Details

Time bar (total: 9.6s)

analyze210.0ms (2.2%)

Algorithm
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)

sample24.0ms (0.3%)

Algorithm
intervals
Results
14.0ms256×body128valid
1.0ms15×body128invalid
Compiler

Compiled 43 to 37 computations (14% saved)

simplify144.0ms (1.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0524129

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
12.7b
Counts
2 → 2
Compiler

Compiled 59 to 47 computations (20.3% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

9.3b
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
2.8b
(-.f64 (*.f64 b b) (*.f64 a a))
0.4b
(/.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))
0.4b
(/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a)))
2.8b
(-.f64 (*.f64 b b) (*.f64 a a))
9.3b
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite111.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
251×times-frac_binary64_766
178×add-sqr-sqrt_binary64_782
153×*-un-lft-identity_binary64_760
121×add-cube-cbrt_binary64_795
58×associate-*l*_binary64_701
46×difference-of-squares_binary64_729
40×cancel-sign-sub-inv_binary64_726
22×div-inv_binary64_757
19×associate-*r*_binary64_700
18×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
14×distribute-lft-in_binary64_709 distribute-rgt-in_binary64_710 distribute-lft-out--_binary64_712
13×associate-/l*_binary64_705
add-log-exp_binary64_799
cbrt-undiv_binary64_794 div-exp_binary64_811 pow1_binary64_821 flip--_binary64_735 flip3--_binary64_764
associate-/r/_binary64_706 associate-/r*_binary64_704 sub-neg_binary64_753
unswap-sqr_binary64_728 prod-exp_binary64_809 frac-times_binary64_770 frac-sub_binary64_769 associate-*r/_binary64_702 cbrt-unprod_binary64_793
diff-log_binary64_852
frac-2neg_binary64_771 associate-*l/_binary64_703 associate-/l/_binary64_707 clear-num_binary64_759 pow-prod-down_binary64_831 *-commutative_binary64_691
Counts
4 → 270
Calls

8 calls:

48.0ms
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
14.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
8.0ms
(/.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))

series489.0ms (5.1%)

Counts
4 → 63
Calls

4 calls:

178.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a)))
148.0ms
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
97.0ms
(-.f64 (*.f64 b b) (*.f64 a a))
66.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
Compiler

Compiled 1842 to 1554 computations (15.6% saved)

simplify135.0ms (1.4%)

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049669384
149669384

prune530.0ms (5.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New32211333
Fresh101
Picked101
Done000
Total32411335
Error
0.0b
Counts
335 → 11
Compiler

Compiled 9617 to 4613 computations (52% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite150.0ms (1.6%)

Algorithm
rewrite-expression-head
Rules
289×times-frac_binary64_766
240×add-sqr-sqrt_binary64_782
221×*-un-lft-identity_binary64_760
129×add-cube-cbrt_binary64_795
78×add-exp-log_binary64_798
72×associate-*r*_binary64_700
50×add-cbrt-cube_binary64_796
45×difference-of-squares_binary64_729
41×distribute-lft-out--_binary64_712
37×associate-*l*_binary64_701
31×prod-exp_binary64_809
26×div-exp_binary64_811
23×div-inv_binary64_757
17×cbrt-unprod_binary64_793
16×cbrt-undiv_binary64_794 frac-times_binary64_770
13×cancel-sign-sub-inv_binary64_726 associate-/l*_binary64_705
11×pow1_binary64_821
10×associate-*l/_binary64_703 associate-*r/_binary64_702
flip--_binary64_735 flip3--_binary64_764
frac-sub_binary64_769
associate-/r/_binary64_706 add-log-exp_binary64_799
associate-/r*_binary64_704
rec-exp_binary64_810 pow-prod-down_binary64_831 1-exp_binary64_804
unswap-sqr_binary64_728 distribute-lft-out_binary64_711
*-commutative_binary64_691
diff-log_binary64_852 frac-2neg_binary64_771 flip3-+_binary64_763 associate-/l/_binary64_707 flip-+_binary64_734 clear-num_binary64_759 sub-neg_binary64_753
Counts
4 → 324
Calls

