Details

Time bar (total: 5.4s)

analyze219.0ms (4.1%)

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)

sample26.0ms (0.5%)

Algorithm
1×intervals
Results
17.0ms256×body128valid
1.0ms14×body128invalid
Compiler

Compiled 43 to 37 computations (14% saved)

simplify212.0ms (4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0520929

prune9.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.9b

Counts
2 → 2
Compiler

Compiled 99 to 79 computations (20.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (/.f64 1 a) (/.f64 1 b))
0.6b
(/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a)))
3.4b
(-.f64 (*.f64 b b) (*.f64 a a))
8.9b
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite121.0ms (2.3%)

Algorithm
1×rewrite-expression-head
Rules
251×times-frac_binary64_773
178×add-sqr-sqrt_binary64_789
153×*-un-lft-identity_binary64_767
121×add-cube-cbrt_binary64_802
58×associate-*l*_binary64_708
46×difference-of-squares_binary64_736
40×cancel-sign-sub-inv_binary64_733
22×div-inv_binary64_764
19×associate-*r*_binary64_707
18×add-exp-log_binary64_805 add-cbrt-cube_binary64_803
14×distribute-rgt-in_binary64_717 distribute-lft-out--_binary64_719 distribute-lft-in_binary64_716
13×associate-/l*_binary64_712
8×add-log-exp_binary64_806
6×cbrt-undiv_binary64_801 pow1_binary64_828 flip--_binary64_742 div-exp_binary64_818 flip3--_binary64_771
4×associate-/r*_binary64_711 associate-/r/_binary64_713 sub-neg_binary64_760
3×frac-times_binary64_777 unswap-sqr_binary64_735 cbrt-unprod_binary64_800 prod-exp_binary64_816 frac-sub_binary64_776 associate-*r/_binary64_709
2×diff-log_binary64_859
1×frac-2neg_binary64_778 associate-/l/_binary64_714 *-commutative_binary64_698 associate-*l/_binary64_710 pow-prod-down_binary64_838 clear-num_binary64_766
Counts
4 → 270
Calls

4 calls:

51.0ms
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
20.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
10.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 a a))

series247.0ms (4.6%)

Counts
4 → 12
Calls

4 calls:

106.0ms
(*.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
76.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 (*.f64 b b) (*.f64 a a)))
44.0ms
(-.f64 (*.f64 b b) (*.f64 a a))
21.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify141.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
049477997
149477997

prune725.0ms (13.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2739282
Fresh101
Picked101
Done000
Total2759284

Merged error: 0.0b

Counts
284 → 9
Compiler

Compiled 14969 to 8597 computations (42.6% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite41.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
98×times-frac_binary64_773
79×*-un-lft-identity_binary64_767
60×add-exp-log_binary64_805
51×add-sqr-sqrt_binary64_789 add-cube-cbrt_binary64_802
39×add-cbrt-cube_binary64_803
29×div-exp_binary64_818
19×prod-exp_binary64_816
17×cbrt-undiv_binary64_801
14×distribute-lft-out_binary64_718 associate-/l*_binary64_712
10×cbrt-unprod_binary64_800
7×div-inv_binary64_764
6×1-exp_binary64_811
5×associate-/r*_binary64_711
2×frac-2neg_binary64_778 associate-/l/_binary64_714 associate-/r/_binary64_713 pow1_binary64_828 add-log-exp_binary64_806 clear-num_binary64_766
1×flip-+_binary64_741 associate-*l/_binary64_710 flip3-+_binary64_770
Counts
2 → 122
Calls

2 calls:

17.0ms
(/.f64 (*.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (*.f64 a b))
10.0ms
(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series150.0ms (2.8%)

Counts
2 → 6
Calls

2 calls:

79.0ms
(/.f64 (*.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (*.f64 a b))
71.0ms
(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify65.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
051762615

prune333.0ms (6.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1226128
Fresh628
Picked011
Done000
Total1289137

Merged error: 0.0b

Counts
137 → 9
Compiler

Compiled 6319 to 4170 computations (34% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite125.0ms (2.3%)

