Details

Time bar (total: 3.7min)

analyze283.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%12.5%87.5%0
0%12.5%87.5%1
0%12.5%87.5%2
3.1%9.3%87.5%3
3.1%6.2%90.7%4
4.7%4.7%90.7%5
4.7%3.5%91.8%6
5.6%2.5%91.8%7
5.9%1.8%92.3%8
6.4%1.3%92.3%9
6.6%0.9%92.5%10
6.8%0.6%92.5%11
6.9%0.5%92.6%12
7%0.3%92.6%13
7.1%0.2%92.7%14
Compiler

Compiled 23 to 18 computations (21.7% saved)

sample32.0ms (0%)

Algorithm
1×intervals
Results
9.0ms256×body128valid
6.0ms258×pre128true
0.0ms2×body128invalid
Compiler

Compiled 39 to 36 computations (7.7% saved)

simplify199.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
3 → 3
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
0492421
1492421

prune4.0ms (0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New123
Fresh033
Picked000
Done000
Total156
Error
0.1b
Counts
6 → 3
Compiler

Compiled 15 to 13 computations (13.3% saved)

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

0.1b
(/.f64 (*.f64 m (-.f64 1 m)) v)
0.0b
(*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
0.1b
(/.f64 (*.f64 m (-.f64 1 m)) v)

rewrite50.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
27×add-sqr-sqrt_binary64
22×*-un-lft-identity_binary64
13×add-cube-cbrt_binary64
12×associate-*r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 cancel-sign-sub-inv_binary64
10×associate-*l*_binary64
8×flip3--_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 flip--_binary64
7×pow1_binary64
6×associate-*r/_binary64 difference-of-squares_binary64
4×sub-neg_binary64 frac-times_binary64
3×associate-/r*_binary64 add-log-exp_binary64 cbrt-unprod_binary64 prod-exp_binary64 distribute-lft-out--_binary64 times-frac_binary64
2×pow-prod-down_binary64 associate-/l/_binary64 cbrt-undiv_binary64 unswap-sqr_binary64 div-exp_binary64 associate-*l/_binary64 *-commutative_binary64
1×difference-of-sqr-1_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64
Counts
3 → 95
Calls

6 calls:

16.0ms
(*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
10.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
8.0ms
(*.f64 m (-.f64 1 m))
0.0ms
(*.f64 m (-.f64 1 m))
0.0ms
(*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

series279.0ms (0.1%)

Counts
3 → 33
Calls

3 calls:

130.0ms
(*.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
108.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
40.0ms
(*.f64 m (-.f64 1 m))
Compiler

Compiled 627 to 518 computations (17.4% saved)

simplify70.0ms (0%)

Algorithm
1×egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
050172129

prune499.0ms (0.2%)

Pruning

62 alts after pruning (61 fresh and 1 done)

PrunedKeptTotal
New6959128
Fresh022
Picked000
Done011
Total6962131
Error
0b
Counts
131 → 62
Compiler

Compiled 2783 to 2023 computations (27.3% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m)))) (/.f64 (pow.f64 m 3) v))
0.0b
(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m))))
0.0b
(+.f64 m (/.f64 m v))
0.0b
(*.f64 2 (*.f64 (/.f64 m v) m))
0.0b
(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m)))) (/.f64 (pow.f64 m 3) v))
0.0b
(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m))))
0.2b
(*.f64 (/.f64 m v) m)
10.6b
(/.f64 (pow.f64 m 3) v)

rewrite71.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
53×*-un-lft-identity_binary64
46×add-sqr-sqrt_binary64 times-frac_binary64
39×add-cube-cbrt_binary64
34×add-log-exp_binary64
14×add-exp-log_binary64
13×associate-*l*_binary64 sum-log_binary64
12×unpow-prod-down_binary64 cube-prod_binary64 associate-/l*_binary64
11×add-cbrt-cube_binary64
9×flip3-+_binary64 flip-+_binary64
8×diff-log_binary64 frac-sub_binary64
6×pow1_binary64 frac-add_binary64 cancel-sign-sub-inv_binary64
5×distribute-lft-out_binary64 associate-+l+_binary64
4×sqr-pow_binary64 distribute-lft-out--_binary64 div-exp_binary64 unpow3_binary64 cube-mult_binary64
3×associate-/r*_binary64 associate-*r*_binary64
2×sub-neg_binary64 flip3--_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 unswap-sqr_binary64 prod-exp_binary64 div-inv_binary64 flip--_binary64 associate--l+_binary64
1×pow-to-exp_binary64 pow-prod-down_binary64 associate--r+_binary64 associate-+l-_binary64 clear-num_binary64 frac-2neg_binary64 difference-of-squares_binary64 +-commutative_binary64 pow-exp_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 153
Calls

