Details

Time bar (total: 1.8min)

analyze236.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
25%74.9%0.1%4
37.5%62.4%0.1%5
62.4%37.5%0.1%6
87.4%12.5%0.1%7
87.4%12.5%0.1%8
93.7%6.2%0.1%9
93.7%6.2%0.1%10
96.8%3.1%0.1%11
96.8%3.1%0.1%12
98.3%1.6%0.1%13
98.3%1.6%0.1%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample17.0ms (0%)

Algorithm
1×intervals
Results
7.0ms256×body128valid
Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify169.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
078210
178210

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 (+.f64 f n) (-.f64 n f))
0.0b
(/.f64 (+.f64 f n) (-.f64 n f))

rewrite15.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
34×*-un-lft-identity_binary64
22×add-sqr-sqrt_binary64
20×times-frac_binary64
12×add-cube-cbrt_binary64
6×distribute-lft-out_binary64
5×associate-/r*_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
4×associate-/l*_binary64
3×add-exp-log_binary64 add-cbrt-cube_binary64
2×associate-/l/_binary64 associate-/r/_binary64
1×flip3-+_binary64 add-log-exp_binary64 pow1_binary64 flip3--_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 flip--_binary64 flip-+_binary64
Counts
1 → 45
Calls

2 calls:

10.0ms
(/.f64 (+.f64 f n) (-.f64 n f))
0.0ms
(/.f64 (+.f64 f n) (-.f64 n f))

series97.0ms (0.1%)

Counts
1 → 21
Calls

1 calls:

96.0ms
(/.f64 (+.f64 f n) (-.f64 n f))
Compiler

Compiled 321 to 297 computations (7.5% saved)

simplify66.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
055911063

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))
0.0b
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))

rewrite18.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
82×*-un-lft-identity_binary64
60×times-frac_binary64
58×add-sqr-sqrt_binary64
32×add-cube-cbrt_binary64
24×distribute-lft-neg-in_binary64 distribute-rgt-neg-in_binary64
13×difference-of-squares_binary64 distribute-lft-out--_binary64
12×distribute-lft-out_binary64 associate-/l*_binary64
6×neg-mul-1_binary64
5×associate-/r*_binary64
3×add-exp-log_binary64 add-cbrt-cube_binary64
2×associate-/l/_binary64 distribute-neg-frac_binary64 associate-/r/_binary64
1×flip3-+_binary64 add-log-exp_binary64 pow1_binary64 flip3--_binary64 neg-sub0_binary64 cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 distribute-frac-neg_binary64 flip--_binary64 flip-+_binary64
Counts
1 → 95
Calls

2 calls:

10.0ms
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))
0.0ms
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))

series90.0ms (0.1%)

Counts
1 → 21
Calls

1 calls:

90.0ms
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))
Compiler

Compiled 321 to 297 computations (7.5% saved)

simplify85.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049382291
149382291

prune674.0ms (0.6%)

Pruning

71 alts after pruning (69 fresh and 2 done)

PrunedKeptTotal
New11369182
Fresh000
Picked000
Done022
Total11371184
Error
0b
Counts
184 → 71
Compiler

Compiled 2718 to 969 computations (64.3% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 (+.f64 f n) (-.f64 n f))
0.0b
(/.f64 (+.f64 f n) (-.f64 n f))

rewrite14.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
34×*-un-lft-identity_binary64
22×add-sqr-sqrt_binary64
20×times-frac_binary64
12×add-cube-cbrt_binary64
6×distribute-lft-out_binary64
5×associate-/r*_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
4×associate-/l*_binary64
3×add-exp-log_binary64 add-cbrt-cube_binary64
2×associate-/l/_binary64 associate-/r/_binary64
1×flip3-+_binary64 add-log-exp_binary64 pow1_binary64 flip3--_binary64 cbrt-undiv_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 flip--_binary64 flip-+_binary64
Counts
1 → 45
Calls

2 calls:

10.0ms
(/.f64 (+.f64 f n) (-.f64 n f))
0.0ms
(/.f64 (+.f64 f n) (-.f64 n f))

series81.0ms (0.1%)

Counts
1 → 21
Calls

1 calls:

