Details

Time bar (total: 38.3s)

analyze214.0ms (0.6%)

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

Compiled 8 to 7 computations (12.5% saved)

sample16.0ms (0%)

Algorithm
1×intervals
Results
8.0ms256×body128valid
Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify104.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01211
11211

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.5b
Counts
2 → 1
Compiler

Compiled 7 to 6 computations (14.3% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

rewrite18.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64
14×sqrt-prod_binary64
10×associate-*l*_binary64
8×*-un-lft-identity_binary64
6×associate-*r*_binary64
5×pow1_binary64 add-cube-cbrt_binary64
4×unswap-sqr_binary64
3×pow-prod-down_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 difference-of-squares_binary64 sqrt-div_binary64 associate-*l/_binary64
1×add-log-exp_binary64 flip3--_binary64 cbrt-unprod_binary64 difference-of-sqr-1_binary64 sqrt-unprod_binary64 prod-exp_binary64 distribute-lft-out--_binary64 flip--_binary64 *-commutative_binary64
Counts
1 → 36
Calls

2 calls:

13.0ms
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
0.0ms
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

series45.0ms (0.1%)

Counts
1 → 5
Calls

1 calls:

45.0ms
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 70 to 61 computations (12.9% saved)

simplify69.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
04977534
14977534

prune132.0ms (0.3%)

Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New172441
Fresh000
Picked000
Done011
Total172542
Error
0b
Counts
42 → 25
Compiler

Compiled 622 to 448 computations (28% saved)

localize5.0ms (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

localize2.0ms (0%)

rewrite0.0ms (0%)

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

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
0.5b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

rewrite14.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64
14×sqrt-prod_binary64
10×associate-*l*_binary64
8×*-un-lft-identity_binary64
6×associate-*r*_binary64
5×pow1_binary64 add-cube-cbrt_binary64
4×unswap-sqr_binary64
3×pow-prod-down_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 difference-of-squares_binary64 sqrt-div_binary64 associate-*l/_binary64
1×add-log-exp_binary64 flip3--_binary64 cbrt-unprod_binary64 difference-of-sqr-1_binary64 sqrt-unprod_binary64 prod-exp_binary64 distribute-lft-out--_binary64 flip--_binary64 *-commutative_binary64
Counts
1 → 36
Calls

2 calls:

11.0ms
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
0.0ms
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))

series29.0ms (0.1%)

Counts
1 → 5
Calls

1 calls:

29.0ms
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 86 to 77 computations (10.5% saved)

simplify68.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
04977534
14977534

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

31.9b
(sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (*.f64 x 1))))
19.9b
(sqrt.f64 (-.f64 (pow.f64 x 3) 1))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (pow.f64 x 3) 1)))
0.0b
(+.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (*.f64 x 1)))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (pow.f64 x 3) 1)))
19.9b
(sqrt.f64 (-.f64 (pow.f64 x 3) 1))
31.9b
(sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (*.f64 x 1))))
32.0b
(/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (pow.f64 x 3) 1))) (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (*.f64 x 1)))))

rewrite71.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
50×add-sqr-sqrt_binary64
48×sqrt-prod_binary64
26×*-un-lft-identity_binary64
19×associate-*r*_binary64
16×difference-of-squares_binary64
14×add-cube-cbrt_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
10×pow1_binary64 sqrt-div_binary64
8×difference-of-sqr-1_binary64
6×associate-/r*_binary64 sqr-pow_binary64 associate-*l*_binary64 unpow-prod-down_binary64 cube-prod_binary64 times-frac_binary64
4×add-log-exp_binary64 pow1/2_binary64 associate-*r/_binary64 sqrt-pow1_binary64 unswap-sqr_binary64
3×pow-prod-down_binary64 flip3--_binary64 flip--_binary64
2×flip3-+_binary64 associate-/l/_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 associate-/r/_binary64 sqrt-unprod_binary64 rem-sqrt-square_binary64 prod-exp_binary64 distribute-lft-out--_binary64 div-exp_binary64 flip-+_binary64
1×sqrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64 *-commutative_binary64
Counts
4 → 120
Calls

8 calls:

21.0ms
(/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (pow.f64 x 3) 1))) (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (*.f64 x 1)))))
21.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (pow.f64 x 3) 1)))
8.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (*.f64 x 1))))
8.0ms
(sqrt.f64 (-.f64 (pow.f64 x 3) 1))
0.0ms
(+.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (*.f64 x 1)))

series115.0ms (0.3%)

Counts
4 → 17
Calls

4 calls:

45.0ms
(/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (pow.f64 x 3) 1))) (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (*.f64 x 1)))))
32.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (pow.f64 x 3) 1)))
21.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 1 1) (*.f64 x 1))))
17.0ms
(sqrt.f64 (-.f64 (pow.f64 x 3) 1))
Compiler

Compiled 469 to 392 computations (16.4% saved)

simplify90.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
052202493

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1)))
0.3b
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1))) (*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1))))
0.1b
(sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1)))
0.1b
(sqrt.f64 (-.f64 (sqrt.f64 x) 1))
0.1b
(sqrt.f64 (-.f64 (sqrt.f64 x) 1))
0.1b
(sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1)))
0.3b
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1))) (*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1))))
0.4b
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1)))

rewrite62.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
51×sqrt-prod_binary64
40×add-sqr-sqrt_binary64
30×*-un-lft-identity_binary64
18×pow1_binary64 sqrt-div_binary64
15×associate-*r*_binary64
14×associate-*l*_binary64
12×add-cube-cbrt_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
10×pow-prod-down_binary64 associate-*r/_binary64
8×difference-of-squares_binary64
7×pow1/2_binary64 sqrt-pow1_binary64
5×flip3--_binary64 flip--_binary64
4×flip3-+_binary64 add-log-exp_binary64 cbrt-unprod_binary64 distribute-lft-out_binary64 difference-of-sqr-1_binary64 unswap-sqr_binary64 prod-exp_binary64 distribute-lft-out--_binary64 flip-+_binary64 frac-times_binary64
3×sqrt-unprod_binary64
2×rem-sqrt-square_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 114
Calls

8 calls:

24.0ms
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1))) (*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1))))
15.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1)))
6.0ms
(sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1)))
6.0ms
(sqrt.f64 (-.f64 (sqrt.f64 x) 1))
0.0ms
(sqrt.f64 (-.f64 (sqrt.f64 x) 1))

series120.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

47.0ms
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1))) (*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1))))
32.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1)))
20.0ms
(sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1)))
20.0ms
(sqrt.f64 (-.f64 (sqrt.f64 x) 1))
Compiler

Compiled 449 to 375 computations (16.5% saved)

simplify129.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (105.0ms)

IterNodesCost
049142037
149142037

prune3.3s (8.6%)

Pruning

168 alts after pruning (162 fresh and 6 done)

PrunedKeptTotal
New159145304
Fresh21719
Picked000
Done066
Total161168329
Error
0b
Counts
329 → 168
Compiler

Compiled 8027 to 5706 computations (28.9% saved)

localize6.0ms (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

localize2.0ms (0%)

rewrite0.0ms (0%)

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

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

21.9b
(sqrt.f64 (*.f64 x (-.f64 (sqrt.f64 x) 1)))
0.3b
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1))) (sqrt.f64 (*.f64 x (-.f64 (sqrt.f64 x) 1))))
0.2b
(*.f64 x (-.f64 (sqrt.f64 x) 1))
0.1b
(sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1)))
0.1b
(sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1)))
0.2b
(*.f64 x (-.f64 (sqrt.f64 x) 1))
0.3b
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1))) (sqrt.f64 (*.f64 x (-.f64 (sqrt.f64 x) 1))))
21.9b
(sqrt.f64 (*.f64 x (-.f64 (sqrt.f64 x) 1)))

rewrite50.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
25×*-un-lft-identity_binary64
21×sqrt-prod_binary64
17×pow1_binary64
16×sqrt-div_binary64
15×associate-*r*_binary64
12×associate-*r/_binary64 add-cube-cbrt_binary64
11×associate-*l*_binary64
8×add-exp-log_binary64 add-cbrt-cube_binary64
7×pow-prod-down_binary64 sqrt-pow1_binary64
6×cancel-sign-sub-inv_binary64
5×flip3--_binary64 flip--_binary64
4×flip3-+_binary64 add-log-exp_binary64 pow1/2_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 difference-of-squares_binary64 flip-+_binary64 frac-times_binary64
3×unswap-sqr_binary64
2×sub-neg_binary64 cbrt-unprod_binary64 difference-of-sqr-1_binary64 prod-exp_binary64 distribute-lft-out--_binary64 associate-*l/_binary64 *-commutative_binary64
1×sqrt-unprod_binary64 rem-sqrt-square_binary64
Counts
4 → 103
Calls