8 calls:

30.0ms
(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m)))) (/.f64 (pow.f64 m 3) v))
12.0ms
(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m))))
6.0ms
(*.f64 (/.f64 m v) m)
5.0ms
(/.f64 (pow.f64 m 3) v)
0.0ms
(*.f64 2 (*.f64 (/.f64 m v) m))

series491.0ms (0.2%)

Counts
4 → 45
Calls

4 calls:

175.0ms
(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m))))
161.0ms
(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m)))) (/.f64 (pow.f64 m 3) v))
87.0ms
(/.f64 (pow.f64 m 3) v)
68.0ms
(*.f64 (/.f64 m v) m)
Compiler

Compiled 1178 to 891 computations (24.4% saved)

simplify74.0ms (0%)

Algorithm
1×egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
049714376
149714376

localize2.0ms (0%)

rewrite0.0ms (0%)

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

series0.0ms (0%)

Counts
0 → 0

simplify6.0ms (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:

0.0b
(*.f64 (-.f64 1 m) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.1b
(/.f64 (*.f64 m (-.f64 1 m)) v)
0.1b
(/.f64 (*.f64 m (-.f64 1 m)) v)
0.4b
(*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v))
12.2b
(/.f64 (*.f64 (-.f64 1 m) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1)) (+.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))

rewrite78.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
55×add-exp-log_binary64 add-cbrt-cube_binary64
22×*-un-lft-identity_binary64 times-frac_binary64
20×add-sqr-sqrt_binary64
18×cbrt-unprod_binary64 cbrt-undiv_binary64 add-cube-cbrt_binary64 prod-exp_binary64 div-exp_binary64
12×associate-/l/_binary64
11×pow1_binary64
10×associate-/r*_binary64
8×flip3--_binary64 flip--_binary64
7×swap-sqr_binary64 associate-*r*_binary64 associate-*r/_binary64 associate-*l*_binary64 div-inv_binary64
5×frac-times_binary64
4×add-log-exp_binary64
3×clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 associate-*l/_binary64
2×distribute-lft-out_binary64 associate-/r/_binary64
1×pow-prod-down_binary64 flip3-+_binary64 pow-prod-up_binary64 pow-plus_binary64 unswap-sqr_binary64 pow-sqr_binary64 flip-+_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 135
Calls

8 calls:

31.0ms
(/.f64 (*.f64 (-.f64 1 m) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1)) (+.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
15.0ms
(*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v))
8.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
7.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
0.0ms
(*.f64 m (-.f64 1 m))

series751.0ms (0.3%)

Counts
4 → 48
Calls

4 calls:

329.0ms
(/.f64 (*.f64 (-.f64 1 m) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1)) (+.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
202.0ms
(*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v))
110.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
109.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
Compiler

Compiled 2105 to 1622 computations (22.9% saved)

simplify88.0ms (0%)

Algorithm
1×egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
050033426

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

4.4b
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
0.1b
(/.f64 (*.f64 m (-.f64 1 m)) v)
0.0b
(*.f64 (-.f64 (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))) 1) (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 (-.f64 (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))) 1) (-.f64 1 m))
0.1b
(/.f64 (*.f64 m (-.f64 1 m)) v)
4.4b
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))

rewrite54.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
35×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
13×add-exp-log_binary64 add-cbrt-cube_binary64 associate-*l*_binary64
12×associate-*r*_binary64 cancel-sign-sub-inv_binary64
10×log-prod_binary64 exp-sum_binary64
9×pow1_binary64
8×flip3--_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 difference-of-squares_binary64 flip--_binary64
6×associate-*r/_binary64 times-frac_binary64
4×add-log-exp_binary64 sub-neg_binary64 frac-times_binary64 exp-prod_binary64
3×associate-/r*_binary64 cbrt-unprod_binary64 prod-exp_binary64 distribute-lft-out--_binary64
2×pow-prod-down_binary64 associate-/l/_binary64 cbrt-undiv_binary64 difference-of-sqr-1_binary64 unswap-sqr_binary64 div-inv_binary64 div-exp_binary64 associate-*l/_binary64 *-commutative_binary64
1×log-pow_binary64 rem-exp-log_binary64 exp-diff_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 log-div_binary64
Counts
4 → 118
Calls

8 calls:

22.0ms
(*.f64 (-.f64 (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))) 1) (-.f64 1 m))
8.0ms
(*.f64 m (-.f64 1 m))
8.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
0.0ms
(*.f64 m (-.f64 1 m))

series650.0ms (0.3%)

Counts
4 → 30
Calls

4 calls:

295.0ms
(*.f64 (-.f64 (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))) 1) (-.f64 1 m))
214.0ms
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
100.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
41.0ms
(*.f64 m (-.f64 1 m))
Compiler

Compiled 955 to 829 computations (13.2% saved)

simplify82.0ms (0%)

Algorithm
1×egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049862308
149862308

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
0.0b
(*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.1b
(/.f64 (*.f64 m (-.f64 1 m)) v)
0.1b
(sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
0.1b
(sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
0.3b
(*.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))))

rewrite110.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
160×sqrt-div_binary64
144×frac-times_binary64
121×flip3--_binary64 flip--_binary64
59×pow1_binary64
50×associate-*r/_binary64
48×associate-*l/_binary64
32×sqrt-pow1_binary64
22×pow-prod-down_binary64
12×pow1/2_binary64 add-sqr-sqrt_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
10×*-un-lft-identity_binary64 pow-prod-up_binary64 add-cube-cbrt_binary64
6×pow-sqr_binary64 sqrt-prod_binary64
4×add-log-exp_binary64 swap-sqr_binary64 associate-*r*_binary64 associate-*l*_binary64
3×associate-/r*_binary64 times-frac_binary64
2×associate-/l/_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64
1×rem-square-sqrt_binary64 pow-plus_binary64 sqrt-unprod_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 190
Calls

8 calls:

36.0ms
(*.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))))
13.0ms
(sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
13.0ms
(sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
8.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
0.0ms
(*.f64 m (-.f64 1 m))

series396.0ms (0.2%)

Counts
4 → 36
Calls

4 calls:

132.0ms
(*.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))))
113.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
76.0ms
(sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
74.0ms
(sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
Compiler

Compiled 1642 to 1306 computations (20.5% saved)

simplify126.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
0500910151

prune12.7s (5.7%)

Pruning

304 alts after pruning (300 fresh and 4 done)

PrunedKeptTotal
New506249755
Fresh55156
Picked000
Done246
Total513304817
Error
0b
Counts
817 → 304
Compiler

Compiled 25655 to 17100 computations (33.3% saved)

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 m (/.f64 m v))
0.0b
(*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2))
0.0b
(+.f64 (+.f64 m (/.f64 m v)) (*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2)))
0.0b
(+.f64 m (/.f64 m v))
0.0b
(+.f64 (+.f64 m (/.f64 m v)) (*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2)))
0.0b
(+.f64 m (/.f64 m v))
0.0b
(*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2))
0.2b
(*.f64 m (/.f64 m v))

rewrite50.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64
21×*-un-lft-identity_binary64
18×associate-*r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
17×add-cube-cbrt_binary64
16×associate-*r/_binary64
12×cancel-sign-sub-inv_binary64
11×add-log-exp_binary64 pow1_binary64
10×frac-add_binary64 times-frac_binary64
8×distribute-lft-in_binary64 distribute-rgt-in_binary64 associate-+r+_binary64
7×flip3-+_binary64 cbrt-unprod_binary64 prod-exp_binary64 flip-+_binary64
6×flip3--_binary64 flip--_binary64 frac-times_binary64
4×pow-prod-down_binary64 sub-neg_binary64 associate-*l*_binary64 sum-log_binary64
3×associate-*l/_binary64
2×cbrt-undiv_binary64 unswap-sqr_binary64 div-exp_binary64 +-commutative_binary64 *-commutative_binary64
1×distribute-lft-out_binary64 associate-+l+_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 div-inv_binary64
Counts
4 → 110
Calls

8 calls:

13.0ms
(+.f64 (+.f64 m (/.f64 m v)) (*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2)))
10.0ms
(*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2))
7.0ms
(*.f64 m (/.f64 m v))
6.0ms
(+.f64 m (/.f64 m v))
0.0ms
(+.f64 m (/.f64 m v))

series470.0ms (0.2%)

Counts
4 → 37
Calls

4 calls:

233.0ms
(+.f64 (+.f64 m (/.f64 m v)) (*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2)))
124.0ms
(*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2))
60.0ms
(*.f64 m (/.f64 m v))
52.0ms
(+.f64 m (/.f64 m v))
Compiler

Compiled 1045 to 807 computations (22.8% saved)

simplify97.0ms (0%)