81.0ms
(/.f64 (+.f64 f n) (-.f64 n f))
Compiler

Compiled 369 to 345 computations (6.5% saved)

simplify64.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
055911063

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 2 (/.f64 f n))
0.0b
(*.f64 2 (/.f64 f n))

rewrite10.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
9×*-un-lft-identity_binary64 add-cube-cbrt_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
3×pow1_binary64 associate-*l*_binary64
2×cbrt-unprod_binary64 unswap-sqr_binary64 prod-exp_binary64
1×pow-prod-down_binary64 add-log-exp_binary64 cbrt-undiv_binary64 associate-*r/_binary64 div-inv_binary64 div-exp_binary64 *-commutative_binary64
Counts
1 → 32
Calls

2 calls:

7.0ms
(*.f64 2 (/.f64 f n))
0.0ms
(*.f64 2 (/.f64 f n))

series55.0ms (0.1%)

Counts
1 → 6
Calls

1 calls:

55.0ms
(*.f64 2 (/.f64 f n))
Compiler

Compiled 84 to 84 computations (0% saved)

simplify84.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
04974369
14974369

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (-.f64 n f) (sqrt.f64 (+.f64 f n)))
0.0b
(/.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 f n))))
0.0b
(/.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 f n))))
0.3b
(/.f64 (-.f64 n f) (sqrt.f64 (+.f64 f n)))

rewrite102.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
602×times-frac_binary64
554×*-un-lft-identity_binary64
378×add-sqr-sqrt_binary64
352×sqrt-prod_binary64
250×add-cube-cbrt_binary64
88×distribute-lft-out_binary64
64×difference-of-squares_binary64 distribute-lft-out--_binary64
48×associate-/r*_binary64
20×sqrt-div_binary64
19×associate-/r/_binary64
12×associate-/l*_binary64
10×flip3-+_binary64 div-inv_binary64 flip-+_binary64
9×add-exp-log_binary64 add-cbrt-cube_binary64
4×associate-/l/_binary64 cbrt-undiv_binary64 div-exp_binary64
2×add-log-exp_binary64 pow1_binary64 clear-num_binary64 frac-2neg_binary64
1×flip3--_binary64 div-sub_binary64 flip--_binary64
Counts
2 → 416
Calls

4 calls:

26.0ms
(/.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 f n))))
9.0ms
(/.f64 (-.f64 n f) (sqrt.f64 (+.f64 f n)))
0.0ms
(/.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 f n))))
0.0ms
(/.f64 (-.f64 n f) (sqrt.f64 (+.f64 f n)))

series147.0ms (0.1%)

Counts
2 → 31
Calls

2 calls:

84.0ms
(/.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (-.f64 n f) (sqrt.f64 (+.f64 f n))))
63.0ms
(/.f64 (-.f64 n f) (sqrt.f64 (+.f64 f n)))
Compiler

Compiled 562 to 499 computations (11.2% saved)

simplify194.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
447 → 447
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
0539613597

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(cbrt.f64 (+.f64 f n))
0.5b
(cbrt.f64 (+.f64 f n))
0.3b
(/.f64 (-.f64 n f) (cbrt.f64 (+.f64 f n)))
0.0b
(/.f64 (*.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n))) (/.f64 (-.f64 n f) (cbrt.f64 (+.f64 f n))))
0.5b
(cbrt.f64 (+.f64 f n))
0.5b
(cbrt.f64 (+.f64 f n))
0.5b
(cbrt.f64 (+.f64 f n))
0.6b
(*.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n)))

rewrite30.0ms (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:

12.0ms
(*.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n)))
3.0ms
(cbrt.f64 (+.f64 f n))
3.0ms
(cbrt.f64 (+.f64 f n))
3.0ms
(cbrt.f64 (+.f64 f n))
0.0ms
(/.f64 (*.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n))) (/.f64 (-.f64 n f) (cbrt.f64 (+.f64 f n))))

series489.0ms (0.5%)

Counts
4 → 51
Calls

4 calls:

157.0ms
(*.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n)))
111.0ms
(cbrt.f64 (+.f64 f n))
111.0ms
(cbrt.f64 (+.f64 f n))
110.0ms
(cbrt.f64 (+.f64 f n))
Compiler

