
6×pow1_binary64 cbrt-unprod_binary64 prod-exp_binary64 associate-/l*_binary64
4×add-log-exp_binary64 associate-/r/_binary64 rem-sqrt-square_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 clear-num_binary64 frac-2neg_binary64 sqrt-div_binary64
Counts
4 → 218
Calls

8 calls:

11.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))
11.0ms
(sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w)))))
11.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))
11.0ms
(sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w)))))
0.0ms
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (*.f64 (sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))) (sqrt.f64 (+.f64 3/8 (*.f64 v -1/4)))) (*.f64 (sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))) (sqrt.f64 (+.f64 3/8 (*.f64 v -1/4))))))

series798.0ms (0.4%)

Counts
4 → 50
Calls

4 calls:

218.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))
198.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))
192.0ms
(sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w)))))
188.0ms
(sqrt.f64 (/.f64 r (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w)))))
Compiler

Compiled 4152 to 3296 computations (20.6% saved)

simplify99.0ms (0%)

Algorithm
1×egg-herbie
Counts
268 → 268
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
051496562

prune51.5s (25.5%)

Pruning

821 alts after pruning (820 fresh and 1 done)

PrunedKeptTotal
New7304581188
Fresh44362406
Picked000
Done415
Total7788211599
Error
0b
Counts
1599 → 821
Compiler

Compiled 62476 to 41122 computations (34.2% saved)

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (*.f64 w r) (/.f64 (*.f64 w r) (-.f64 1 v)))
0.1b
(/.f64 (*.f64 w r) (-.f64 1 v))
0.0b
(-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 w r) (/.f64 (*.f64 w r) (-.f64 1 v)))))
0.0b
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 w r) (/.f64 (*.f64 w r) (-.f64 1 v))))) 9/2)
0.1b
(/.f64 (*.f64 w r) (-.f64 1 v))
0.3b
(*.f64 (*.f64 w r) (/.f64 (*.f64 w r) (-.f64 1 v)))
0.6b
(/.f64 2 (*.f64 r r))
4.3b
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 w r) (/.f64 (*.f64 w r) (-.f64 1 v))))

rewrite63.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
100×add-exp-log_binary64 add-cbrt-cube_binary64
56×cbrt-unprod_binary64 prod-exp_binary64
30×pow1_binary64
19×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
18×pow-prod-down_binary64
16×cbrt-undiv_binary64 div-exp_binary64
15×times-frac_binary64
13×associate-*r*_binary64
10×add-cube-cbrt_binary64
9×associate-*r/_binary64
7×associate-/r*_binary64
6×difference-of-squares_binary64
4×add-log-exp_binary64 flip3--_binary64 associate-/r/_binary64 associate-/l*_binary64 flip--_binary64
3×distribute-lft-out--_binary64 div-inv_binary64
2×associate-*l*_binary64 clear-num_binary64 frac-2neg_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 135
Calls

8 calls:

18.0ms
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 w r) (/.f64 (*.f64 w r) (-.f64 1 v))))
12.0ms
(*.f64 (*.f64 w r) (/.f64 (*.f64 w r) (-.f64 1 v)))
7.0ms
(/.f64 (*.f64 w r) (-.f64 1 v))
5.0ms
(/.f64 2 (*.f64 r r))
0.0ms
(-.f64 (-.f64 (+.f64 3 (/.f64 2 (*.f64 r r))) (*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 w r) (/.f64 (*.f64 w r) (-.f64 1 v))))) 9/2)

series709.0ms (0.4%)

Counts
4 → 49
Calls

4 calls:

320.0ms
(*.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (*.f64 (*.f64 w r) (/.f64 (*.f64 w r) (-.f64 1 v))))
207.0ms
(*.f64 (*.f64 w r) (/.f64 (*.f64 w r) (-.f64 1 v)))
157.0ms
(/.f64 (*.f64 w r) (-.f64 1 v))
25.0ms
(/.f64 2 (*.f64 r r))
Compiler

Compiled 2423 to 2013 computations (16.9% saved)

simplify91.0ms (0%)

Algorithm
1×egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049503698
149503698

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b
(/.f64 (/.f64 2 r) r)
0.2b
(/.f64 (/.f64 2 r) r)

rewrite17.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
75×times-frac_binary64
43×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
13×associate-/l*_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
5×div-inv_binary64
3×associate-/r*_binary64 cbrt-undiv_binary64 div-exp_binary64
1×associate-/l/_binary64 add-log-exp_binary64 pow1_binary64 clear-num_binary64 frac-2neg_binary64
Counts
1 → 70
Calls

2 calls:

7.0ms
(/.f64 (/.f64 2 r) r)
0.0ms
(/.f64 (/.f64 2 r) r)

series26.0ms (0%)