Algorithm
1×rewrite-expression-head
Rules
621×times-frac_binary64_773
410×*-un-lft-identity_binary64_767
278×add-sqr-sqrt_binary64_789 add-cube-cbrt_binary64_802
202×add-exp-log_binary64_805
120×div-exp_binary64_818
71×associate-/r*_binary64_711
66×distribute-lft-out_binary64_718
62×add-cbrt-cube_binary64_803
61×prod-exp_binary64_816
35×1-exp_binary64_811
31×cbrt-undiv_binary64_801
28×div-inv_binary64_764
15×rec-exp_binary64_817
13×cbrt-unprod_binary64_800
8×associate-/l*_binary64_712
6×associate-/r/_binary64_713
4×pow1_binary64_828
3×frac-2neg_binary64_778 associate-/l/_binary64_714 add-log-exp_binary64_806 clear-num_binary64_766
1×pow-flip_binary64_841 flip-+_binary64_741 associate-*l/_binary64_710 flip3-+_binary64_770 inv-pow_binary64_852
Counts
3 → 408
Calls

3 calls:

31.0ms
(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (*.f64 a b))
20.0ms
(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
9.0ms
(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

series215.0ms (4%)

Counts
3 → 9
Calls

3 calls:

82.0ms
(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (*.f64 a b))
68.0ms
(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
65.0ms
(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

simplify166.0ms (3.1%)

Algorithm
1×egg-herbie
Counts
417 → 417
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0495310043
1495310043

prune568.0ms (10.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4152417
Fresh347
Picked011
Done011
Total4188426

Merged error: 0b

Counts
426 → 8
Compiler

Compiled 10609 to 5776 computations (45.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite178.0ms (3.3%)

Algorithm
1×rewrite-expression-head
Rules
289×times-frac_binary64_773
240×add-sqr-sqrt_binary64_789
221×*-un-lft-identity_binary64_767
129×add-cube-cbrt_binary64_802
78×add-exp-log_binary64_805
72×associate-*r*_binary64_707
50×add-cbrt-cube_binary64_803
45×difference-of-squares_binary64_736
41×distribute-lft-out--_binary64_719
37×associate-*l*_binary64_708
31×prod-exp_binary64_816
26×div-exp_binary64_818
23×div-inv_binary64_764
17×cbrt-unprod_binary64_800
16×frac-times_binary64_777 cbrt-undiv_binary64_801
13×associate-/l*_binary64_712 cancel-sign-sub-inv_binary64_733
11×pow1_binary64_828
10×associate-*r/_binary64_709 associate-*l/_binary64_710
9×flip--_binary64_742 flip3--_binary64_771
7×frac-sub_binary64_776
6×associate-/r/_binary64_713 add-log-exp_binary64_806
5×associate-/r*_binary64_711
4×1-exp_binary64_811 rec-exp_binary64_817 pow-prod-down_binary64_838
3×unswap-sqr_binary64_735 distribute-lft-out_binary64_718
2×*-commutative_binary64_698
1×frac-2neg_binary64_778 associate-/l/_binary64_714 sub-neg_binary64_760 flip-+_binary64_741 diff-log_binary64_859 flip3-+_binary64_770 clear-num_binary64_766
Counts
4 → 324
Calls

4 calls:

60.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
44.0ms
(*.f64 (/.f64 1 (+.f64 b a)) (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
17.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))
10.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 b a))

series273.0ms (5.1%)

Counts
4 → 12
Calls

4 calls:

102.0ms
(*.f64 (/.f64 1 (+.f64 b a)) (*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a))))
84.0ms
(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 (/.f64 PI.f64 2) (-.f64 b a)))
63.0ms
(/.f64 (/.f64 PI.f64 2) (-.f64 b a))
24.0ms
(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify115.0ms (2.1%)

Algorithm
1×egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
050158389

prune538.0ms (10%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New3360336
Fresh055
Picked011
Done022
Total3368344

Merged error: 0b

Counts
344 → 8
Compiler

Compiled 9850 to 5481 computations (44.4% saved)

regimes38.0ms (0.7%)

Compiler

Compiled 280 to 236 computations (15.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01617
11617

end0.0ms (0%)

sample809.0ms (15.1%)

Algorithm
1×intervals
Results
449.0ms8000×body128valid
22.0ms347×body128invalid
Compiler

Compiled 171 to 143 computations (16.4% saved)

Profiling

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