8 calls:

17.0ms
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1))) (sqrt.f64 (*.f64 x (-.f64 (sqrt.f64 x) 1))))
10.0ms
(*.f64 x (-.f64 (sqrt.f64 x) 1))
6.0ms
(sqrt.f64 (*.f64 x (-.f64 (sqrt.f64 x) 1)))
6.0ms
(sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1)))
0.0ms
(sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1)))

series116.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

54.0ms
(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1))) (sqrt.f64 (*.f64 x (-.f64 (sqrt.f64 x) 1))))
27.0ms
(sqrt.f64 (*.f64 x (-.f64 (sqrt.f64 x) 1)))
18.0ms
(sqrt.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 1)))
18.0ms
(*.f64 x (-.f64 (sqrt.f64 x) 1))
Compiler

Compiled 449 to 376 computations (16.3% saved)

simplify101.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
058651689

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite50.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
94×cbrt-prod_binary64
76×add-sqr-sqrt_binary64
65×sqrt-prod_binary64
51×*-un-lft-identity_binary64
22×add-cube-cbrt_binary64
19×swap-sqr_binary64
18×cbrt-div_binary64 sqrt-div_binary64
16×difference-of-squares_binary64
13×associate-*r*_binary64 associate-*l*_binary64
11×pow1_binary64
9×flip3--_binary64 pow1/3_binary64 difference-of-sqr-1_binary64 unswap-sqr_binary64 distribute-lft-out--_binary64 flip--_binary64
6×add-exp-log_binary64
4×add-log-exp_binary64 add-cbrt-cube_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 → 140
Calls

8 calls:

19.0ms
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 x 1))) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))
5.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
5.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
5.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
0.0ms
(*.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))

series177.0ms (0.5%)

Counts
4 → 20
Calls

4 calls:

50.0ms
(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 x 1))) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))
45.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
41.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
40.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
Compiler

Compiled 894 to 778 computations (13% saved)

simplify119.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (87.0ms)

IterNodesCost
048422775
148422775

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))))
0.3b
(*.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1)))) (*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1))))
0.2b
(sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1)))
0.1b
(sqrt.f64 (-.f64 (sqrt.f64 x) 1))
0.3b
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))))
0.4b
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1)))
0.5b
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))
0.5b
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))

rewrite50.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64
35×sqrt-prod_binary64
28×*-un-lft-identity_binary64
25×associate-*r*_binary64
16×cbrt-prod_binary64
14×add-cube-cbrt_binary64
10×pow1_binary64
9×associate-*l*_binary64
8×add-exp-log_binary64 add-cbrt-cube_binary64
7×unswap-sqr_binary64
6×cbrt-div_binary64 distribute-lft-out_binary64
4×pow-prod-down_binary64 add-log-exp_binary64 associate-*r/_binary64 difference-of-squares_binary64 sqrt-div_binary64
3×flip3-+_binary64 flip-+_binary64
2×pow1/2_binary64 cbrt-unprod_binary64 pow1/3_binary64 difference-of-sqr-1_binary64 sqrt-pow1_binary64 prod-exp_binary64 distribute-lft-out--_binary64 *-commutative_binary64
1×flip3--_binary64 sqrt-unprod_binary64 flip--_binary64
Counts
4 → 100
Calls

8 calls:

17.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1)))
11.0ms
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))))
5.0ms
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))
5.0ms
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))
0.0ms
(sqrt.f64 (-.f64 (sqrt.f64 x) 1))

series149.0ms (0.4%)

Counts
4 → 12
Calls

4 calls:

52.0ms
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))))
38.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1)))
29.0ms
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))
29.0ms
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))
Compiler

Compiled 692 to 559 computations (19.2% saved)

simplify53.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
050421865

prune7.3s (19%)

Pruning

319 alts after pruning (308 fresh and 11 done)