8 calls:

50.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
38.0ms
(*.f64 (/.f64 1 (+.f64 b a)) (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
14.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
8.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
0.0ms
(/.f64 1 (+.f64 b a))

series462.0ms (4.8%)

Counts
4 → 60
Calls

4 calls:

150.0ms
(*.f64 (/.f64 1 (+.f64 b a)) (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
130.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
116.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
66.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
Compiler

Compiled 1923 to 1563 computations (18.7% saved)

simplify127.0ms (1.3%)

Algorithm
egg-herbie
Counts
384 → 384
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049829763
149829763

prune606.0ms (6.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3795384
Fresh6410
Picked101
Done000
Total3869395
Error
0.0b
Counts
395 → 9
Compiler

Compiled 11189 to 6131 computations (45.2% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite144.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
281×times-frac_binary64_766
234×add-sqr-sqrt_binary64_782
213×*-un-lft-identity_binary64_760
123×add-cube-cbrt_binary64_795
71×associate-*r*_binary64_700
45×difference-of-squares_binary64_729
41×distribute-lft-out--_binary64_712
32×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
23×div-inv_binary64_757
19×associate-*l*_binary64_701
14×associate-/l*_binary64_705
13×cbrt-undiv_binary64_794 cancel-sign-sub-inv_binary64_726 div-exp_binary64_811
associate-/r*_binary64_704
associate-/l/_binary64_707
flip--_binary64_735 flip3--_binary64_764
associate-*l/_binary64_703 prod-exp_binary64_809 associate-/r/_binary64_706 add-log-exp_binary64_799 frac-times_binary64_770 cbrt-unprod_binary64_793 pow1_binary64_821
frac-sub_binary64_769
unswap-sqr_binary64_728
frac-2neg_binary64_771 distribute-lft-out_binary64_711 associate-*r/_binary64_702 clear-num_binary64_759
diff-log_binary64_852 flip3-+_binary64_763 flip-+_binary64_734 sub-neg_binary64_753 pow-prod-down_binary64_831 *-commutative_binary64_691
Counts
4 → 292
Calls

8 calls:

52.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
29.0ms
(/.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))) (+.f64 b a))
15.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
0.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))

series449.0ms (4.7%)

Counts
4 → 63
Calls

4 calls:

147.0ms
(/.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))) (+.f64 b a))
124.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
115.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
63.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
Compiler

Compiled 1815 to 1455 computations (19.8% saved)

simplify115.0ms (1.2%)

Algorithm
egg-herbie
Counts
355 → 355
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
050018785

prune506.0ms (5.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3523355
Fresh358
Picked101
Done000
Total3568364
Error
0.0b
Counts
364 → 8
Compiler

Compiled 9843 to 5085 computations (48.3% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a)))
0.1b
(/.f64 (*.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a))) (+.f64 b a))
0.0b
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.0b
(/.f64 (/.f64 1 2) (-.f64 b a))
0.0b
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.1b
(/.f64 (*.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a))) (+.f64 b a))
0.3b
(*.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a)))
0.4b
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64)

rewrite132.0ms (1.4%)