Compiled 2412 to 1791 computations (25.7% saved)

simplify117.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
049092073
149092073

localize13.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 (/.f64 (sqrt.f64 (+.f64 f n)) (sqrt.f64 (-.f64 f n))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))))
0.0b
(*.f64 (/.f64 (sqrt.f64 (+.f64 f n)) (sqrt.f64 (-.f64 f n))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))))

rewrite206.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
238×sqrt-prod_binary64
222×times-frac_binary64
211×add-sqr-sqrt_binary64
207×*-un-lft-identity_binary64
150×associate-*r*_binary64
109×add-cube-cbrt_binary64
62×associate-*l*_binary64
56×distribute-lft-neg-in_binary64 distribute-rgt-neg-in_binary64
25×difference-of-squares_binary64 distribute-lft-out--_binary64
24×distribute-lft-out_binary64
15×unswap-sqr_binary64
13×add-exp-log_binary64 add-cbrt-cube_binary64
8×neg-mul-1_binary64
4×cbrt-unprod_binary64 cbrt-undiv_binary64 associate-/r/_binary64 prod-exp_binary64 div-exp_binary64 sqrt-div_binary64
3×pow1_binary64
2×flip3--_binary64 div-inv_binary64 flip--_binary64
1×pow-prod-down_binary64 add-log-exp_binary64 distribute-rgt-neg-out_binary64 associate-*r/_binary64 distribute-frac-neg_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
1 → 248
Calls

2 calls:

163.0ms
(*.f64 (/.f64 (sqrt.f64 (+.f64 f n)) (sqrt.f64 (-.f64 f n))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))))
0.0ms
(*.f64 (/.f64 (sqrt.f64 (+.f64 f n)) (sqrt.f64 (-.f64 f n))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))))

series88.0ms (0.1%)

Counts
1 → 19
Calls

1 calls:

88.0ms
(*.f64 (/.f64 (sqrt.f64 (+.f64 f n)) (sqrt.f64 (-.f64 f n))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))))
Compiler

Compiled 289 to 269 computations (6.9% saved)

simplify121.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
267 → 267
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
055698011

prune9.5s (8.8%)

Pruning

330 alts after pruning (323 fresh and 7 done)

PrunedKeptTotal
New692272964
Fresh135164
Picked000
Done077
Total7053301035
Error
0b
Counts
1035 → 330
Compiler

Compiled 17777 to 5975 computations (66.4% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))
0.0b
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))

rewrite19.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
82×*-un-lft-identity_binary64
60×times-frac_binary64
58×add-sqr-sqrt_binary64
32×add-cube-cbrt_binary64
24×distribute-lft-neg-in_binary64 distribute-rgt-neg-in_binary64
13×difference-of-squares_binary64 distribute-lft-out--_binary64
12×distribute-lft-out_binary64 associate-/l*_binary64
6×neg-mul-1_binary64
5×associate-/r*_binary64
3×add-exp-log_binary64 add-cbrt-cube_binary64
2×associate-/l/_binary64 distribute-neg-frac_binary64 associate-/r/_binary64
1×flip3-+_binary64 add-log-exp_binary64 pow1_binary64 flip3--_binary64 neg-sub0_binary64 cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 distribute-frac-neg_binary64 flip--_binary64 flip-+_binary64
Counts
1 → 95
Calls

2 calls:

10.0ms
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))
0.0ms
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))

series96.0ms (0.1%)

Counts
1 → 21
Calls

1 calls:

96.0ms
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))
Compiler

Compiled 369 to 345 computations (6.5% saved)

simplify89.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049382291
149382291

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 2 (/.f64 n f))
0.0b
(*.f64 2 (/.f64 n f))

rewrite11.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
9×*-un-lft-identity_binary64 add-cube-cbrt_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
3×pow1_binary64 associate-*l*_binary64
2×cbrt-unprod_binary64 unswap-sqr_binary64 prod-exp_binary64
1×pow-prod-down_binary64 add-log-exp_binary64 cbrt-undiv_binary64 associate-*r/_binary64 div-inv_binary64 div-exp_binary64 *-commutative_binary64
Counts
1 → 32
Calls

2 calls:

8.0ms
(*.f64 2 (/.f64 n f))
0.0ms
(*.f64 2 (/.f64 n f))

series56.0ms (0.1%)

Counts
1 → 6
Calls

1 calls:

56.0ms
(*.f64 2 (/.f64 n f))
Compiler

Compiled 84 to 84 computations (0% saved)

simplify89.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
04974369
14974369