PrunedKeptTotal
New232155387
Fresh4153157
Picked000
Done01111
Total236319555
Error
0b
Counts
555 → 319
Compiler

Compiled 13669 to 10067 computations (26.4% saved)

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

localize4.0ms (0%)

Local error

Found 4 expressions with local error:

31.9b
(sqrt.f64 (*.f64 x (-.f64 x 1)))
0.0b
(*.f64 x (-.f64 x 1))
0.0b
(*.f64 x (-.f64 x 1))
31.9b
(sqrt.f64 (*.f64 x (-.f64 x 1)))

rewrite16.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64
9×*-un-lft-identity_binary64
7×pow1_binary64 associate-*r*_binary64
6×add-cube-cbrt_binary64 cancel-sign-sub-inv_binary64
4×associate-*r/_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64
3×associate-*l*_binary64
2×pow-prod-down_binary64 add-log-exp_binary64 sub-neg_binary64 flip3--_binary64 sqrt-pow1_binary64 difference-of-squares_binary64 flip--_binary64 sqrt-div_binary64
1×pow1/2_binary64 cbrt-unprod_binary64 difference-of-sqr-1_binary64 unswap-sqr_binary64 prod-exp_binary64 distribute-lft-out--_binary64 sqrt-prod_binary64 *-commutative_binary64
Counts
2 → 45
Calls

4 calls:

8.0ms
(*.f64 x (-.f64 x 1))
5.0ms
(sqrt.f64 (*.f64 x (-.f64 x 1)))
0.0ms
(*.f64 x (-.f64 x 1))
0.0ms
(sqrt.f64 (*.f64 x (-.f64 x 1)))

series56.0ms (0.1%)

Counts
2 → 11
Calls

2 calls:

34.0ms
(*.f64 x (-.f64 x 1))
21.0ms
(sqrt.f64 (*.f64 x (-.f64 x 1)))
Compiler

Compiled 104 to 91 computations (12.5% saved)

simplify72.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
04941460
14941460

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
0.5b
(*.f64 (pow.f64 x 1/6) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))
0.3b
(*.f64 (*.f64 (pow.f64 x 1/6) (cbrt.f64 (sqrt.f64 (-.f64 x 1)))) (*.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 (-.f64 x 1)))))
0.3b
(*.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))
0.5b
(*.f64 (pow.f64 x 1/6) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))
0.5b
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
0.5b
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
4.2b
(pow.f64 x 1/6)

rewrite38.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64
36×cbrt-prod_binary64
24×*-un-lft-identity_binary64 sqrt-prod_binary64
15×add-cube-cbrt_binary64
13×associate-*r*_binary64
10×add-exp-log_binary64
9×unswap-sqr_binary64 unpow-prod-down_binary64
7×associate-*l*_binary64
6×cbrt-div_binary64 difference-of-squares_binary64 sqrt-div_binary64
5×pow1_binary64 sqr-pow_binary64 add-cbrt-cube_binary64
4×add-log-exp_binary64
3×pow-unpow_binary64 flip3--_binary64 difference-of-sqr-1_binary64 prod-exp_binary64 distribute-lft-out--_binary64 flip--_binary64
2×pow-to-exp_binary64 associate-*r/_binary64 pow1/3_binary64 pow-exp_binary64
1×cbrt-unprod_binary64 pow-pow_binary64 *-commutative_binary64
Counts
4 → 100
Calls

8 calls:

13.0ms
(*.f64 (pow.f64 x 1/6) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))
4.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
4.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
2.0ms
(pow.f64 x 1/6)
0.0ms
(*.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))

series185.0ms (0.5%)

Counts
4 → 15
Calls

4 calls:

77.0ms
(pow.f64 x 1/6)
46.0ms
(*.f64 (pow.f64 x 1/6) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))
32.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
30.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
Compiler

Compiled 665 to 571 computations (14.1% saved)

simplify85.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
050511681

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite46.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
40×cbrt-prod_binary64
29×add-sqr-sqrt_binary64
28×sqrt-prod_binary64
25×*-un-lft-identity_binary64
18×cbrt-div_binary64 sqrt-div_binary64
13×associate-*r*_binary64 add-cube-cbrt_binary64
9×pow1_binary64 flip3--_binary64 add-exp-log_binary64 flip--_binary64
8×difference-of-squares_binary64 associate-*l/_binary64
6×pow1/3_binary64
5×pow-prod-down_binary64 add-cbrt-cube_binary64
4×add-log-exp_binary64 difference-of-sqr-1_binary64 distribute-lft-out--_binary64 frac-times_binary64
3×cbrt-unprod_binary64 prod-exp_binary64
2×associate-*r/_binary64
1×associate-*l*_binary64 *-commutative_binary64
Counts
4 → 97
Calls