Counts
1 → 3
Calls

1 calls:

26.0ms
(/.f64 (/.f64 2 r) r)
Compiler

Compiled 30 to 42 computations (-40% saved)

simplify85.0ms (0%)

Algorithm
1×egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
049801058
149801058

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 (+.f64 3 (/.f64 (/.f64 2 r) r)) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v)))))
0.0b
(sqrt.f64 (-.f64 1 v))
0.0b
(sqrt.f64 (-.f64 1 v))
0.0b
(-.f64 (-.f64 (+.f64 3 (/.f64 (/.f64 2 r) r)) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v))))) 9/2)
0.1b
(/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v)))
0.2b
(/.f64 (/.f64 2 r) r)
0.9b
(*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v))))
20.7b
(*.f64 (*.f64 w w) (*.f64 r r))

rewrite99.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
119×add-exp-log_binary64 add-cbrt-cube_binary64
102×times-frac_binary64
70×add-sqr-sqrt_binary64
68×*-un-lft-identity_binary64
57×cbrt-unprod_binary64 prod-exp_binary64
56×add-cube-cbrt_binary64
34×pow1_binary64
32×cbrt-undiv_binary64 div-exp_binary64
24×sqrt-prod_binary64
16×associate-*r*_binary64 associate-*l*_binary64
15×pow-prod-down_binary64
14×associate-/l*_binary64
12×associate-/r*_binary64
8×difference-of-squares_binary64 div-inv_binary64
6×associate-/r/_binary64 sqrt-div_binary64
4×add-log-exp_binary64 flip3--_binary64 pow-prod-up_binary64 pow-plus_binary64 distribute-lft-out--_binary64 flip--_binary64
3×associate-/l/_binary64 associate-*r/_binary64
2×unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 pow-sqr_binary64 pow2_binary64 *-commutative_binary64
1×frac-times_binary64 associate-*l/_binary64
Counts
4 → 215
Calls

8 calls:

35.0ms
(*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v))))
12.0ms
(/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v)))
9.0ms
(*.f64 (*.f64 w w) (*.f64 r r))
7.0ms
(/.f64 (/.f64 2 r) r)
0.0ms
(-.f64 (-.f64 (+.f64 3 (/.f64 (/.f64 2 r) r)) (*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v))))) 9/2)

series487.0ms (0.2%)

Counts
4 → 28
Calls

4 calls:

335.0ms
(*.f64 (/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v))) (/.f64 (*.f64 (*.f64 w w) (*.f64 r r)) (sqrt.f64 (-.f64 1 v))))
89.0ms
(*.f64 (*.f64 w w) (*.f64 r r))
33.0ms
(/.f64 (*.f64 1/8 (-.f64 3 (*.f64 2 v))) (sqrt.f64 (-.f64 1 v)))
29.0ms
(/.f64 (/.f64 2 r) r)
Compiler

Compiled 1554 to 1352 computations (13% saved)

simplify130.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
049375190
149375190

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (sqrt.f64 r) (sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))
0.1b
(/.f64 (sqrt.f64 r) (sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w)))))
0.1b
(*.f64 (*.f64 (/.f64 (sqrt.f64 r) (sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))) (+.f64 3/8 (*.f64 v -1/4))) (/.f64 (sqrt.f64 r) (sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))))
0.0b
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (*.f64 (/.f64 (sqrt.f64 r) (sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))) (+.f64 3/8 (*.f64 v -1/4))) (/.f64 (sqrt.f64 r) (sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))))
1.3b
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
1.3b
(/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w)))
9.0b
(sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))
9.0b
(sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))

rewrite50.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
32×add-sqr-sqrt_binary64
30×*-un-lft-identity_binary64
24×times-frac_binary64
22×add-exp-log_binary64 add-cbrt-cube_binary64
20×sqrt-prod_binary64
12×add-cube-cbrt_binary64 difference-of-squares_binary64 associate-/l*_binary64
6×pow1_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 distribute-lft-out--_binary64 div-exp_binary64
4×associate-/l/_binary64 add-log-exp_binary64 div-inv_binary64
2×associate-/r*_binary64 pow1/2_binary64 flip3--_binary64 sqrt-pow1_binary64 div-sub_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 flip--_binary64 sqrt-div_binary64
Counts
4 → 106
Calls

8 calls:

10.0ms
(/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w)))
9.0ms
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
9.0ms
(sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))
7.0ms
(sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))
0.0ms
(-.f64 (+.f64 (/.f64 2 (*.f64 r r)) -3/2) (*.f64 (*.f64 (/.f64 (sqrt.f64 r) (sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))) (+.f64 3/8 (*.f64 v -1/4))) (/.f64 (sqrt.f64 r) (sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))))

series769.0ms (0.4%)

