Details

Time bar (total: 2.5min)

analyze13.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50%13
49.9%0%50%14
Compiler

Compiled 12 to 11 computations (8.3% saved)

sample22.0ms (0%)

Algorithm
1×intervals
Results
13.0ms256×body128valid
Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify131.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
046617
146617

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Compiler

Compiled 11 to 10 computations (9.1% saved)

localize19.0ms (0%)

Local error

Found 6 expressions with local error:

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

rewrite46.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
79×*-un-lft-identity_binary64
56×add-sqr-sqrt_binary64
49×times-frac_binary64
30×sqrt-prod_binary64
26×add-cube-cbrt_binary64
18×difference-of-squares_binary64
13×distribute-lft-out_binary64
9×distribute-lft-out--_binary64
6×associate-/l*_binary64
5×add-exp-log_binary64 add-cbrt-cube_binary64
4×associate-/r*_binary64 pow1_binary64 associate-/r/_binary64
3×add-log-exp_binary64
2×flip3-+_binary64 associate-/l/_binary64 rem-sqrt-square_binary64 div-inv_binary64 flip-+_binary64
1×pow1/2_binary64 flip3--_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64 flip--_binary64 sqrt-div_binary64
Counts
3 → 100
Calls

6 calls:

19.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
14.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
1.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series73.0ms (0%)

Counts
3 → 17
Calls

3 calls:

34.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
20.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
19.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
Compiler

Compiled 260 to 252 computations (3.1% saved)

simplify82.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
064192047

prune459.0ms (0.3%)

Pruning

53 alts after pruning (52 fresh and 1 done)

PrunedKeptTotal
New6552117
Fresh000
Picked000
Done011
Total6553118
Error
0b
Counts
118 → 53
Compiler

Compiled 2334 to 1941 computations (16.8% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
0.0b
(sqrt.f64 (-.f64 1 x))
0.0b
(atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))
0.0b
(sqrt.f64 (-.f64 1 x))
0.0b
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))

rewrite33.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
98×sqrt-prod_binary64
91×*-un-lft-identity_binary64
71×add-sqr-sqrt_binary64
63×times-frac_binary64
42×add-cube-cbrt_binary64
18×difference-of-squares_binary64
11×distribute-lft-out_binary64
9×associate-/l*_binary64 distribute-lft-out--_binary64
8×sqrt-div_binary64
7×associate-/r*_binary64
6×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
4×add-log-exp_binary64
2×flip3-+_binary64 associate-/l/_binary64 pow1/2_binary64 flip3--_binary64 associate-/r/_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip--_binary64 flip-+_binary64
1×cbrt-undiv_binary64 sqrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
4 → 137
Calls

8 calls:

11.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
4.0ms
(sqrt.f64 (-.f64 1 x))
3.0ms
(sqrt.f64 (+.f64 1 x))
1.0ms
(atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))
0.0ms
(sqrt.f64 (+.f64 1 x))

series77.0ms (0.1%)

Counts
4 → 21
Calls

4 calls:

21.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
21.0ms
(sqrt.f64 (+.f64 1 x))
18.0ms
(sqrt.f64 (-.f64 1 x))
17.0ms
(atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))
Compiler

Compiled 414 to 380 computations (8.2% saved)

simplify114.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 0 (83.0ms)

IterNodesCost
056473055

localize3.0ms (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 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))
0.0b
(sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))
0.0b
(atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))))
0.0b
(-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))
0.0b
(atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))))
0.0b
(-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))
0.0b
(sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))
0.0b
(*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))

rewrite29.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
15×*-un-lft-identity_binary64
14×add-sqr-sqrt_binary64
12×associate-*l*_binary64
11×add-cube-cbrt_binary64
7×pow1_binary64
6×flip3-+_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip-+_binary64
4×distribute-lft-out_binary64 associate-*r*_binary64 frac-times_binary64
3×distribute-rgt-out_binary64 sqrt-prod_binary64
2×associate--r+_binary64 flip3--_binary64 associate-*r/_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 flip--_binary64 sqrt-div_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 count-2_binary64 distribute-lft1-in_binary64 sub-neg_binary64 pow1/2_binary64 diff-log_binary64 cbrt-unprod_binary64 distribute-rgt1-in_binary64 cancel-sign-sub-inv_binary64 sqrt-pow1_binary64 unswap-sqr_binary64 rem-sqrt-square_binary64 prod-exp_binary64 *-commutative_binary64
Counts
4 → 74
Calls