8 calls:

20.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 x 1))) (cbrt.f64 1)) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))
5.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
5.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
5.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
0.0ms
(*.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))

series172.0ms (0.4%)

Counts
4 → 20
Calls

4 calls:

45.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
45.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 x 1))) (cbrt.f64 1)) (cbrt.f64 (sqrt.f64 (-.f64 x 1))))
41.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
40.0ms
(cbrt.f64 (sqrt.f64 (-.f64 x 1)))
Compiler

Compiled 966 to 850 computations (12% saved)

simplify87.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
054091763

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))) (sqrt.f64 (cbrt.f64 1))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))))
0.3b
(*.f64 (*.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))) (sqrt.f64 (cbrt.f64 1))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1)))) (*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1))))
0.2b
(sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1)))
0.1b
(sqrt.f64 (-.f64 (sqrt.f64 x) 1))
0.3b
(*.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))) (sqrt.f64 (cbrt.f64 1))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))))
0.4b
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1)))
0.5b
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))
0.5b
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))

rewrite52.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64 sqrt-prod_binary64
27×*-un-lft-identity_binary64
25×associate-*r*_binary64
15×cbrt-prod_binary64
13×pow1_binary64 add-cube-cbrt_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
7×associate-*l*_binary64
6×cbrt-div_binary64 pow-prod-down_binary64 distribute-lft-out_binary64
4×add-log-exp_binary64 cbrt-unprod_binary64 associate-*r/_binary64 unswap-sqr_binary64 prod-exp_binary64 difference-of-squares_binary64 sqrt-div_binary64
3×flip3-+_binary64 flip-+_binary64
2×pow1/2_binary64 pow1/3_binary64 difference-of-sqr-1_binary64 sqrt-pow1_binary64 distribute-lft-out--_binary64 *-commutative_binary64
1×flip3--_binary64 sqrt-unprod_binary64 flip--_binary64
Counts
4 → 98
Calls

8 calls:

15.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1)))
15.0ms
(*.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))) (sqrt.f64 (cbrt.f64 1))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))))
5.0ms
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))
5.0ms
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))
0.0ms
(sqrt.f64 (-.f64 (sqrt.f64 x) 1))

series154.0ms (0.4%)

Counts
4 → 12
Calls

4 calls:

52.0ms
(*.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))) (sqrt.f64 (cbrt.f64 1))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 x) 1))))
35.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (sqrt.f64 x) 1)))
35.0ms
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))
31.0ms
(cbrt.f64 (+.f64 (sqrt.f64 x) 1))
Compiler

Compiled 764 to 631 computations (17.4% saved)

simplify56.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
051391889

prune9.8s (25.7%)

Pruning

456 alts after pruning (440 fresh and 16 done)

PrunedKeptTotal
New255143398
Fresh6297303
Picked000
Done01616
Total261456717
Error
0b
Counts
717 → 456
Compiler

Compiled 6797 to 5001 computations (26.4% saved)

simplify425.0ms (1.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
0255925556
1255925556

regimes1.4s (3.7%)

Compiler

Compiled 12436 to 9705 computations (22% saved)

bsearch0.0ms (0%)

regimes14.0ms (0%)

Compiler

Compiled 11 to 14 computations (-27.3% saved)

bsearch0.0ms (0%)

regimes9.0ms (0%)

Accuracy

Total 0.4b remaining (100%)

Threshold costs 0.4b (100%)

Compiler

Compiled 8 to 11 computations (-37.5% saved)

bsearch2.0ms (0%)

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03315
13315

end0.0ms (0%)

sample12.6s (33%)

Algorithm
1×intervals
Results
239.0ms8000×body128valid
0.0ms6×body128nan
Compiler

Compiled 12475 to 9741 computations (21.9% saved)

Pareto

0.42860463674114596

Profiling

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