Algorithm
1×egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
049392569
149392569

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

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
0.1b
(/.f64 (*.f64 m (-.f64 1 m)) v)
0.0b
(*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
0.1b
(/.f64 (*.f64 m (-.f64 1 m)) v)
0.1b
(sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
0.3b
(pow.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) 2)

rewrite62.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64
13×pow1_binary64 flip3--_binary64 flip--_binary64
12×add-cube-cbrt_binary64 add-exp-log_binary64
11×add-cbrt-cube_binary64
8×frac-times_binary64 sqrt-div_binary64
7×associate-*r*_binary64
6×associate-*r/_binary64 associate-*l*_binary64 cancel-sign-sub-inv_binary64
4×add-log-exp_binary64 pow-pow_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 sqrt-pow1_binary64 unpow-prod-down_binary64 difference-of-squares_binary64 associate-*l/_binary64
3×pow-prod-down_binary64 pow-unpow_binary64 associate-/r*_binary64 times-frac_binary64
2×associate-/l/_binary64 sub-neg_binary64 pow1/2_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 distribute-lft-out--_binary64 div-exp_binary64 sqrt-prod_binary64
1×pow-to-exp_binary64 sqrt-pow2_binary64 unpow2_binary64 difference-of-sqr-1_binary64 sqr-pow_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64 pow-exp_binary64 *-commutative_binary64
Counts
4 → 106
Calls

8 calls:

16.0ms
(*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
16.0ms
(pow.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) 2)
13.0ms
(sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
8.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
0.0ms
(*.f64 m (-.f64 1 m))

series4.7s (2.1%)

Counts
4 → 41
Calls

4 calls:

4.4s
(pow.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) 2)
140.0ms
(*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
106.0ms
(/.f64 (*.f64 m (-.f64 1 m)) v)
74.0ms
(sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
Compiler

Compiled 1334 to 1124 computations (15.7% saved)

simplify96.0ms (0%)

Algorithm
1×egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
049652928
149652928

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m)))) (/.f64 (/.f64 (pow.f64 m 3) (sqrt.f64 v)) (sqrt.f64 v)))
0.0b
(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m))))
0.0b
(+.f64 m (/.f64 m v))
0.0b
(*.f64 2 (*.f64 (/.f64 m v) m))
0.0b
(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m))))
0.2b
(*.f64 (/.f64 m v) m)
4.4b
(/.f64 (pow.f64 m 3) (sqrt.f64 v))
6.0b
(/.f64 (/.f64 (pow.f64 m 3) (sqrt.f64 v)) (sqrt.f64 v))

rewrite174.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
1042×times-frac_binary64
522×add-sqr-sqrt_binary64 sqrt-prod_binary64
520×*-un-lft-identity_binary64
515×add-cube-cbrt_binary64
147×unpow-prod-down_binary64 cube-prod_binary64
88×associate-/l*_binary64
49×sqr-pow_binary64 unpow3_binary64 cube-mult_binary64
24×add-exp-log_binary64
16×add-log-exp_binary64 add-cbrt-cube_binary64
13×associate-*l*_binary64
12×associate-/r*_binary64
11×div-exp_binary64
10×div-inv_binary64
6×pow1_binary64
5×cbrt-undiv_binary64
4×flip3-+_binary64 diff-log_binary64 flip-+_binary64 frac-sub_binary64 sum-log_binary64
3×associate-*r*_binary64 cancel-sign-sub-inv_binary64
2×pow-to-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 distribute-lft-out--_binary64 pow-exp_binary64
1×pow-prod-down_binary64 associate-/l/_binary64 sub-neg_binary64 associate--r+_binary64 flip3--_binary64 distribute-lft-out_binary64 difference-of-squares_binary64 flip--_binary64 associate--l+_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 717
Calls

8 calls:

25.0ms
(/.f64 (/.f64 (pow.f64 m 3) (sqrt.f64 v)) (sqrt.f64 v))
12.0ms
(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m))))
11.0ms
(/.f64 (pow.f64 m 3) (sqrt.f64 v))
7.0ms
(*.f64 (/.f64 m v) m)
0.0ms
(*.f64 2 (*.f64 (/.f64 m v) m))

series422.0ms (0.2%)

Counts
4 → 33
Calls

4 calls:

182.0ms
(-.f64 (+.f64 m (/.f64 m v)) (+.f64 1 (*.f64 2 (*.f64 (/.f64 m v) m))))
83.0ms
(/.f64 (pow.f64 m 3) (sqrt.f64 v))
82.0ms
(/.f64 (/.f64 (pow.f64 m 3) (sqrt.f64 v)) (sqrt.f64 v))
75.0ms
(*.f64 (/.f64 m v) m)
Compiler

