Details

Time bar (total: 3.5s)

analyze269.0ms (7.7%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
12.5%87.4%0.1%7
18.7%81.1%0.1%8
31.2%68.6%0.1%9
43.3%49.9%6.8%10
49.7%40.8%9.5%11
55.7%34%10.3%12
61.3%24.4%14.3%13
65%19.8%15.3%14
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample14.0ms (0.4%)

Algorithm
1×intervals
Results
6.0ms256×body128valid
0.0ms13×body128invalid
Compiler

Compiled 15 to 16 computations (-6.7% saved)

simplify21.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (15.0ms)

IterNodesCost
027410
127410

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1
Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 x (*.f64 (-.f64 y x) z))
0.0b
(*.f64 (-.f64 y x) z)

rewrite13.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
8×add-sqr-sqrt_binary64
6×*-un-lft-identity_binary64
5×associate-*l*_binary64
4×add-log-exp_binary64 pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
3×associate-*r*_binary64
2×associate-*l/_binary64
1×pow-prod-down_binary64 flip3-+_binary64 flip3--_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 prod-exp_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 +-commutative_binary64 flip--_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
2 → 33
Calls

2 calls:

8.0ms
(*.f64 (-.f64 y x) z)
4.0ms
(+.f64 x (*.f64 (-.f64 y x) z))

series116.0ms (3.3%)

Counts
2 → 6
Calls

2 calls:

59.0ms
(*.f64 (-.f64 y x) z)
56.0ms
(+.f64 x (*.f64 (-.f64 y x) z))

simplify53.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
05151448

prune55.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New36339
Fresh000
Picked011
Done000
Total36440

Merged error: 0.0b

Counts
40 → 4
Compiler

Compiled 985 to 439 computations (55.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 (*.f64 (-.f64 y x) z)) (cbrt.f64 (*.f64 (-.f64 y x) z)))
3.9b
(cbrt.f64 (*.f64 (-.f64 y x) z))
3.9b
(cbrt.f64 (*.f64 (-.f64 y x) z))
3.9b
(cbrt.f64 (*.f64 (-.f64 y x) z))

rewrite36.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
20×associate-*l/_binary64
18×cbrt-div_binary64
11×pow1_binary64
10×add-sqr-sqrt_binary64
9×flip3--_binary64 pow1/3_binary64 flip--_binary64
8×*-un-lft-identity_binary64 add-cube-cbrt_binary64
7×cbrt-prod_binary64
6×add-exp-log_binary64
4×add-log-exp_binary64 swap-sqr_binary64 associate-*r*_binary64 add-cbrt-cube_binary64 associate-*l*_binary64 frac-times_binary64
2×pow-prod-down_binary64 pow-prod-up_binary64 associate-*r/_binary64 pow-sqr_binary64
1×cbrt-unprod_binary64 pow-plus_binary64 unswap-sqr_binary64 prod-exp_binary64 pow2_binary64 *-commutative_binary64
Counts
4 → 72
Calls

4 calls:

9.0ms
(*.f64 (cbrt.f64 (*.f64 (-.f64 y x) z)) (cbrt.f64 (*.f64 (-.f64 y x) z)))
6.0ms
(cbrt.f64 (*.f64 (-.f64 y x) z))
6.0ms
(cbrt.f64 (*.f64 (-.f64 y x) z))
6.0ms
(cbrt.f64 (*.f64 (-.f64 y x) z))

series1.2s (33.7%)

Counts
4 → 12
Calls

4 calls:

353.0ms
(*.f64 (cbrt.f64 (*.f64 (-.f64 y x) z)) (cbrt.f64 (*.f64 (-.f64 y x) z)))
288.0ms
(cbrt.f64 (*.f64 (-.f64 y x) z))
272.0ms
(cbrt.f64 (*.f64 (-.f64 y x) z))
269.0ms
(cbrt.f64 (*.f64 (-.f64 y x) z))

simplify70.0ms (2%)

Algorithm
1×egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049461376
149461376

prune90.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New83184
Fresh022
Picked011
Done011
Total83588