8 calls:

15.0ms
(*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))
3.0ms
(-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))
3.0ms
(sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))
1.0ms
(atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))))
0.0ms
(-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))

series122.0ms (0.1%)

Counts
4 → 26
Calls

4 calls:

40.0ms
(-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))
32.0ms
(*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))
27.0ms
(atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))))
23.0ms
(sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))
Compiler

Compiled 508 to 471 computations (7.3% saved)

simplify78.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
048621987
148621987

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite142.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
774×times-frac_binary64
762×*-un-lft-identity_binary64
564×add-sqr-sqrt_binary64
540×sqrt-prod_binary64
292×add-cube-cbrt_binary64
180×difference-of-squares_binary64
100×distribute-lft-out_binary64
90×distribute-lft-out--_binary64
51×associate-/r*_binary64
28×sqrt-div_binary64
23×associate-/r/_binary64
14×flip3--_binary64 flip--_binary64
13×associate-/l*_binary64
12×div-inv_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
6×pow1_binary64
4×associate-/l/_binary64 add-log-exp_binary64 cbrt-undiv_binary64 div-exp_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64
1×flip3-+_binary64 flip-+_binary64
Counts
4 → 547
Calls

8 calls:

28.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
9.0ms
(/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))
4.0ms
(sqrt.f64 (-.f64 1 x))
4.0ms
(sqrt.f64 (-.f64 1 x))
0.0ms
(sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))))

series92.0ms (0.1%)

Counts
4 → 26
Calls

4 calls:

25.0ms
(sqrt.f64 (-.f64 1 x))
24.0ms
(/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))
24.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
18.0ms
(sqrt.f64 (-.f64 1 x))
Compiler

Compiled 574 to 516 computations (10.1% saved)

simplify216.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
573 → 573
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
0507117663

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite36.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
36×cbrt-prod_binary64
35×*-un-lft-identity_binary64
23×add-sqr-sqrt_binary64
18×cbrt-div_binary64
15×add-cube-cbrt_binary64
11×pow1_binary64
9×flip3-+_binary64 swap-sqr_binary64 distribute-lft-out_binary64 pow1/3_binary64 flip-+_binary64
7×associate-*r*_binary64 associate-*l*_binary64
6×add-exp-log_binary64
4×add-log-exp_binary64 add-cbrt-cube_binary64 unswap-sqr_binary64 frac-times_binary64
2×pow-prod-down_binary64 pow-prod-up_binary64 associate-*r/_binary64 pow-sqr_binary64 associate-*l/_binary64
1×cbrt-unprod_binary64 pow-plus_binary64 prod-exp_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 95
Calls

8 calls:

16.0ms
(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
3.0ms
(cbrt.f64 (+.f64 1 x))
3.0ms
(cbrt.f64 (+.f64 1 x))
3.0ms
(cbrt.f64 (+.f64 1 x))
0.0ms
(sqrt.f64 (/.f64 (/.f64 (-.f64 1 x) (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 1 x))))

series146.0ms (0.1%)

Counts
4 → 26
Calls

4 calls:

46.0ms
(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
36.0ms
(cbrt.f64 (+.f64 1 x))
33.0ms
(cbrt.f64 (+.f64 1 x))
30.0ms
(cbrt.f64 (+.f64 1 x))
Compiler

Compiled 933 to 818 computations (12.3% saved)

simplify77.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
050821439

prune11.3s (7.5%)

Pruning

219 alts after pruning (213 fresh and 6 done)

PrunedKeptTotal
New774178952
Fresh123547
Picked000
Done066
Total7862191005
Error
0b
Counts
1005 → 219
Compiler