Compiled 1357 to 964 computations (29% saved)

simplify241.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
750 → 750
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
0497016968
1497016968

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(+.f64 1 (+.f64 m (*.f64 m m)))
0.0b
(*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1))
0.2b
(/.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1))) (sqrt.f64 (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v)))))
0.2b
(*.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) (/.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1))) (sqrt.f64 (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v))))))
0.4b
(*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v))
5.7b
(sqrt.f64 (*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1)))

rewrite180.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
48×sqrt-div_binary64
47×add-exp-log_binary64 add-cbrt-cube_binary64
45×times-frac_binary64
39×add-sqr-sqrt_binary64
35×associate-*r*_binary64
33×frac-times_binary64
32×*-un-lft-identity_binary64 add-cube-cbrt_binary64
24×flip3--_binary64 flip--_binary64
21×associate-*l/_binary64
20×sqrt-prod_binary64
17×cbrt-unprod_binary64 prod-exp_binary64
16×pow1_binary64 associate-/r/_binary64
14×cbrt-undiv_binary64 associate-*r/_binary64 div-exp_binary64
12×flip3-+_binary64 flip-+_binary64
11×associate-*l*_binary64
8×associate-/l/_binary64
7×swap-sqr_binary64
6×div-inv_binary64
4×associate-/r*_binary64 add-log-exp_binary64 associate-/l*_binary64
3×pow-prod-down_binary64 unswap-sqr_binary64
2×sqrt-undiv_binary64 sqrt-pow1_binary64 *-commutative_binary64
1×pow1/2_binary64 pow-prod-up_binary64 pow-plus_binary64 sqrt-unprod_binary64 clear-num_binary64 frac-2neg_binary64 pow-sqr_binary64 pow2_binary64
Counts
4 → 193
Calls

8 calls:

55.0ms
(*.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) (/.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1))) (sqrt.f64 (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v))))))
40.0ms
(/.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1))) (sqrt.f64 (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v)))))
22.0ms
(sqrt.f64 (*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1)))
21.0ms
(*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v))
0.0ms
(*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1))

series4.6s (2.1%)

Counts
4 → 35
Calls

4 calls:

3.6s
(*.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) (/.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1))) (sqrt.f64 (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v))))))
456.0ms
(/.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1))) (sqrt.f64 (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v)))))
363.0ms
(sqrt.f64 (*.f64 (-.f64 1 (pow.f64 m 3)) (-.f64 (*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v)) 1)))
160.0ms
(*.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) (/.f64 (*.f64 m (-.f64 1 m)) v))
Compiler

Compiled 11523 to 9285 computations (19.4% saved)

simplify158.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
228 → 228
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0500414705

prune39.2s (17.7%)

Pruning

661 alts after pruning (654 fresh and 7 done)

PrunedKeptTotal
New8783941272
Fresh35260295
Picked000
Done279
Total9156611576
Error
0b
Counts
1576 → 661
Compiler

Compiled 56772 to 35721 computations (37.1% saved)

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

0.2b
(*.f64 m (/.f64 m v))
0.0b
(*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2))
0.0b
(+.f64 (/.f64 m v) (*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2)))
0.0b
(+.f64 (/.f64 m v) (*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2)))
0.0b
(*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2))
0.2b
(*.f64 m (/.f64 m v))

rewrite35.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64 associate-*r*_binary64
17×add-exp-log_binary64 add-cbrt-cube_binary64
16×add-cube-cbrt_binary64
12×cancel-sign-sub-inv_binary64
11×associate-*r/_binary64
10×pow1_binary64 times-frac_binary64
8×distribute-lft-in_binary64 distribute-rgt-in_binary64 associate-+r+_binary64
7×cbrt-unprod_binary64 prod-exp_binary64
5×add-log-exp_binary64 frac-add_binary64
4×pow-prod-down_binary64 sub-neg_binary64 flip3--_binary64 associate-*l*_binary64 flip--_binary64 frac-times_binary64
2×cbrt-undiv_binary64 unswap-sqr_binary64 div-exp_binary64 associate-*l/_binary64 *-commutative_binary64
1×flip3-+_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 div-inv_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64
Counts
3 → 91
Calls

6 calls:

10.0ms
(*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2))
9.0ms
(+.f64 (/.f64 m v) (*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2)))
7.0ms
(*.f64 m (/.f64 m v))
0.0ms
(+.f64 (/.f64 m v) (*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2)))
0.0ms
(*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2))

series448.0ms (0.2%)

Counts
3 → 27
Calls

3 calls:

244.0ms
(+.f64 (/.f64 m v) (*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2)))
139.0ms
(*.f64 (*.f64 m (/.f64 m v)) (-.f64 m 2))
65.0ms
(*.f64 m (/.f64 m v))
Compiler

Compiled 701 to 575 computations (18% saved)

simplify83.0ms (0%)

Algorithm
1×egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049391707
149391707

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 m (/.f64 m v))
0.0b
(+.f64 m (/.f64 m v))

rewrite7.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
3×*-un-lft-identity_binary64 add-log-exp_binary64
1×flip3-+_binary64 pow1_binary64 distribute-lft-out_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-sqr-sqrt_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64
Counts
1 → 12
Calls

2 calls:

6.0ms
(+.f64 m (/.f64 m v))
0.0ms
(+.f64 m (/.f64 m v))

series55.0ms (0%)

Counts
1 → 8
Calls

1 calls:

55.0ms
(+.f64 m (/.f64 m v))
Compiler

Compiled 100 to 97 computations (3% saved)

simplify80.0ms (0%)

Algorithm
1×egg-herbie
Counts
20 → 20
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
04830181
14830181

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(pow.f64 (/.f64 m v) 3)
0.1b
(*.f64 (*.f64 m m) (-.f64 m 2))
0.0b
(-.f64 (/.f64 m v) m)
0.0b
(-.f64 (/.f64 m v) m)
7.4b
(*.f64 (*.f64 (*.f64 m m) (-.f64 m 2)) (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m))))
9.9b
(*.f64 v (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m))))
10.0b
(*.f64 v (+.f64 (pow.f64 m 3) (pow.f64 (/.f64 m v) 3)))
24.3b
(/.f64 (+.f64 (*.f64 v (+.f64 (pow.f64 m 3) (pow.f64 (/.f64 m v) 3))) (*.f64 (*.f64 (*.f64 m m) (-.f64 m 2)) (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m))))) (*.f64 v (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m)))))

rewrite117.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
46×associate-*r/_binary64
22×add-exp-log_binary64 add-cbrt-cube_binary64
21×flip3-+_binary64 *-un-lft-identity_binary64 flip-+_binary64
18×associate-/l/_binary64
17×pow1_binary64
16×frac-add_binary64
15×associate-*r*_binary64 add-sqr-sqrt_binary64
12×frac-times_binary64
11×add-cube-cbrt_binary64
9×flip3--_binary64 cbrt-unprod_binary64 prod-exp_binary64 flip--_binary64
8×pow-prod-down_binary64
7×associate-*l*_binary64
6×associate-*l/_binary64
5×distribute-lft-out_binary64
4×add-log-exp_binary64 unpow-prod-down_binary64 cube-prod_binary64
3×distribute-lft-in_binary64 distribute-rgt-in_binary64 associate-/l*_binary64 times-frac_binary64 *-commutative_binary64
2×cbrt-undiv_binary64 associate-/r/_binary64 unswap-sqr_binary64 div-exp_binary64
1×associate-/r*_binary64 sum-cubes_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64
Counts
4 → 122
Calls

8 calls:

41.0ms
(/.f64 (+.f64 (*.f64 v (+.f64 (pow.f64 m 3) (pow.f64 (/.f64 m v) 3))) (*.f64 (*.f64 (*.f64 m m) (-.f64 m 2)) (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m))))) (*.f64 v (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m)))))
26.0ms
(*.f64 v (+.f64 (pow.f64 m 3) (pow.f64 (/.f64 m v) 3)))
14.0ms
(*.f64 (*.f64 (*.f64 m m) (-.f64 m 2)) (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m))))
7.0ms
(*.f64 v (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m))))
0.0ms
(-.f64 (/.f64 m v) m)

series2.1s (1%)

Counts
4 → 42
Calls

4 calls:

1.4s
(/.f64 (+.f64 (*.f64 v (+.f64 (pow.f64 m 3) (pow.f64 (/.f64 m v) 3))) (*.f64 (*.f64 (*.f64 m m) (-.f64 m 2)) (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m))))) (*.f64 v (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m)))))
275.0ms
(*.f64 (*.f64 (*.f64 m m) (-.f64 m 2)) (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m))))
227.0ms
(*.f64 v (+.f64 (*.f64 m m) (*.f64 (/.f64 m v) (-.f64 (/.f64 m v) m))))
222.0ms
(*.f64 v (+.f64 (pow.f64 m 3) (pow.f64 (/.f64 m v) 3)))
Compiler