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(cbrt.f64 (+.f64 f n))
0.5b
(cbrt.f64 (+.f64 f n))
0.3b
(/.f64 (cbrt.f64 (+.f64 f n)) (-.f64 f n))
0.3b
(*.f64 (*.f64 (cbrt.f64 (+.f64 f n)) (neg.f64 (cbrt.f64 (+.f64 f n)))) (/.f64 (cbrt.f64 (+.f64 f n)) (-.f64 f n)))
0.5b
(cbrt.f64 (+.f64 f n))
0.5b
(cbrt.f64 (+.f64 f n))
0.5b
(cbrt.f64 (+.f64 f n))
0.6b
(*.f64 (cbrt.f64 (+.f64 f n)) (neg.f64 (cbrt.f64 (+.f64 f n))))

rewrite32.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
26×*-un-lft-identity_binary64
25×cbrt-prod_binary64
18×cbrt-div_binary64 associate-*r*_binary64 add-sqr-sqrt_binary64
14×add-cube-cbrt_binary64
9×flip3-+_binary64 flip-+_binary64
7×distribute-lft-neg-in_binary64 associate-*l*_binary64 distribute-rgt-neg-in_binary64
6×pow1_binary64 distribute-lft-out_binary64 add-exp-log_binary64 distribute-neg-frac_binary64
5×add-cbrt-cube_binary64
4×add-log-exp_binary64 frac-times_binary64
3×pow1/3_binary64
2×associate-*r/_binary64 unswap-sqr_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 cbrt-unprod_binary64 distribute-rgt-neg-out_binary64 neg-mul-1_binary64 prod-exp_binary64 *-commutative_binary64
Counts
4 → 89
Calls

8 calls:

15.0ms
(*.f64 (cbrt.f64 (+.f64 f n)) (neg.f64 (cbrt.f64 (+.f64 f n))))
3.0ms
(cbrt.f64 (+.f64 f n))
3.0ms
(cbrt.f64 (+.f64 f n))
3.0ms
(cbrt.f64 (+.f64 f n))
0.0ms
(*.f64 (*.f64 (cbrt.f64 (+.f64 f n)) (neg.f64 (cbrt.f64 (+.f64 f n)))) (/.f64 (cbrt.f64 (+.f64 f n)) (-.f64 f n)))

series525.0ms (0.5%)

Counts
4 → 51
Calls

4 calls:

189.0ms
(*.f64 (cbrt.f64 (+.f64 f n)) (neg.f64 (cbrt.f64 (+.f64 f n))))
116.0ms
(cbrt.f64 (+.f64 f n))
113.0ms
(cbrt.f64 (+.f64 f n))
107.0ms
(cbrt.f64 (+.f64 f n))
Compiler

Compiled 2484 to 1863 computations (25% saved)

simplify90.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
048792186
148792186

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 (/.f64 (neg.f64 (cbrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))) (cbrt.f64 (+.f64 f n)))
0.2b
(/.f64 (cbrt.f64 (+.f64 f n)) (sqrt.f64 (-.f64 f n)))
0.2b
(/.f64 (neg.f64 (cbrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n)))
0.1b
(*.f64 (*.f64 (/.f64 (neg.f64 (cbrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))) (cbrt.f64 (+.f64 f n))) (/.f64 (cbrt.f64 (+.f64 f n)) (sqrt.f64 (-.f64 f n))))
0.2b
(*.f64 (/.f64 (neg.f64 (cbrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))) (cbrt.f64 (+.f64 f n)))
0.5b
(cbrt.f64 (+.f64 f n))
0.5b
(cbrt.f64 (+.f64 f n))
0.5b
(cbrt.f64 (+.f64 f n))

rewrite95.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
162×*-un-lft-identity_binary64
150×associate-*l*_binary64
148×times-frac_binary64
138×add-sqr-sqrt_binary64
92×sqrt-prod_binary64
86×add-cube-cbrt_binary64
83×cbrt-prod_binary64
56×distribute-lft-neg-in_binary64 distribute-rgt-neg-in_binary64
20×distribute-lft-out_binary64
18×difference-of-squares_binary64 distribute-lft-out--_binary64
10×cbrt-div_binary64
9×add-exp-log_binary64
8×neg-mul-1_binary64
7×associate-*r*_binary64 add-cbrt-cube_binary64
6×pow1_binary64 unswap-sqr_binary64
5×flip3-+_binary64 flip-+_binary64
4×add-log-exp_binary64
3×pow1/3_binary64
2×cbrt-unprod_binary64 associate-*r/_binary64 associate-/r/_binary64 prod-exp_binary64 frac-times_binary64 sqrt-div_binary64
1×pow-prod-down_binary64 flip3--_binary64 cbrt-undiv_binary64 distribute-lft-neg-out_binary64 div-inv_binary64 div-exp_binary64 distribute-frac-neg_binary64 flip--_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 224
Calls