Compiled 16370 to 12941 computations (20.9% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite132.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
237×*-un-lft-identity_binary64
233×sqrt-prod_binary64
218×add-sqr-sqrt_binary64
212×times-frac_binary64
110×add-cube-cbrt_binary64
69×associate-*r*_binary64
50×difference-of-squares_binary64
38×associate-*l*_binary64
36×distribute-lft-out_binary64
20×add-exp-log_binary64 add-cbrt-cube_binary64
17×associate-/l*_binary64
15×unswap-sqr_binary64 distribute-lft-out--_binary64
11×associate-/r*_binary64
10×sqrt-div_binary64
8×associate-/r/_binary64
7×pow1_binary64
6×cbrt-undiv_binary64 div-exp_binary64
4×flip3-+_binary64 associate-/l/_binary64 add-log-exp_binary64 cbrt-unprod_binary64 prod-exp_binary64 div-inv_binary64 flip-+_binary64
3×flip3--_binary64 flip--_binary64
2×clear-num_binary64 frac-2neg_binary64
1×pow-prod-down_binary64 pow1/2_binary64 associate-*r/_binary64 sqrt-undiv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 315
Calls

8 calls:

61.0ms
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
13.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
11.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
3.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms
(sqrt.f64 (+.f64 1 x))

series107.0ms (0.1%)

Counts
4 → 24
Calls

4 calls:

27.0ms
(sqrt.f64 (-.f64 1 (*.f64 x x)))
27.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
27.0ms
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
25.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
Compiler

Compiled 633 to 565 computations (10.7% saved)

simplify204.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
339 → 339
Iterations

Useful iterations: 0 (122.0ms)

IterNodesCost
049459026
149459026

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(atan.f64 (-.f64 1 x))
0.0b
(atan.f64 (-.f64 1 x))

rewrite2.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
1×*-un-lft-identity_binary64 add-log-exp_binary64 pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-sqr-sqrt_binary64
Counts
1 → 7
Calls

2 calls:

1.0ms
(atan.f64 (-.f64 1 x))
0.0ms
(atan.f64 (-.f64 1 x))

series13.0ms (0%)

Counts
1 → 3
Calls

1 calls:

13.0ms
(atan.f64 (-.f64 1 x))
Compiler

Compiled 36 to 36 computations (0% saved)

simplify151.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
10 → 10
Iterations

Useful iterations: 0 (144.0ms)

IterNodesCost
0474285
1474285

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))
0.0b
(sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))
0.0b
(atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))))
0.0b
(-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))
0.0b
(sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))
0.0b
(*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))
0.0b
(cbrt.f64 (pow.f64 (atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))) 3))
1.0b
(pow.f64 (atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))) 3)

rewrite31.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
21×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
17×add-cube-cbrt_binary64
12×associate-*l*_binary64 cbrt-prod_binary64
8×pow1_binary64
7×add-exp-log_binary64 add-cbrt-cube_binary64
6×flip3-+_binary64 unpow-prod-down_binary64 cube-prod_binary64 flip-+_binary64
4×add-log-exp_binary64 distribute-lft-out_binary64 associate-*r*_binary64 frac-times_binary64
3×pow-unpow_binary64 distribute-rgt-out_binary64 sqrt-prod_binary64
2×associate-*r/_binary64 sqr-pow_binary64 unpow3_binary64 sqrt-div_binary64 associate-*l/_binary64 cube-mult_binary64
1×pow-to-exp_binary64 pow-prod-down_binary64 count-2_binary64 distribute-lft1-in_binary64 pow1/2_binary64 rem-cbrt-cube_binary64 flip3--_binary64 cbrt-unprod_binary64 pow1/3_binary64 pow-pow_binary64 distribute-lft-in_binary64 distribute-rgt1-in_binary64 distribute-rgt-in_binary64 sqrt-pow1_binary64 unswap-sqr_binary64 rem-sqrt-square_binary64 rem-cube-cbrt_binary64 prod-exp_binary64 flip--_binary64 pow-exp_binary64 *-commutative_binary64
Counts
4 → 97
Calls