Compiled 3576 to 2397 computations (33% saved)

simplify80.0ms (0%)

Algorithm
1×egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
051557110

localize35.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(pow.f64 (-.f64 1 m) 2)
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(+.f64 1 (+.f64 m (*.f64 m m)))
0.3b
(*.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) (sqrt.f64 (*.f64 (/.f64 (-.f64 1 (pow.f64 m 3)) (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v)))) (+.f64 (*.f64 (/.f64 (*.f64 m m) (*.f64 v v)) (pow.f64 (-.f64 1 m) 2)) -1))))
1.2b
(/.f64 (-.f64 1 (pow.f64 m 3)) (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v))))
11.4b
(*.f64 (/.f64 (-.f64 1 (pow.f64 m 3)) (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v)))) (+.f64 (*.f64 (/.f64 (*.f64 m m) (*.f64 v v)) (pow.f64 (-.f64 1 m) 2)) -1))
28.2b
(/.f64 (*.f64 m m) (*.f64 v v))

rewrite163.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
93×sqrt-div_binary64
92×frac-times_binary64
45×add-sqr-sqrt_binary64
41×associate-*r/_binary64
37×flip3--_binary64 flip--_binary64
34×associate-*l/_binary64
32×flip3-+_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip-+_binary64
29×*-un-lft-identity_binary64
28×associate-*l*_binary64
25×times-frac_binary64
24×difference-of-squares_binary64
20×pow1_binary64
16×associate-/r/_binary64
13×associate-/l*_binary64
11×pow-prod-down_binary64 add-cube-cbrt_binary64
10×cbrt-unprod_binary64 prod-exp_binary64
8×cbrt-undiv_binary64 sqrt-pow1_binary64 div-exp_binary64
7×associate-*r*_binary64
6×sqr-pow_binary64 unpow-prod-down_binary64 cube-prod_binary64
4×add-log-exp_binary64
3×distribute-lft-out--_binary64 div-inv_binary64
2×associate-/l/_binary64 associate-/r*_binary64 pow1/2_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 sqrt-prod_binary64 *-commutative_binary64
1×distribute-lft-in_binary64 distribute-rgt-in_binary64 sqrt-unprod_binary64 div-sub_binary64
Counts
4 → 200
Calls

8 calls:

56.0ms
(*.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) (sqrt.f64 (*.f64 (/.f64 (-.f64 1 (pow.f64 m 3)) (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v)))) (+.f64 (*.f64 (/.f64 (*.f64 m m) (*.f64 v v)) (pow.f64 (-.f64 1 m) 2)) -1))))
36.0ms
(*.f64 (/.f64 (-.f64 1 (pow.f64 m 3)) (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v)))) (+.f64 (*.f64 (/.f64 (*.f64 m m) (*.f64 v v)) (pow.f64 (-.f64 1 m) 2)) -1))
20.0ms
(/.f64 (-.f64 1 (pow.f64 m 3)) (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v))))
6.0ms
(/.f64 (*.f64 m m) (*.f64 v v))
0.0ms
(+.f64 1 (+.f64 m (*.f64 m m)))

series4.5s (2%)

Counts
4 → 45
Calls

4 calls:

3.7s
(*.f64 (sqrt.f64 (*.f64 (-.f64 1 m) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))) (sqrt.f64 (*.f64 (/.f64 (-.f64 1 (pow.f64 m 3)) (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v)))) (+.f64 (*.f64 (/.f64 (*.f64 m m) (*.f64 v v)) (pow.f64 (-.f64 1 m) 2)) -1))))
511.0ms
(*.f64 (/.f64 (-.f64 1 (pow.f64 m 3)) (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v)))) (+.f64 (*.f64 (/.f64 (*.f64 m m) (*.f64 v v)) (pow.f64 (-.f64 1 m) 2)) -1))
194.0ms
(/.f64 (-.f64 1 (pow.f64 m 3)) (*.f64 (+.f64 1 (+.f64 m (*.f64 m m))) (+.f64 1 (/.f64 (*.f64 m (-.f64 1 m)) v))))
101.0ms
(/.f64 (*.f64 m m) (*.f64 v v))
Compiler

Compiled 11667 to 9305 computations (20.2% saved)

simplify149.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
245 → 245
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0500417159