Counts
4 → 46
Calls

4 calls:

210.0ms
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
204.0ms
(/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w)))
177.0ms
(sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))
177.0ms
(sqrt.f64 (/.f64 (-.f64 1 v) (*.f64 w (*.f64 r w))))
Compiler

Compiled 3882 to 2892 computations (25.5% saved)

simplify73.0ms (0%)

Algorithm
1×egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049522475
149522475

localize33.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (*.f64 r w) (pow.f64 r 2/3))
0.1b
(*.f64 (cbrt.f64 (pow.f64 r 2/3)) (sqrt.f64 w))
0.0b
(*.f64 (*.f64 (*.f64 (*.f64 r w) (pow.f64 r 2/3)) (*.f64 (cbrt.f64 (pow.f64 r 2/3)) (sqrt.f64 w))) (/.f64 (cbrt.f64 (cbrt.f64 r)) (/.f64 (-.f64 1 v) (sqrt.f64 w))))
0.0b
(*.f64 (*.f64 (*.f64 r w) (pow.f64 r 2/3)) (*.f64 (cbrt.f64 (pow.f64 r 2/3)) (sqrt.f64 w)))
0.7b
(/.f64 (cbrt.f64 (cbrt.f64 r)) (/.f64 (-.f64 1 v) (sqrt.f64 w)))
0.8b
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (*.f64 (*.f64 (*.f64 r w) (pow.f64 r 2/3)) (*.f64 (cbrt.f64 (pow.f64 r 2/3)) (sqrt.f64 w))) (/.f64 (cbrt.f64 (cbrt.f64 r)) (/.f64 (-.f64 1 v) (sqrt.f64 w)))))
2.6b
(pow.f64 r 2/3)
2.6b
(pow.f64 r 2/3)

rewrite221.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
720×times-frac_binary64
502×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
369×cbrt-prod_binary64
322×add-cube-cbrt_binary64
298×add-exp-log_binary64
208×prod-exp_binary64
180×sqrt-prod_binary64
120×difference-of-squares_binary64
115×add-cbrt-cube_binary64
88×cbrt-unprod_binary64
60×distribute-lft-out--_binary64
48×div-exp_binary64
40×associate-/r*_binary64
24×cbrt-undiv_binary64
20×pow1_binary64
14×pow-to-exp_binary64 pow-exp_binary64
11×div-inv_binary64
10×pow-prod-down_binary64
9×associate-/l*_binary64
6×pow-unpow_binary64 unpow-prod-down_binary64
4×add-log-exp_binary64 associate-*r/_binary64
3×associate-*l*_binary64
2×flip3-+_binary64 pow-pow_binary64 sqr-pow_binary64 flip-+_binary64 frac-times_binary64 associate-*l/_binary64
1×associate-*r*_binary64 associate-/r/_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 547
Calls

8 calls:

53.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (*.f64 (*.f64 (*.f64 r w) (pow.f64 r 2/3)) (*.f64 (cbrt.f64 (pow.f64 r 2/3)) (sqrt.f64 w))) (/.f64 (cbrt.f64 (cbrt.f64 r)) (/.f64 (-.f64 1 v) (sqrt.f64 w)))))
26.0ms
(/.f64 (cbrt.f64 (cbrt.f64 r)) (/.f64 (-.f64 1 v) (sqrt.f64 w)))
3.0ms
(pow.f64 r 2/3)
2.0ms
(pow.f64 r 2/3)
0.0ms
(*.f64 (*.f64 (*.f64 r w) (pow.f64 r 2/3)) (*.f64 (cbrt.f64 (pow.f64 r 2/3)) (sqrt.f64 w)))

series796.0ms (0.4%)

Counts
4 → 36
Calls

4 calls:

328.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (*.f64 (*.f64 (*.f64 r w) (pow.f64 r 2/3)) (*.f64 (cbrt.f64 (pow.f64 r 2/3)) (sqrt.f64 w))) (/.f64 (cbrt.f64 (cbrt.f64 r)) (/.f64 (-.f64 1 v) (sqrt.f64 w)))))
307.0ms
(/.f64 (cbrt.f64 (cbrt.f64 r)) (/.f64 (-.f64 1 v) (sqrt.f64 w)))
84.0ms
(pow.f64 r 2/3)
77.0ms
(pow.f64 r 2/3)
Compiler

Compiled 2339 to 1885 computations (19.4% saved)

simplify293.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
583 → 583
Iterations

Useful iterations: 0 (109.0ms)

IterNodesCost
0493220422
1493220422

prune1.2min (34.8%)

Pruning

1077 alts after pruning (1072 fresh and 5 done)

PrunedKeptTotal
New9402951235
Fresh38777815
Picked000
Done156
Total97910772056
Error
0b
Counts
2056 → 1077
Compiler