8 calls:

14.0ms
(*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))
3.0ms
(sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))
2.0ms
(pow.f64 (atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))) 3)
2.0ms
(cbrt.f64 (pow.f64 (atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))) 3))
0.0ms
(-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x))))

series213.0ms (0.1%)

Counts
4 → 17
Calls

4 calls:

127.0ms
(pow.f64 (atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))) 3)
36.0ms
(*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))
26.0ms
(cbrt.f64 (pow.f64 (atan.f64 (sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))) 3))
23.0ms
(sqrt.f64 (-.f64 1 (*.f64 (+.f64 x x) (+.f64 1 (-.f64 (*.f64 x x) x)))))
Compiler

Compiled 522 to 485 computations (7.1% saved)

simplify88.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
048592782
148592782

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite33.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
20×*-un-lft-identity_binary64
18×cbrt-div_binary64 cbrt-prod_binary64
9×flip3-+_binary64 pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-sqr-sqrt_binary64 flip-+_binary64
8×associate-*r/_binary64
7×associate-*l*_binary64
6×pow1/3_binary64
5×pow-prod-down_binary64 distribute-lft-out_binary64 add-cbrt-cube_binary64
4×add-log-exp_binary64 frac-times_binary64
3×cbrt-unprod_binary64 prod-exp_binary64
2×swap-sqr_binary64 associate-*l/_binary64
1×associate-*r*_binary64 *-commutative_binary64
Counts
4 → 75
Calls

8 calls:

15.0ms
(*.f64 (cbrt.f64 (+.f64 1 x)) (*.f64 (cbrt.f64 1) (cbrt.f64 (+.f64 1 x))))
3.0ms
(cbrt.f64 (+.f64 1 x))
3.0ms
(cbrt.f64 (+.f64 1 x))
3.0ms
(cbrt.f64 (+.f64 1 x))
0.0ms
(sqrt.f64 (/.f64 (/.f64 (-.f64 1 x) (*.f64 (cbrt.f64 (+.f64 1 x)) (*.f64 (cbrt.f64 1) (cbrt.f64 (+.f64 1 x))))) (cbrt.f64 (+.f64 1 x))))

series147.0ms (0.1%)

Counts
4 → 26
Calls

4 calls:

48.0ms
(*.f64 (cbrt.f64 (+.f64 1 x)) (*.f64 (cbrt.f64 1) (cbrt.f64 (+.f64 1 x))))
36.0ms
(cbrt.f64 (+.f64 1 x))
32.0ms
(cbrt.f64 (+.f64 1 x))
31.0ms
(cbrt.f64 (+.f64 1 x))
Compiler

Compiled 1005 to 890 computations (11.4% saved)

simplify94.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
048781205
148781205

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite62.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
62×add-sqr-sqrt_binary64
56×cbrt-prod_binary64
48×*-un-lft-identity_binary64 sqrt-prod_binary64
28×sqrt-div_binary64
24×cbrt-div_binary64
20×add-cube-cbrt_binary64
16×swap-sqr_binary64
14×flip3--_binary64 flip--_binary64
13×pow1_binary64
12×associate-*r*_binary64 associate-*l*_binary64 difference-of-squares_binary64
11×add-exp-log_binary64
9×unswap-sqr_binary64
8×associate-/r/_binary64 distribute-lft-out--_binary64 frac-times_binary64
7×add-cbrt-cube_binary64
6×pow1/3_binary64
4×add-log-exp_binary64 associate-*r/_binary64 associate-/l*_binary64 times-frac_binary64 associate-*l/_binary64
2×pow-prod-down_binary64 associate-/l/_binary64 pow1/2_binary64 cbrt-unprod_binary64 distribute-lft-out_binary64 pow-prod-up_binary64 cbrt-undiv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 prod-exp_binary64 div-exp_binary64 pow-sqr_binary64
1×flip3-+_binary64 associate-/r*_binary64 pow-plus_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 flip-+_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 144
Calls

8 calls:

18.0ms
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 x))) (cbrt.f64 (sqrt.f64 (-.f64 1 x))))
17.0ms
(/.f64 (+.f64 1 x) (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 x))) (cbrt.f64 (sqrt.f64 (-.f64 1 x)))))
4.0ms
(sqrt.f64 (-.f64 1 x))
4.0ms
(sqrt.f64 (-.f64 1 x))
0.0ms
(atan.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (/.f64 (+.f64 1 x) (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 x))) (cbrt.f64 (sqrt.f64 (-.f64 1 x))))) (cbrt.f64 (sqrt.f64 (-.f64 1 x)))))))

series133.0ms (0.1%)

Counts
4 → 24
Calls

4 calls:

42.0ms
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 x))) (cbrt.f64 (sqrt.f64 (-.f64 1 x))))
41.0ms
(/.f64 (+.f64 1 x) (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 x))) (cbrt.f64 (sqrt.f64 (-.f64 1 x)))))
26.0ms
(sqrt.f64 (-.f64 1 x))
23.0ms
(sqrt.f64 (-.f64 1 x))
Compiler

Compiled 986 to 859 computations (12.9% saved)

simplify70.0ms (0%)

Algorithm
1×egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049732753
149732753

prune26.4s (17.6%)

Pruning

353 alts after pruning (343 fresh and 10 done)

PrunedKeptTotal
New561171732
Fresh36172208
Picked000
Done11011
Total598353951
Error
0b
Counts
951 → 353
Compiler

Compiled 24546 to 19277 computations (21.5% saved)

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite179.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
311×*-un-lft-identity_binary64
290×sqrt-prod_binary64
255×times-frac_binary64
229×add-sqr-sqrt_binary64
146×add-cube-cbrt_binary64
140×log-pow_binary64
138×exp-prod_binary64
73×associate-*r*_binary64
62×difference-of-squares_binary64
45×distribute-lft-out_binary64
38×associate-*l*_binary64
22×distribute-lft-out--_binary64
17×associate-/l*_binary64
13×add-exp-log_binary64 add-cbrt-cube_binary64
11×associate-/r*_binary64
10×associate-/r/_binary64 sqrt-div_binary64
9×log-prod_binary64
8×pow1_binary64
5×flip3-+_binary64 div-inv_binary64 flip-+_binary64
4×associate-/l/_binary64 add-log-exp_binary64
3×cbrt-undiv_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 div-exp_binary64
2×flip3--_binary64 cbrt-unprod_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 flip--_binary64
1×pow-prod-down_binary64 rem-log-exp_binary64 sqrt-undiv_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 371
Calls

8 calls:

76.0ms
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x)) (log.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))
19.0ms
(log.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))
11.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
8.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
0.0ms
(sqrt.f64 (+.f64 1 x))

series128.0ms (0.1%)

Counts
4 → 24
Calls

4 calls:

44.0ms
(*.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x)) (log.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))
30.0ms
(log.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))
29.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
25.0ms
(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (+.f64 1 x))
Compiler

Compiled 664 to 598 computations (9.9% saved)

simplify153.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
395 → 395
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
056099560

localize10.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(atan.f64 (-.f64 1 x))
0.0b
(atan.f64 (-.f64 1 x))

rewrite2.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
1×*-un-lft-identity_binary64 add-log-exp_binary64 pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-sqr-sqrt_binary64
Counts
1 → 7
Calls

2 calls:

1.0ms
(atan.f64 (-.f64 1 x))
0.0ms
(atan.f64 (-.f64 1 x))

series10.0ms (0%)

Counts
1 → 3
Calls

1 calls:

10.0ms
(atan.f64 (-.f64 1 x))
Compiler

Compiled 48 to 48 computations (0% saved)

simplify165.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
10 → 10
Iterations

Useful iterations: 0 (158.0ms)