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 m (-.f64 1 m))
0.0b
(*.f64 (-.f64 1 m) (+.f64 (pow.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 3) -1))
4.4b
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
4.4b
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
4.4b
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
12.0b
(/.f64 (*.f64 (-.f64 1 m) (+.f64 (pow.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 3) -1)) (+.f64 (*.f64 (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))) (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))) (+.f64 (*.f64 1 1) (*.f64 (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))) 1))))

rewrite87.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
21×log-prod_binary64 exp-sum_binary64
15×*-un-lft-identity_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
12×times-frac_binary64 exp-prod_binary64
11×exp-diff_binary64 log-div_binary64
9×add-exp-log_binary64 add-cbrt-cube_binary64
8×associate-/l/_binary64 associate-/r/_binary64
7×flip3-+_binary64 pow1_binary64 flip-+_binary64
6×frac-add_binary64 frac-times_binary64
4×add-log-exp_binary64 associate-*r/_binary64 div-inv_binary64 associate-*l/_binary64
3×associate-/r*_binary64 flip3--_binary64 log-pow_binary64 rem-exp-log_binary64 flip--_binary64
2×cbrt-undiv_binary64 div-exp_binary64
1×cbrt-unprod_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 associate-/l*_binary64
Counts
4 → 97
Calls

8 calls:

50.0ms
(/.f64 (*.f64 (-.f64 1 m) (+.f64 (pow.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 3) -1)) (+.f64 (*.f64 (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))) (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))) (+.f64 (*.f64 1 1) (*.f64 (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))) 1))))
6.0ms
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
6.0ms
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
6.0ms
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
0.0ms
(*.f64 (-.f64 1 m) (+.f64 (pow.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 3) -1))

series2.9s (1.3%)

Counts
4 → 31
Calls

4 calls:

2.3s
(/.f64 (*.f64 (-.f64 1 m) (+.f64 (pow.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 3) -1)) (+.f64 (*.f64 (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))) (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))) (+.f64 (*.f64 1 1) (*.f64 (exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v))) 1))))
221.0ms
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
213.0ms
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
174.0ms
(exp.f64 (log.f64 (/.f64 (*.f64 m (-.f64 1 m)) v)))
Compiler

Compiled 5099 to 4020 computations (21.2% saved)

simplify90.0ms (0%)

Algorithm
1×egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
051665160

prune1.1min (29.4%)

Pruning

970 alts after pruning (960 fresh and 10 done)

PrunedKeptTotal
New335340675
Fresh29620649
Picked000
Done21012
Total3669701336
Error
0b
Counts
1336 → 970
Compiler

Compiled 32175 to 16709 computations (48.1% saved)

simplify1.5s (0.7%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
05726109889

regimes17.0s (7.7%)

Compiler

Compiled 213479 to 140857 computations (34% saved)

bsearch0.0ms (0%)

regimes154.0ms (0.1%)

Compiler

Compiled 1116 to 960 computations (14% saved)

bsearch0.0ms (0%)

regimes70.0ms (0%)

Compiler

Compiled 404 to 358 computations (11.4% saved)

bsearch0.0ms (0%)

regimes67.0ms (0%)

Compiler

Compiled 378 to 336 computations (11.1% saved)

bsearch0.0ms (0%)

regimes88.0ms (0%)

Compiler

Compiled 274 to 254 computations (7.3% saved)

bsearch16.0ms (0%)

Steps
ItersRangePoint
6
5.240945624695797e-16
3.5299494502360443e-15
3.4909940996176206e-15
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes49.0ms (0%)

Compiler

Compiled 158 to 158 computations (0% saved)

bsearch17.0ms (0%)

Steps
ItersRangePoint
8
0.12626713037107096
89.64195145052182
0.43812959892688524
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes38.0ms (0%)

Compiler

Compiled 136 to 142 computations (-4.4% saved)

bsearch0.0ms (0%)

regimes20.0ms (0%)

Compiler

Compiled 16 to 34 computations (-112.5% saved)

bsearch0.0ms (0%)

regimes16.0ms (0%)

Accuracy

Total 0.1b remaining (100%)

Threshold costs 0.1b (100%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch11.0ms (0%)

Compiler

Compiled 115 to 93 computations (19.1% saved)

simplify18.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
0543164
1543164

end0.0ms (0%)

sample58.8s (26.5%)

Algorithm
1×intervals
Results
292.0ms8000×body128valid
177.0ms8058×pre128true
2.0ms58×body128invalid
Compiler

Compiled 71368 to 47117 computations (34% saved)

Pareto

0.42983922566502086

Profiling

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