Details

Time bar (total: 6.2s)

analyze214.0ms (3.5%)

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
15.6%84.3%0.1%6
37.5%62.4%0.1%7
46.8%53.1%0.1%8
57.8%39.8%2.4%9
64.6%30.4%5%10
71.8%20.3%7.9%11
74.1%16.2%9.7%12
77.4%10.7%12%13
78.6%8.4%13%14
Compiler

Compiled 22 to 18 computations (18.2% saved)

sample28.0ms (0.4%)

Algorithm
1×intervals
Results
17.0ms256×body128valid
1.0ms20×body128invalid
Compiler

Compiled 43 to 37 computations (14% saved)

simplify146.0ms (2.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0524129

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
14.8b
Counts
2 → 2
Compiler

Compiled 59 to 47 computations (20.3% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

9.5b
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
4.8b
(-.f64 (*.f64 b b) (*.f64 a a))
0.1b
(/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a)))
0.0b
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.0b
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.1b
(/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a)))
4.8b
(-.f64 (*.f64 b b) (*.f64 a a))
9.5b
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite112.0ms (1.8%)

Algorithm
1×rewrite-expression-head
Rules
251×times-frac_binary64_743
178×add-sqr-sqrt_binary64_759
153×*-un-lft-identity_binary64_737
121×add-cube-cbrt_binary64_772
58×associate-*l*_binary64_678
46×difference-of-squares_binary64_706
40×cancel-sign-sub-inv_binary64_703
22×div-inv_binary64_734
19×associate-*r*_binary64_677
18×add-cbrt-cube_binary64_773 add-exp-log_binary64_775
14×distribute-lft-in_binary64_686 distribute-lft-out--_binary64_689 distribute-rgt-in_binary64_687
13×associate-/l*_binary64_682
8×add-log-exp_binary64_776
6×pow1_binary64_798 flip3--_binary64_741 cbrt-undiv_binary64_771 div-exp_binary64_788 flip--_binary64_712
4×associate-/r/_binary64_683 associate-/r*_binary64_681 sub-neg_binary64_730
3×unswap-sqr_binary64_705 frac-times_binary64_747 cbrt-unprod_binary64_770 prod-exp_binary64_786 frac-sub_binary64_746 associate-*r/_binary64_679
2×diff-log_binary64_829
1×frac-2neg_binary64_748 clear-num_binary64_736 associate-*l/_binary64_680 associate-/l/_binary64_684 pow-prod-down_binary64_808 *-commutative_binary64_668
Counts
4 → 270
Calls

8 calls:

47.0ms
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
15.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 a a))
0.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))

series483.0ms (7.8%)

Counts
4 → 63
Calls

4 calls:

164.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a)))
151.0ms
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
98.0ms
(-.f64 (*.f64 b b) (*.f64 a a))
70.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
Compiler

Compiled 1842 to 1554 computations (15.6% saved)

simplify141.0ms (2.3%)

Algorithm
1×egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049669384
149669384

prune532.0ms (8.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New32013333
Fresh101
Picked101
Done000
Total32213335
Error
0.0b
Counts
335 → 13
Compiler

Compiled 9660 to 4646 computations (51.9% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 PI.f64 (+.f64 b a))
0.2b
(*.f64 (/.f64 PI.f64 (+.f64 b a)) (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
0.0b
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.0b
(/.f64 1/2 (-.f64 b a))
0.0b
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.2b
(*.f64 (/.f64 PI.f64 (+.f64 b a)) (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
0.2b
(/.f64 PI.f64 (+.f64 b a))
0.3b
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

rewrite106.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Rules
101×add-sqr-sqrt_binary64_759
94×*-un-lft-identity_binary64_737
85×times-frac_binary64_743
42×add-cube-cbrt_binary64_772
37×associate-*l*_binary64_678
32×add-cbrt-cube_binary64_773 add-exp-log_binary64_775
22×associate-*r*_binary64_677
21×difference-of-squares_binary64_706
17×distribute-lft-out--_binary64_689
16×frac-times_binary64_747
13×cancel-sign-sub-inv_binary64_703
12×cbrt-unprod_binary64_770 prod-exp_binary64_786 div-inv_binary64_734
11×pow1_binary64_798
10×associate-*l/_binary64_680 associate-*r/_binary64_679
8×flip3--_binary64_741 flip--_binary64_712
7×cbrt-undiv_binary64_771 div-exp_binary64_788 distribute-lft-out_binary64_688 frac-sub_binary64_746
6×associate-/r/_binary64_683 add-log-exp_binary64_776
4×associate-/r*_binary64_681 pow-prod-down_binary64_808
3×associate-/l*_binary64_682
2×unswap-sqr_binary64_705 flip3-+_binary64_740 flip-+_binary64_711 *-commutative_binary64_668
1×diff-log_binary64_829 frac-2neg_binary64_748 clear-num_binary64_736 sub-neg_binary64_730
Counts
4 → 192
Calls

8 calls:

32.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
29.0ms
(*.f64 (/.f64 PI.f64 (+.f64 b a)) (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
15.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
5.0ms
(/.f64 PI.f64 (+.f64 b a))
0.0ms
(/.f64 1/2 (-.f64 b a))

series427.0ms (6.9%)

Counts
4 → 60
Calls

4 calls:

153.0ms
(*.f64 (/.f64 PI.f64 (+.f64 b a)) (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
108.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
98.0ms
(/.f64 PI.f64 (+.f64 b a))
67.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
Compiler

Compiled 1734 to 1374 computations (20.8% saved)

simplify102.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
050735295

prune346.0ms (5.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2475252
Fresh10212
Picked101
Done000
Total2587265
Error
0b
Counts
265 → 7
Compiler

