Details

Time bar (total: 10.3s)

analyze6.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%49.7%50.3%0
0%49.7%50.3%1
0%49.7%50.3%2
24.8%24.8%50.3%3
37.3%12.4%50.3%4
43.5%6.2%50.3%5
46.6%3.1%50.3%6
48.1%1.6%50.3%7
48.9%0.8%50.3%8
49.3%0.4%50.3%9
49.5%0.2%50.3%10
49.6%0.1%50.3%11
49.6%0%50.3%12
49.7%0%50.3%13
49.7%0%50.3%14
Compiler

Compiled 15 to 12 computations (20% saved)

sample218.0ms (2.1%)

Algorithm
1×intervals
Results
176.0ms128×body2048valid
18.0ms64×body1024valid
7.0ms12×body4096valid
5.0ms256×pre128true
4.0ms31×body512valid
1.0ms15×body256valid
0.0ms6×body128valid
Compiler

Compiled 23 to 20 computations (13% saved)

simplify160.0ms (1.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
07212
17212

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 59.9b

Counts
2 → 1
Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 1 (tan.f64 x))
2.2b
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite31.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
36×add-sqr-sqrt_binary64_772
28×*-un-lft-identity_binary64_751
27×times-frac_binary64_757
12×add-cube-cbrt_binary64_783
9×difference-of-squares_binary64_720
7×distribute-lft-out--_binary64_705
6×add-exp-log_binary64_786
5×div-inv_binary64_748
4×add-log-exp_binary64_787 add-cbrt-cube_binary64_784
3×associate-/r*_binary64_697 pow1_binary64_809 associate-/l*_binary64_698
2×div-exp_binary64_799
1×1-exp_binary64_792 tan-quot_binary64_907 frac-sub_binary64_760 rec-exp_binary64_798 flip--_binary64_726 inv-pow_binary64_833 associate-/r/_binary64_699 diff-log_binary64_840 cbrt-undiv_binary64_782 frac-2neg_binary64_762 clear-num_binary64_750 sub-neg_binary64_744 flip3--_binary64_755 pow-flip_binary64_822
Counts
2 → 60
Calls

2 calls:

22.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms
(/.f64 1 (tan.f64 x))

series250.0ms (2.4%)

Counts
2 → 6
Calls

2 calls:

149.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
100.0ms
(/.f64 1 (tan.f64 x))

simplify62.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049381005
149381005

prune65.0ms (0.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New65166
Fresh000
Picked101
Done000
Total66167

Merged error: 0.3b

Counts
67 → 1
Compiler

Compiled 928 to 583 computations (37.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 x 1/3) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 2/945 (pow.f64 x 5))))
0.1b
(*.f64 2/945 (pow.f64 x 5))
0.1b
(*.f64 1/45 (pow.f64 x 3))
0.3b
(*.f64 x 1/3)

rewrite33.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
27×add-sqr-sqrt_binary64_772
22×associate-*r*_binary64_693
16×add-exp-log_binary64_786
13×add-cube-cbrt_binary64_783 *-un-lft-identity_binary64_751
10×add-cbrt-cube_binary64_784
9×add-log-exp_binary64_787 associate-*l*_binary64_694
8×unswap-sqr_binary64_719 unpow-prod-down_binary64_827
7×prod-exp_binary64_797
6×pow1_binary64_809
4×sqr-pow_binary64_723 cube-prod_binary64_776
3×*-commutative_binary64_684 sum-log_binary64_839 cbrt-unprod_binary64_781
2×pow-to-exp_binary64_817 pow-exp_binary64_816
1×cube-mult_binary64_778 +-commutative_binary64_683 flip3-+_binary64_754 pow-prod-down_binary64_819 associate-+r+_binary64_685 unpow3_binary64_814 flip-+_binary64_725
Counts
4 → 87
Calls

4 calls:

9.0ms
(+.f64 (*.f64 x 1/3) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 2/945 (pow.f64 x 5))))
7.0ms
(*.f64 1/45 (pow.f64 x 3))
6.0ms
(*.f64 2/945 (pow.f64 x 5))
4.0ms
(*.f64 x 1/3)

series199.0ms (1.9%)

Counts
4 → 12
Calls

4 calls:

60.0ms
(*.f64 2/945 (pow.f64 x 5))
59.0ms
(+.f64 (*.f64 x 1/3) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 2/945 (pow.f64 x 5))))
51.0ms
(*.f64 1/45 (pow.f64 x 3))
29.0ms
(*.f64 x 1/3)

simplify76.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049191176
149191176

prune138.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New92799
Fresh000
Picked011
Done000
Total928100

Merged error: 0.1b

Counts
100 → 8
Compiler

Compiled 2163 to 1726 computations (20.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b
(cbrt.f64 x)
0.6b
(cbrt.f64 x)
0.6b
(cbrt.f64 x)

rewrite17.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
25×cbrt-prod_binary64_779
23×add-sqr-sqrt_binary64_772
15×add-cube-cbrt_binary64_783 *-un-lft-identity_binary64_751
11×pow1_binary64_809
9×pow1/3_binary64_830
6×swap-sqr_binary64_718 associate-*l*_binary64_694 add-exp-log_binary64_786 associate-*r*_binary64_693
4×unswap-sqr_binary64_719 add-log-exp_binary64_787 add-cbrt-cube_binary64_784
2×pow-sqr_binary64_724 pow-prod-up_binary64_818 pow-prod-down_binary64_819
1×prod-exp_binary64_797 pow-plus_binary64_811 *-commutative_binary64_684 cbrt-unprod_binary64_781 pow2_binary64_829
Counts
4 → 73
Calls

4 calls:

6.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)

series620.0ms (6%)

Counts
4 → 12
Calls

4 calls:

169.0ms
(*.f64 (cbrt.f64 x) (cbrt.f64 x))
159.0ms
(cbrt.f64 x)
152.0ms
(cbrt.f64 x)
140.0ms
(cbrt.f64 x)

simplify67.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
04957563
14957563

prune126.0ms (1.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New82385
Fresh066
Picked011
Done011
Total821193

Merged error: 0.1b

Counts
93 → 11
Compiler

Compiled 2372 to 1558 computations (34.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 (*.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
0.7b
(cbrt.f64 (*.f64 x 1/3))
0.7b
(cbrt.f64 (*.f64 x 1/3))
0.7b
(cbrt.f64 (*.f64 x 1/3))

rewrite19.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
11×pow1_binary64_809
10×add-sqr-sqrt_binary64_772
9×pow1/3_binary64_830
8×add-cube-cbrt_binary64_783 *-un-lft-identity_binary64_751
7×cbrt-prod_binary64_779
6×add-exp-log_binary64_786
4×add-log-exp_binary64_787 add-cbrt-cube_binary64_784 swap-sqr_binary64_718 associate-*l*_binary64_694 associate-*r*_binary64_693
2×pow-sqr_binary64_724 pow-prod-up_binary64_818 pow-prod-down_binary64_819
1×prod-exp_binary64_797 unswap-sqr_binary64_719 pow-plus_binary64_811 *-commutative_binary64_684 cbrt-unprod_binary64_781 pow2_binary64_829
Counts
4 → 58
Calls

4 calls:

6.0ms
(*.f64 (cbrt.f64 (*.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
3.0ms
(cbrt.f64 (*.f64 x 1/3))
2.0ms
(cbrt.f64 (*.f64 x 1/3))
2.0ms
(cbrt.f64 (*.f64 x 1/3))

series788.0ms (7.7%)

Counts
4 → 12
Calls

4 calls:

229.0ms
(*.f64 (cbrt.f64 (*.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
191.0ms
(cbrt.f64 (*.f64 x 1/3))
184.0ms
(cbrt.f64 (*.f64 x 1/3))
184.0ms
(cbrt.f64 (*.f64 x 1/3))

simplify64.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
04987556
14987556

prune114.0ms (1.1%)

Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New65570
Fresh178
Picked011
Done022
Total661581

Merged error: 0.1b

Counts
81 → 15
Compiler

Compiled 1917 to 1556 computations (18.8% saved)

regimes44.0ms (0.4%)

Compiler

Compiled 435 to 357 computations (17.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01922
11922

end0.0ms (0%)

sample7.1s (69.4%)

Algorithm
1×intervals
Results
5.3s4072×body2048valid
674.0ms1969×body1024valid
143.0ms8000×pre128true
135.0ms230×body4096valid
129.0ms991×body512valid
44.0ms503×body256valid
11.0ms235×body128valid
Compiler

Compiled 487 to 400 computations (17.9% saved)

Profiling

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