IterNodesCost
0474285
1474285

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(sqrt.f64 (-.f64 1 x))
0.0b
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
0.0b
(sqrt.f64 (/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))))
0.0b
(atan.f64 (sqrt.f64 (/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))))
0.0b
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
0.0b
(sqrt.f64 (-.f64 1 x))
0.0b
(sqrt.f64 (-.f64 1 x))
0.0b
(/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))

rewrite81.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
306×times-frac_binary64
302×*-un-lft-identity_binary64
212×add-sqr-sqrt_binary64
141×add-cube-cbrt_binary64
138×sqrt-prod_binary64
51×associate-/r*_binary64
46×distribute-lft-out_binary64 difference-of-squares_binary64
23×distribute-lft-out--_binary64
14×sqrt-div_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64 associate-/r/_binary64
7×flip3--_binary64 associate-/l*_binary64 flip--_binary64
6×pow1_binary64 div-inv_binary64
4×add-log-exp_binary64 cbrt-undiv_binary64 div-exp_binary64
2×associate-/l/_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64
1×flip3-+_binary64 flip-+_binary64
Counts
4 → 287
Calls

8 calls:

16.0ms
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
10.0ms
(/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))
4.0ms
(sqrt.f64 (-.f64 1 x))
4.0ms
(sqrt.f64 (-.f64 1 x))
0.0ms
(atan.f64 (sqrt.f64 (/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))))

series126.0ms (0.1%)

Counts
4 → 24
Calls

4 calls:

56.0ms
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
25.0ms
(/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))
25.0ms
(sqrt.f64 (-.f64 1 x))
19.0ms
(sqrt.f64 (-.f64 1 x))
Compiler

Compiled 674 to 593 computations (12% saved)

simplify147.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
311 → 311
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
053778058

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite570.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
1368×times-frac_binary64
1272×*-un-lft-identity_binary64
949×sqrt-prod_binary64
922×add-sqr-sqrt_binary64
534×add-cube-cbrt_binary64
299×associate-*l*_binary64
249×distribute-lft-out_binary64
160×difference-of-squares_binary64
80×distribute-lft-out--_binary64
69×associate-*r*_binary64
58×associate-/r*_binary64
40×sqrt-div_binary64
38×associate-/r/_binary64
35×unswap-sqr_binary64
34×add-exp-log_binary64 add-cbrt-cube_binary64
20×associate-/l*_binary64 div-inv_binary64
17×flip3--_binary64 flip--_binary64
14×cbrt-undiv_binary64 div-exp_binary64
6×associate-/l/_binary64 pow1_binary64 cbrt-unprod_binary64 prod-exp_binary64
4×flip3-+_binary64 add-log-exp_binary64 flip-+_binary64
3×clear-num_binary64 frac-2neg_binary64
1×pow-prod-down_binary64 associate-*r/_binary64 sqrt-undiv_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 948
Calls

8 calls:

303.0ms
(*.f64 (/.f64 (sqrt.f64 (+.f64 (sqrt.f64 1) x)) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))) (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
24.0ms
(/.f64 (sqrt.f64 (+.f64 (sqrt.f64 1) x)) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
11.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
10.0ms
(/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))
0.0ms
(sqrt.f64 (+.f64 (sqrt.f64 1) x))

series109.0ms (0.1%)

Counts
4 → 26
Calls

4 calls:

29.0ms
(/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))
29.0ms
(/.f64 (sqrt.f64 (+.f64 (sqrt.f64 1) x)) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x))))
26.0ms
(*.f64 (/.f64 (sqrt.f64 (+.f64 (sqrt.f64 1) x)) (/.f64 (+.f64 1 x) (sqrt.f64 (-.f64 1 x)))) (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
24.0ms
(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
Compiler

Compiled 702 to 632 computations (10% saved)

simplify339.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
974 → 974
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
0495929782
1495929782