Compiled 6311 to 3161 computations (49.9% saved)

localize7.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.6b
(/.f64 1/2 (*.f64 a b))
0.2b
(/.f64 PI.f64 (+.f64 b a))
0.2b
(*.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (*.f64 a b)))
0.2b
(*.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (*.f64 a b)))
0.2b
(/.f64 PI.f64 (+.f64 b a))
0.6b
(/.f64 1/2 (*.f64 a b))

rewrite31.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
38×*-un-lft-identity_binary64_737
31×add-cbrt-cube_binary64_773 add-exp-log_binary64_775 times-frac_binary64_743
29×add-sqr-sqrt_binary64_759
24×add-cube-cbrt_binary64_772
18×associate-*l*_binary64_678
10×cbrt-undiv_binary64_771 div-exp_binary64_788
9×cbrt-unprod_binary64_770 prod-exp_binary64_786
7×associate-*r*_binary64_677 distribute-lft-out_binary64_688
6×associate-/l*_binary64_682
5×associate-/r*_binary64_681 pow1_binary64_798
4×associate-/r/_binary64_683 div-inv_binary64_734
3×add-log-exp_binary64_776
2×unswap-sqr_binary64_705 flip3-+_binary64_740 frac-2neg_binary64_748 clear-num_binary64_736 flip-+_binary64_711
1×frac-times_binary64_747 associate-*l/_binary64_680 pow-prod-down_binary64_808 *-commutative_binary64_668 associate-*r/_binary64_679
Counts
3 → 105
Calls

6 calls:

13.0ms
(*.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (*.f64 a b)))
5.0ms
(/.f64 PI.f64 (+.f64 b a))
4.0ms
(/.f64 1/2 (*.f64 a b))
0.0ms
(*.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (*.f64 a b)))
0.0ms
(/.f64 PI.f64 (+.f64 b a))

series286.0ms (4.6%)

Counts
3 → 48
Calls

3 calls:

136.0ms
(*.f64 (/.f64 PI.f64 (+.f64 b a)) (/.f64 1/2 (*.f64 a b)))
88.0ms
(/.f64 PI.f64 (+.f64 b a))
62.0ms
(/.f64 1/2 (*.f64 a b))
Compiler

Compiled 1224 to 978 computations (20.1% saved)

simplify86.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049662711
149662711

prune127.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1521153
Fresh156
Picked011
Done000
Total1537160
Error
0b
Counts
160 → 7
Compiler

Compiled 2692 to 1031 computations (61.7% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (*.f64 1/2 (/.f64 PI.f64 (+.f64 a b))))
0.2b
(/.f64 PI.f64 (+.f64 a b))
0.1b
(/.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (*.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))) (-.f64 b a))
0.0b
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.0b
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.1b
(/.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (*.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))) (-.f64 b a))
0.2b
(/.f64 PI.f64 (+.f64 a b))
0.3b
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (*.f64 1/2 (/.f64 PI.f64 (+.f64 a b))))

rewrite89.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Rules
79×add-sqr-sqrt_binary64_759
71×*-un-lft-identity_binary64_737
62×times-frac_binary64_743
29×add-cbrt-cube_binary64_773 add-exp-log_binary64_775
27×add-cube-cbrt_binary64_772
20×difference-of-squares_binary64_706
19×associate-*l*_binary64_678
16×distribute-lft-out--_binary64_689
13×cancel-sign-sub-inv_binary64_703
11×div-inv_binary64_734
10×cbrt-unprod_binary64_770 prod-exp_binary64_786 associate-*r/_binary64_679
9×associate-/r*_binary64_681 pow1_binary64_798
7×cbrt-undiv_binary64_771 div-exp_binary64_788 associate-/l/_binary64_684
6×add-log-exp_binary64_776 frac-times_binary64_747 associate-*l/_binary64_680 flip3--_binary64_741 flip--_binary64_712
5×frac-sub_binary64_746
4×associate-/r/_binary64_683 associate-/l*_binary64_682 distribute-lft-out_binary64_688
3×pow-prod-down_binary64_808
2×frac-2neg_binary64_748 clear-num_binary64_736
1×diff-log_binary64_829 flip3-+_binary64_740 sub-neg_binary64_730 flip-+_binary64_711 associate-*r*_binary64_677 *-commutative_binary64_668
Counts
4 → 155
Calls

8 calls:

26.0ms
(/.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (*.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))) (-.f64 b a))
26.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (*.f64 1/2 (/.f64 PI.f64 (+.f64 a b))))
14.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
5.0ms
(/.f64 PI.f64 (+.f64 a b))
0.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))

series418.0ms (6.8%)

Counts
4 → 72
Calls

4 calls:

154.0ms
(/.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (*.f64 1/2 (/.f64 PI.f64 (+.f64 a b)))) (-.f64 b a))
104.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (*.f64 1/2 (/.f64 PI.f64 (+.f64 a b))))
95.0ms
(/.f64 PI.f64 (+.f64 a b))
65.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
Compiler

Compiled 2025 to 1581 computations (21.9% saved)

simplify82.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
053184818

prune238.0ms (3.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2270227
Fresh055
Picked011
Done011
Total2277234
Error
0b
Counts
234 → 7
Compiler

Compiled 5440 to 2632 computations (51.6% saved)

regimes349.0ms (5.6%)

Accuracy

Total 0.2b remaining (99.7%)

Threshold costs 0.2b (99.7%)

Compiler

Compiled 4555 to 3429 computations (24.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01317
11317

end0.0ms (0%)

sample1.8s (28.9%)

Algorithm
1×intervals
Results
445.0ms8000×body128valid
20.0ms374×body128invalid
Compiler

Compiled 1536 to 1158 computations (24.6% saved)

Pareto

0

Profiling

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