Algorithm
rewrite-expression-head
Rules
159×times-frac_binary64_766
144×add-sqr-sqrt_binary64_782
130×*-un-lft-identity_binary64_760
88×add-exp-log_binary64_798
74×associate-*r*_binary64_700
68×add-cube-cbrt_binary64_795
56×add-cbrt-cube_binary64_796
35×div-exp_binary64_811
31×prod-exp_binary64_809 difference-of-squares_binary64_729
27×distribute-lft-out--_binary64_712
21×associate-*l/_binary64_703
20×associate-*l*_binary64_701
19×cbrt-undiv_binary64_794 cbrt-unprod_binary64_793
16×div-inv_binary64_757
13×cancel-sign-sub-inv_binary64_726
11×pow1_binary64_821
associate-/l/_binary64_707 flip--_binary64_735 flip3--_binary64_764
add-log-exp_binary64_799 frac-times_binary64_770 frac-sub_binary64_769
associate-/r/_binary64_706 associate-/r*_binary64_704 rec-exp_binary64_810 pow-prod-down_binary64_831 1-exp_binary64_804
distribute-lft-out_binary64_711 associate-*r/_binary64_702 *-commutative_binary64_691
diff-log_binary64_852 unswap-sqr_binary64_728 frac-2neg_binary64_771 flip3-+_binary64_763 flip-+_binary64_734 associate-/l*_binary64_705 clear-num_binary64_759 sub-neg_binary64_753
Counts
4 → 229
Calls

8 calls:

35.0ms
(/.f64 (*.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a))) (+.f64 b a))
34.0ms
(*.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a)))
21.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64)
14.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.0ms
(/.f64 (/.f64 1 2) (-.f64 b a))

series446.0ms (4.6%)

Counts
4 → 51
Calls

4 calls:

148.0ms
(/.f64 (*.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a))) (+.f64 b a))
131.0ms
(*.f64 (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64) (/.f64 (/.f64 1 2) (-.f64 b a)))
99.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) PI.f64)
67.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
Compiler

Compiled 1362 to 1104 computations (18.9% saved)

simplify92.0ms (1%)

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
053316285

prune347.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2782280
Fresh347
Picked101
Done000
Total2826288
Error
0b
Counts
288 → 6
Compiler

Compiled 7239 to 4053 computations (44% saved)

simplify37.0ms (0.4%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (9.0ms)

IterNodesCost
05462705
15462705

regimes264.0ms (2.7%)

Compiler

Compiled 3430 to 2544 computations (25.8% saved)

bsearch0.0ms (0%)

regimes242.0ms (2.5%)

Compiler

Compiled 3330 to 2444 computations (26.6% saved)

bsearch0.0ms (0%)

regimes244.0ms (2.5%)

Compiler

Compiled 3278 to 2402 computations (26.7% saved)

bsearch0.0ms (0%)

regimes215.0ms (2.2%)

Compiler

Compiled 3058 to 2222 computations (27.3% saved)

bsearch0.0ms (0%)

regimes395.0ms (4.1%)

Compiler

Compiled 2872 to 2078 computations (27.6% saved)

bsearch0.0ms (0%)

regimes197.0ms (2.1%)

Compiler

Compiled 2834 to 2048 computations (27.7% saved)

bsearch0.0ms (0%)

regimes170.0ms (1.8%)

Compiler

Compiled 2454 to 1760 computations (28.3% saved)

bsearch0.0ms (0%)

regimes142.0ms (1.5%)

Compiler

Compiled 2084 to 1490 computations (28.5% saved)

bsearch0.0ms (0%)

regimes99.0ms (1%)

Compiler

Compiled 1490 to 1044 computations (29.9% saved)

bsearch0.0ms (0%)

regimes93.0ms (1%)

Compiler

Compiled 1392 to 962 computations (30.9% saved)

bsearch0.0ms (0%)

regimes86.0ms (0.9%)

Compiler

Compiled 1342 to 922 computations (31.3% saved)

bsearch0.0ms (0%)

regimes22.0ms (0.2%)

Accuracy

Total 0.2b remaining (99.3%)

Threshold costs 0.2b (99.3%)

Compiler

Compiled 202 to 134 computations (33.7% saved)

bsearch13.0ms (0.1%)

Compiler

Compiled 285 to 216 computations (24.2% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0122445
1122445

end0.0ms (0%)

sample2.1s (22.1%)

Algorithm
intervals
Results
438.0ms8000×body128valid
20.0ms367×body128invalid
Compiler

Compiled 2020 to 1504 computations (25.5% saved)

Pareto

-0.33268411896728417

Profiling

Loading profile data...