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 x))) (fabs.f64 (cbrt.f64 (-.f64 1 x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (cbrt.f64 (-.f64 1 x))))))
0.0b
(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 x))) (fabs.f64 (cbrt.f64 (-.f64 1 x))))
0.0b
(sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 x))) (fabs.f64 (cbrt.f64 (-.f64 1 x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (cbrt.f64 (-.f64 1 x)))))))
0.0b
(atan.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 x))) (fabs.f64 (cbrt.f64 (-.f64 1 x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (cbrt.f64 (-.f64 1 x))))))))
0.0b
(sqrt.f64 (cbrt.f64 (-.f64 1 x)))
0.0b
(/.f64 (+.f64 1 x) (sqrt.f64 (cbrt.f64 (-.f64 1 x))))
0.0b
(cbrt.f64 (-.f64 1 x))
0.0b
(cbrt.f64 (-.f64 1 x))

rewrite42.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
86×*-un-lft-identity_binary64
62×add-sqr-sqrt_binary64
54×sqrt-prod_binary64
49×cbrt-prod_binary64
48×times-frac_binary64
36×add-cube-cbrt_binary64
16×difference-of-squares_binary64
13×distribute-lft-out_binary64
12×associate-/r*_binary64
8×cbrt-div_binary64 distribute-lft-out--_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
5×pow1_binary64
4×add-log-exp_binary64 flip3--_binary64 associate-/l*_binary64 flip--_binary64 sqrt-div_binary64
3×pow1/3_binary64
2×associate-/l/_binary64 associate-/r/_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
1×flip3-+_binary64 pow1/2_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 flip-+_binary64
Counts
4 → 135
Calls

8 calls:

11.0ms
(/.f64 (+.f64 1 x) (sqrt.f64 (cbrt.f64 (-.f64 1 x))))
5.0ms
(sqrt.f64 (cbrt.f64 (-.f64 1 x)))
4.0ms
(cbrt.f64 (-.f64 1 x))
4.0ms
(cbrt.f64 (-.f64 1 x))
0.0ms
(atan.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 x))) (fabs.f64 (cbrt.f64 (-.f64 1 x)))) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 x))) (/.f64 (+.f64 1 x) (sqrt.f64 (cbrt.f64 (-.f64 1 x))))))))

series166.0ms (0.1%)

Counts
4 → 25
Calls

4 calls:

43.0ms
(cbrt.f64 (-.f64 1 x))
42.0ms
(cbrt.f64 (-.f64 1 x))
41.0ms
(sqrt.f64 (cbrt.f64 (-.f64 1 x)))
39.0ms
(/.f64 (+.f64 1 x) (sqrt.f64 (cbrt.f64 (-.f64 1 x))))
Compiler

Compiled 1228 to 1081 computations (12% saved)

simplify111.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
049012948
149012948

prune1.4min (54.3%)

Pruning

500 alts after pruning (488 fresh and 12 done)

PrunedKeptTotal
New15922581850
Fresh108230338
Picked000
Done31215
Total17035002203
Error
0b
Counts
2203 → 500
Compiler

Compiled 31967 to 25925 computations (18.9% saved)

simplify1.4s (0.9%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
0837983627

regimes16.9s (11.2%)

Compiler

Compiled 239494 to 201635 computations (15.8% saved)

bsearch0.0ms (0%)

regimes4.6s (3%)

Compiler

Compiled 63773 to 53599 computations (16% saved)

bsearch0.0ms (0%)

regimes390.0ms (0.3%)

Compiler

Compiled 4382 to 3759 computations (14.2% saved)

bsearch0.0ms (0%)

regimes23.0ms (0%)

Compiler

Compiled 122 to 120 computations (1.6% saved)

bsearch0.0ms (0%)

regimes15.0ms (0%)

Compiler

Compiled 45 to 47 computations (-4.4% saved)

bsearch0.0ms (0%)

regimes12.0ms (0%)

Compiler

Compiled 33 to 37 computations (-12.1% saved)

bsearch0.0ms (0%)

regimes9.0ms (0%)

Compiler

Compiled 9 to 13 computations (-44.4% saved)

bsearch0.0ms (0%)

regimes10.0ms (0%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch7.0ms (0%)

Compiler

Compiled 90 to 80 computations (11.1% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
072139
172139

end0.0ms (0%)

sample1.8s (1.2%)

Algorithm
1×intervals
Results
389.0ms8000×body128valid
Compiler

Compiled 47867 to 40291 computations (15.8% saved)

Profiling

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