Compiled 25605 to 14894 computations (41.8% saved)

simplify2.1s (1.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
07780119245

regimes35.6s (17.6%)

Compiler

Compiled 466868 to 352246 computations (24.6% saved)

bsearch0.0ms (0%)

regimes1.0s (0.5%)

Compiler

Compiled 13225 to 10860 computations (17.9% saved)

bsearch0.0ms (0%)

regimes1000.0ms (0.5%)

Compiler

Compiled 12819 to 10529 computations (17.9% saved)

bsearch0.0ms (0%)

regimes1.2s (0.6%)

Compiler

Compiled 12587 to 10337 computations (17.9% saved)

bsearch7.0ms (0%)

Compiler

Compiled 3 to 4 computations (-33.3% saved)

regimes1.0s (0.5%)

Compiler

Compiled 9535 to 7863 computations (17.5% saved)

bsearch4.0ms (0%)

Compiler

Compiled 3 to 4 computations (-33.3% saved)

regimes967.0ms (0.5%)

Compiler

Compiled 6238 to 5216 computations (16.4% saved)

bsearch3.0ms (0%)

Compiler

Compiled 3 to 4 computations (-33.3% saved)

regimes588.0ms (0.3%)

Compiler

Compiled 5013 to 4236 computations (15.5% saved)

bsearch81.0ms (0%)

Steps
ItersRangePoint
9
1448122102403790.2
3.2557943563511497e+20
3112772480630809.0
7
-5.473627740473432e+61
-1.720123865534641e+60
-1.7514718148497125e+60
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes494.0ms (0.2%)

Compiler

Compiled 4813 to 4080 computations (15.2% saved)

bsearch77.0ms (0%)

Steps
ItersRangePoint
9
1.704551844854633e-19
2.102221200016068e-13
2.0797092502220554e-13
6
-1.781818031037959
-0.4296383054965157
-0.9959872356613901
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes462.0ms (0.2%)

Compiler

Compiled 3030 to 2663 computations (12.1% saved)

bsearch66.0ms (0%)

Steps
ItersRangePoint
9
1.704551844854633e-19
2.102221200016068e-13
2.0797092502220554e-13
6
-1.781818031037959
-0.4296383054965157
-1.4110751356614466
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes250.0ms (0.1%)

Compiler

Compiled 1032 to 1038 computations (-0.6% saved)

bsearch69.0ms (0%)

Steps
ItersRangePoint
9
1.704551844854633e-19
2.102221200016068e-13
2.0797092502220554e-13
6
-1.781818031037959
-0.4296383054965157
-1.282121085095703
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes256.0ms (0.1%)

Compiler

Compiled 964 to 986 computations (-2.3% saved)

bsearch68.0ms (0%)

Steps
ItersRangePoint
9
1.704551844854633e-19
2.102221200016068e-13
2.0797092502220554e-13
6
-1.781818031037959
-0.4296383054965157
-1.1531670345299596
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes131.0ms (0.1%)

Compiler

Compiled 556 to 650 computations (-16.9% saved)

bsearch0.0ms (0%)

regimes155.0ms (0.1%)

Compiler

Compiled 388 to 474 computations (-22.2% saved)

bsearch56.0ms (0%)

Steps
ItersRangePoint
7
0.4792776566796621
58.71575014483263
57.85103057416921
9
-0.106981066292436
-9.414356357500667e-07
-0.10595949870001081
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes107.0ms (0.1%)

Compiler

Compiled 344 to 434 computations (-26.2% saved)

bsearch77.0ms (0%)

Steps
ItersRangePoint
11
-2.0496872019599987e+130
-4.324356220602991e+106
-2.028385926279712e+130
7
-2.213467307099648e+241
-2.1469473205979486e+239
-2.2009087362557417e+239
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes60.0ms (0%)

Compiler

Compiled 228 to 300 computations (-31.6% saved)

bsearch0.0ms (0%)

regimes54.0ms (0%)

Compiler

Compiled 102 to 156 computations (-52.9% saved)

bsearch50.0ms (0%)

Steps
ItersRangePoint
7
0.4792776566796621
58.71575014483263
1.1331225229640847
9
-0.106981066292436
-9.414356357500667e-07
-0.10595949870001081
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes27.0ms (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch0.0ms (0%)

regimes23.0ms (0%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch27.0ms (0%)

Compiler

Compiled 681 to 472 computations (30.7% saved)

simplify20.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (12.0ms)

IterNodesCost
0720926
1720926

end0.0ms (0%)

sample4.3s (2.1%)

Algorithm
1×intervals
Results
549.0ms8000×body128valid
323.0ms4818×body128invalid
Compiler

Compiled 75645 to 56886 computations (24.8% saved)

Profiling

Loading profile data...