8 calls:

51.0ms
(*.f64 (/.f64 (neg.f64 (cbrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))) (cbrt.f64 (+.f64 f n)))
4.0ms
(cbrt.f64 (+.f64 f n))
3.0ms
(cbrt.f64 (+.f64 f n))
3.0ms
(cbrt.f64 (+.f64 f n))
0.0ms
(*.f64 (*.f64 (/.f64 (neg.f64 (cbrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))) (cbrt.f64 (+.f64 f n))) (/.f64 (cbrt.f64 (+.f64 f n)) (sqrt.f64 (-.f64 f n))))

series375.0ms (0.3%)

Counts
4 → 30
Calls

4 calls:

151.0ms
(*.f64 (/.f64 (neg.f64 (cbrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 f n))) (cbrt.f64 (+.f64 f n)))
78.0ms
(cbrt.f64 (+.f64 f n))
74.0ms
(cbrt.f64 (+.f64 f n))
71.0ms
(cbrt.f64 (+.f64 f n))
Compiler

Compiled 1855 to 1261 computations (32% saved)

simplify103.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
254 → 254
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
050465623

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(/.f64 (cbrt.f64 (-.f64 n f)) (sqrt.f64 (cbrt.f64 (+.f64 n f))))
0.2b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f))) (fabs.f64 (cbrt.f64 (+.f64 n f)))) (/.f64 (cbrt.f64 (-.f64 n f)) (sqrt.f64 (cbrt.f64 (+.f64 n f)))))
0.1b
(sqrt.f64 (cbrt.f64 (+.f64 n f)))
0.0b
(/.f64 (sqrt.f64 (+.f64 f n)) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f))) (fabs.f64 (cbrt.f64 (+.f64 n f)))) (/.f64 (cbrt.f64 (-.f64 n f)) (sqrt.f64 (cbrt.f64 (+.f64 n f))))))
0.5b
(cbrt.f64 (-.f64 n f))
0.5b
(cbrt.f64 (-.f64 n f))
0.5b
(/.f64 (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f))) (fabs.f64 (cbrt.f64 (+.f64 n f))))
0.6b
(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))

rewrite52.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
38×cbrt-prod_binary64
36×add-sqr-sqrt_binary64
34×*-un-lft-identity_binary64
28×cbrt-div_binary64
16×add-cube-cbrt_binary64
14×flip3--_binary64 flip--_binary64
11×pow1_binary64 add-exp-log_binary64
10×swap-sqr_binary64
8×associate-/l/_binary64 associate-*r*_binary64 pow1/3_binary64 associate-*l*_binary64 distribute-lft-out--_binary64 frac-times_binary64
7×add-cbrt-cube_binary64
6×difference-of-squares_binary64
4×add-log-exp_binary64 associate-*r/_binary64 unswap-sqr_binary64 associate-*l/_binary64
3×associate-/r*_binary64 times-frac_binary64
2×pow-prod-down_binary64 cbrt-unprod_binary64 pow-prod-up_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64 pow-sqr_binary64
1×pow-plus_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 115
Calls

8 calls:

17.0ms
(/.f64 (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f))) (fabs.f64 (cbrt.f64 (+.f64 n f))))
13.0ms
(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))
4.0ms
(cbrt.f64 (-.f64 n f))
3.0ms
(cbrt.f64 (-.f64 n f))
0.0ms
(/.f64 (sqrt.f64 (+.f64 f n)) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f))) (fabs.f64 (cbrt.f64 (+.f64 n f)))) (/.f64 (cbrt.f64 (-.f64 n f)) (sqrt.f64 (cbrt.f64 (+.f64 n f))))))

series717.0ms (0.7%)

Counts
4 → 50
Calls

4 calls:

310.0ms
(/.f64 (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f))) (fabs.f64 (cbrt.f64 (+.f64 n f))))
190.0ms
(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))
110.0ms
(cbrt.f64 (-.f64 n f))
107.0ms
(cbrt.f64 (-.f64 n f))
Compiler

Compiled 3562 to 2534 computations (28.9% saved)

simplify80.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
050143253

prune22.1s (20.4%)

Pruning

558 alts after pruning (546 fresh and 12 done)

PrunedKeptTotal
New462251713
Fresh23295318
Picked000
Done01212
Total4855581043
Error
0b
Counts
1043 → 558
Compiler

Compiled 30225 to 10916 computations (63.9% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))
0.0b
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))

rewrite19.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
82×*-un-lft-identity_binary64
60×times-frac_binary64
58×add-sqr-sqrt_binary64
32×add-cube-cbrt_binary64
24×distribute-lft-neg-in_binary64 distribute-rgt-neg-in_binary64
13×difference-of-squares_binary64 distribute-lft-out--_binary64
12×distribute-lft-out_binary64 associate-/l*_binary64
6×neg-mul-1_binary64
5×associate-/r*_binary64
3×add-exp-log_binary64 add-cbrt-cube_binary64
2×associate-/l/_binary64 distribute-neg-frac_binary64 associate-/r/_binary64
1×flip3-+_binary64 add-log-exp_binary64 pow1_binary64 flip3--_binary64 neg-sub0_binary64 cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 distribute-frac-neg_binary64 flip--_binary64 flip-+_binary64
Counts
1 → 95
Calls

2 calls:

10.0ms
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))
0.0ms
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))

series92.0ms (0.1%)

Counts
1 → 21
Calls

1 calls:

91.0ms
(/.f64 (neg.f64 (+.f64 f n)) (-.f64 f n))
Compiler

Compiled 369 to 345 computations (6.5% saved)

simplify88.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049382291
149382291

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b
(*.f64 (+.f64 f f) (/.f64 1 n))
0.2b
(*.f64 (+.f64 f f) (/.f64 1 n))

rewrite17.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
13×associate-*r*_binary64 add-cube-cbrt_binary64
12×associate-*l*_binary64
11×times-frac_binary64
10×add-exp-log_binary64
6×add-cbrt-cube_binary64
4×prod-exp_binary64
3×pow1_binary64 distribute-lft-out_binary64 distribute-rgt-out_binary64 unswap-sqr_binary64
2×flip3-+_binary64 cbrt-unprod_binary64 div-exp_binary64 flip-+_binary64 frac-times_binary64 associate-*l/_binary64
1×pow-prod-down_binary64 count-2_binary64 distribute-lft1-in_binary64 add-log-exp_binary64 1-exp_binary64 cbrt-undiv_binary64 associate-*r/_binary64 distribute-rgt1-in_binary64 rec-exp_binary64 un-div-inv_binary64 div-inv_binary64 *-commutative_binary64
Counts
1 → 49
Calls

2 calls:

13.0ms
(*.f64 (+.f64 f f) (/.f64 1 n))
0.0ms
(*.f64 (+.f64 f f) (/.f64 1 n))

series58.0ms (0.1%)

Counts
1 → 6
Calls

1 calls:

58.0ms
(*.f64 (+.f64 f f) (/.f64 1 n))
Compiler

Compiled 84 to 84 computations (0% saved)

simplify73.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
04926523
14926523

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(cbrt.f64 (-.f64 n f))
0.5b
(cbrt.f64 (-.f64 n f))
0.2b
(/.f64 (+.f64 f n) (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f))))
0.0b
(/.f64 (/.f64 (+.f64 f n) (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))) (cbrt.f64 (-.f64 n f)))
0.5b
(cbrt.f64 (-.f64 n f))
0.5b
(cbrt.f64 (-.f64 n f))
0.5b
(cbrt.f64 (-.f64 n f))
0.6b
(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))

rewrite34.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
43×cbrt-prod_binary64
37×add-sqr-sqrt_binary64
35×*-un-lft-identity_binary64
18×cbrt-div_binary64
15×add-cube-cbrt_binary64
11×pow1_binary64
10×swap-sqr_binary64
9×flip3--_binary64 pow1/3_binary64 distribute-lft-out--_binary64 flip--_binary64
8×associate-*r*_binary64 associate-*l*_binary64
7×difference-of-squares_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 → 101
Calls