Merged error: 0.0b

Counts
88 → 5
Compiler

Compiled 2522 to 699 computations (72.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 x (/.f64 (*.f64 z (-.f64 (*.f64 y y) (*.f64 x x))) (+.f64 y x)))
1.7b
(-.f64 (*.f64 y y) (*.f64 x x))
8.8b
(*.f64 z (-.f64 (*.f64 y y) (*.f64 x x)))
18.4b
(/.f64 (*.f64 z (-.f64 (*.f64 y y) (*.f64 x x))) (+.f64 y x))

rewrite42.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
14×*-un-lft-identity_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
10×add-sqr-sqrt_binary64
8×add-log-exp_binary64 add-cube-cbrt_binary64
6×pow1_binary64
4×associate-/r*_binary64 associate-*r*_binary64 associate-*r/_binary64 times-frac_binary64
3×sub-neg_binary64 flip3--_binary64 distribute-lft-out_binary64 associate-*l*_binary64 cancel-sign-sub-inv_binary64 flip--_binary64
2×flip3-+_binary64 associate-/l/_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 distribute-lft-in_binary64 associate-/r/_binary64 distribute-rgt-in_binary64 prod-exp_binary64 difference-of-squares_binary64 div-exp_binary64 flip-+_binary64
1×pow-prod-down_binary64 diff-log_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64 +-commutative_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 77
Calls

4 calls:

12.0ms
(+.f64 x (/.f64 (*.f64 z (-.f64 (*.f64 y y) (*.f64 x x))) (+.f64 y x)))
12.0ms
(/.f64 (*.f64 z (-.f64 (*.f64 y y) (*.f64 x x))) (+.f64 y x))
8.0ms
(*.f64 z (-.f64 (*.f64 y y) (*.f64 x x)))
5.0ms
(-.f64 (*.f64 y y) (*.f64 x x))

series434.0ms (12.4%)

Counts
4 → 12
Calls

4 calls:

170.0ms
(/.f64 (*.f64 z (-.f64 (*.f64 y y) (*.f64 x x))) (+.f64 y x))
112.0ms
(*.f64 z (-.f64 (*.f64 y y) (*.f64 x x)))
111.0ms
(+.f64 x (/.f64 (*.f64 z (-.f64 (*.f64 y y) (*.f64 x x))) (+.f64 y x)))
41.0ms
(-.f64 (*.f64 y y) (*.f64 x x))

simplify60.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049641253
149641253

prune75.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New88189
Fresh112
Picked101
Done022
Total90494

Merged error: 0b

Counts
94 → 4
Compiler

Compiled 1829 to 498 computations (72.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 x (/.f64 z (/.f64 1 (-.f64 y x))))
0.0b
(/.f64 1 (-.f64 y x))
0.2b
(/.f64 z (/.f64 1 (-.f64 y x)))

rewrite60.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Rules
138×times-frac_binary64
105×*-un-lft-identity_binary64
103×add-sqr-sqrt_binary64
71×add-cube-cbrt_binary64
26×associate-/r*_binary64
16×difference-of-squares_binary64 distribute-lft-out--_binary64
13×add-exp-log_binary64
11×associate-/r/_binary64
10×add-cbrt-cube_binary64
6×associate-/l*_binary64 div-inv_binary64
5×add-log-exp_binary64 flip3--_binary64 div-exp_binary64 flip--_binary64
4×pow1_binary64 cbrt-undiv_binary64
2×clear-num_binary64 frac-2neg_binary64 rec-exp_binary64
1×flip3-+_binary64 distribute-lft-out_binary64 inv-pow_binary64 +-commutative_binary64 pow-flip_binary64 flip-+_binary64 sum-log_binary64
Counts
3 → 155
Calls

3 calls:

24.0ms
(+.f64 x (/.f64 z (/.f64 1 (-.f64 y x))))
11.0ms
(/.f64 z (/.f64 1 (-.f64 y x)))
7.0ms
(/.f64 1 (-.f64 y x))

series148.0ms (4.2%)

Counts
3 → 9
Calls

3 calls:

61.0ms
(/.f64 z (/.f64 1 (-.f64 y x)))
48.0ms
(+.f64 x (/.f64 z (/.f64 1 (-.f64 y x))))
39.0ms
(/.f64 1 (-.f64 y x))

simplify88.0ms (2.5%)

Algorithm
1×egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
053412724

prune126.0ms (3.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1631164
Fresh101
Picked011
Done022
Total1644168

Merged error: 0b

Counts
168 → 4
Compiler

Compiled 2655 to 953 computations (64.1% saved)

regimes43.0ms (1.2%)

Compiler

Compiled 232 to 162 computations (30.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01910
11910

end0.0ms (0%)

sample476.0ms (13.6%)

Algorithm
1×intervals
Results
196.0ms8000×body128valid
17.0ms585×body128invalid
Compiler

Compiled 68 to 49 computations (27.9% saved)

Profiling

Loading profile data...