8 calls:

14.0ms
(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))
3.0ms
(cbrt.f64 (-.f64 n f))
3.0ms
(cbrt.f64 (-.f64 n f))
3.0ms
(cbrt.f64 (-.f64 n f))
0.0ms
(/.f64 (/.f64 (+.f64 f n) (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))) (cbrt.f64 (-.f64 n f)))

series606.0ms (0.6%)

Counts
4 → 54
Calls

4 calls:

181.0ms
(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))
146.0ms
(cbrt.f64 (-.f64 n f))
144.0ms
(cbrt.f64 (-.f64 n f))
134.0ms
(cbrt.f64 (-.f64 n f))
Compiler

Compiled 2798 to 2147 computations (23.3% saved)

simplify100.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
049212411
149212411

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (sqrt.f64 (+.f64 f n)))
0.0b
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 n f))) 3) (sqrt.f64 (-.f64 n f))) (/.f64 (sqrt.f64 (-.f64 n f)) (sqrt.f64 (sqrt.f64 (+.f64 f n)))))
0.0b
(sqrt.f64 (-.f64 n f))
0.0b
(sqrt.f64 (-.f64 n f))
0.1b
(sqrt.f64 (sqrt.f64 (+.f64 f n)))
0.1b
(/.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 n f))) 3) (sqrt.f64 (-.f64 n f)))
0.1b
(/.f64 (sqrt.f64 (-.f64 n f)) (sqrt.f64 (sqrt.f64 (+.f64 f n))))
0.3b
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 n f))) 3)

rewrite118.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
521×sqrt-prod_binary64
315×*-un-lft-identity_binary64
288×times-frac_binary64
257×add-sqr-sqrt_binary64
179×add-cube-cbrt_binary64
100×unpow-prod-down_binary64 cube-prod_binary64
38×difference-of-squares_binary64 distribute-lft-out--_binary64
34×associate-/l*_binary64
30×distribute-lft-out_binary64
20×sqrt-div_binary64
18×associate-/r*_binary64
12×add-exp-log_binary64
10×sqr-pow_binary64 unpow3_binary64 cube-mult_binary64
9×pow1_binary64 add-cbrt-cube_binary64
8×sqrt-pow1_binary64
5×pow-pow_binary64
4×flip3-+_binary64 associate-/l/_binary64 add-log-exp_binary64 pow1/2_binary64 associate-/r/_binary64 cube-div_binary64 div-exp_binary64 flip-+_binary64
3×pow-unpow_binary64
2×pow-to-exp_binary64 flip3--_binary64 cbrt-undiv_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 flip--_binary64 pow-exp_binary64
1×sqrt-pow2_binary64 sqrt-undiv_binary64 rem-cube-cbrt_binary64
Counts
4 → 441
Calls

8 calls:

19.0ms
(/.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 n f))) 3) (sqrt.f64 (-.f64 n f)))
16.0ms
(/.f64 (sqrt.f64 (-.f64 n f)) (sqrt.f64 (sqrt.f64 (+.f64 f n))))
7.0ms
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 n f))) 3)
4.0ms
(sqrt.f64 (sqrt.f64 (+.f64 f n)))
0.0ms
(sqrt.f64 (-.f64 n f))

series546.0ms (0.5%)

Counts
4 → 34
Calls

4 calls:

199.0ms
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 n f))) 3)
142.0ms
(/.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 n f))) 3) (sqrt.f64 (-.f64 n f)))
128.0ms
(/.f64 (sqrt.f64 (-.f64 n f)) (sqrt.f64 (sqrt.f64 (+.f64 f n))))
76.0ms
(sqrt.f64 (sqrt.f64 (+.f64 f n)))
Compiler

Compiled 2042 to 1594 computations (21.9% saved)

simplify175.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0506112873

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (sqrt.f64 (+.f64 n f)))
0.1b
(sqrt.f64 (sqrt.f64 (+.f64 n f)))
0.0b
(sqrt.f64 (-.f64 n f))
0.0b
(sqrt.f64 (-.f64 n f))
0.1b
(/.f64 (sqrt.f64 (-.f64 n f)) (sqrt.f64 (cbrt.f64 (+.f64 n f))))
0.2b
(/.f64 (sqrt.f64 (-.f64 n f)) (fabs.f64 (cbrt.f64 (+.f64 n f))))
0.5b
(cbrt.f64 (+.f64 n f))
0.5b
(cbrt.f64 (+.f64 n f))

rewrite53.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
138×sqrt-prod_binary64
124×*-un-lft-identity_binary64
104×times-frac_binary64
102×add-sqr-sqrt_binary64
72×add-cube-cbrt_binary64
44×cbrt-prod_binary64
16×associate-/l*_binary64
15×difference-of-squares_binary64 distribute-lft-out--_binary64
13×associate-/r*_binary64
11×distribute-lft-out_binary64
8×add-exp-log_binary64 add-cbrt-cube_binary64
6×cbrt-div_binary64 sqrt-div_binary64
4×associate-/l/_binary64 add-log-exp_binary64 pow1_binary64
3×flip3-+_binary64 flip-+_binary64
2×flip3--_binary64 cbrt-undiv_binary64 pow1/3_binary64 associate-/r/_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 flip--_binary64
1×sqrt-undiv_binary64
Counts
4 → 192
Calls

8 calls:

12.0ms
(/.f64 (sqrt.f64 (-.f64 n f)) (sqrt.f64 (cbrt.f64 (+.f64 n f))))
7.0ms
(/.f64 (sqrt.f64 (-.f64 n f)) (fabs.f64 (cbrt.f64 (+.f64 n f))))
3.0ms
(cbrt.f64 (+.f64 n f))
3.0ms
(cbrt.f64 (+.f64 n f))
0.0ms
(sqrt.f64 (-.f64 n f))

series469.0ms (0.4%)

Counts
4 → 37
Calls

4 calls:

150.0ms
(/.f64 (sqrt.f64 (-.f64 n f)) (sqrt.f64 (cbrt.f64 (+.f64 n f))))
110.0ms
(cbrt.f64 (+.f64 n f))
105.0ms
(cbrt.f64 (+.f64 n f))
104.0ms
(/.f64 (sqrt.f64 (-.f64 n f)) (fabs.f64 (cbrt.f64 (+.f64 n f))))
Compiler

Compiled 2845 to 1826 computations (35.8% saved)

simplify104.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
229 → 229
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
050325807

prune36.5s (33.6%)

Pruning

844 alts after pruning (827 fresh and 17 done)

PrunedKeptTotal
New7053251030
Fresh39502541
Picked000
Done01717
Total7448441588
Error
0b
Counts
1588 → 844
Compiler

Compiled 15612 to 3533 computations (77.4% saved)

simplify1.2s (1.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0587263726

regimes8.3s (7.6%)

Compiler

Compiled 95846 to 49305 computations (48.6% saved)

bsearch0.0ms (0%)

regimes62.0ms (0.1%)

Compiler

Compiled 76 to 92 computations (-21.1% saved)

bsearch23.0ms (0%)

Steps
ItersRangePoint
5
1.7623941396121706e+32
6.3103520202735336e+32
2.09220074073275e+32
8
-4.204517096237458e-57
-9.288460660884222e-62
-1.0407031435936754e-58
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes55.0ms (0.1%)

Compiler

Compiled 48 to 66 computations (-37.5% saved)

bsearch19.0ms (0%)

Steps
ItersRangePoint
5
1.7623941396121706e+32
6.3103520202735336e+32
2.09220074073275e+32
8
-4.204517096237458e-57
-9.288460660884222e-62
-2.2610510955328207e-57
Compiler

Compiled 1 to 2 computations (-100% saved)

regimes47.0ms (0%)

Accuracy

Total 0.0b remaining (100%)

Threshold costs 0.0b (100%)

Compiler

Compiled 20 to 40 computations (-100% saved)

bsearch24.0ms (0%)

Steps
ItersRangePoint
5
1.7623941396121706e+32
6.3103520202735336e+32
1.8095093683436817e+32
8
-4.204517096237458e-57
-9.288460660884222e-62
-1.4025444141795704e-59
Compiler

Compiled 66 to 55 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
07884
17884

end0.0ms (0%)

sample22.2s (20.5%)

Algorithm
1×intervals
Results
220.0ms8000×body128valid
Compiler

Compiled 32091 to 16568 computations (48.4% saved)

Pareto

0.10887914765742279

Profiling

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