Details

Time bar (total: 2.5min)

analyze127.0ms (0.1%)

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
25%74.9%0.1%5
25%68.7%6.3%6
25%53.1%22%7
25%46.8%28.2%8
25%33.6%41.5%9
28.1%18%54%10
31.6%12.1%56.3%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 30 to 20 computations (33.3% saved)

sample24.0ms (0%)

Algorithm
intervals
Results
16.0ms256×body80valid
Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify63.0ms (0%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0514743

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.1b

Counts
2 → 1
Compiler

Compiled 58 to 38 computations (34.5% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b
(*.f64 (*.f64 a a) (-.f64 1 a))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.4b
(*.f64 (*.f64 b b) (+.f64 3 a))

rewrite42.0ms (0%)

Algorithm
rewrite-expression-head
Rules
15×pow1_binary64 add-exp-log_binary64
14×add-cbrt-cube_binary64
13×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
10×associate-*r*_binary64
add-cube-cbrt_binary64
pow-prod-down_binary64 add-log-exp_binary64 cbrt-unprod_binary64 prod-exp_binary64
associate-*r/_binary64 insert-posit16
pow-unpow_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unpow-prod-down_binary64
flip3-+_binary64 sub-neg_binary64 associate-*l*_binary64 unswap-sqr_binary64 difference-of-squares_binary64 flip-+_binary64 associate-+r+_binary64 *-commutative_binary64
pow-to-exp_binary64 flip3--_binary64 distribute-lft-out_binary64 unpow2_binary64 pow-pow_binary64 sqr-pow_binary64 distribute-lft-out--_binary64 +-commutative_binary64 flip--_binary64 pow-exp_binary64 sum-log_binary64
Counts
4 → 85
Calls

4 calls:

12.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
11.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
10.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
6.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

series323.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

144.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
69.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
56.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
53.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))

simplify63.0ms (0%)

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
052271816

prune146.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New94397
Fresh000
Picked101
Done000
Total95398

Merged error: 0.0b

Counts
98 → 3
Compiler

Compiled 3505 to 1791 computations (48.9% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 b b) (*.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
0.1b
(*.f64 (*.f64 a a) (-.f64 1 a))
0.4b
(*.f64 (*.f64 b b) (+.f64 3 a))
1.4b
(*.f64 (*.f64 b b) (*.f64 a a))

rewrite74.0ms (0%)

Algorithm
rewrite-expression-head
Rules
42×pow1_binary64
32×associate-*r/_binary64
26×add-exp-log_binary64 add-cbrt-cube_binary64
20×pow-prod-down_binary64 frac-add_binary64
14×flip3-+_binary64 cbrt-unprod_binary64 prod-exp_binary64 flip-+_binary64
13×add-log-exp_binary64
11×*-un-lft-identity_binary64 associate-*r*_binary64 add-sqr-sqrt_binary64
add-cube-cbrt_binary64 sum-log_binary64
flip3--_binary64 flip--_binary64
pow-prod-up_binary64 pow-plus_binary64 insert-posit16
distribute-lft-in_binary64 associate-*l*_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 *-commutative_binary64
sub-neg_binary64 difference-of-squares_binary64 pow-sqr_binary64 associate-+r+_binary64 pow2_binary64
distribute-lft-out_binary64 associate-+l+_binary64 distribute-lft-out--_binary64 +-commutative_binary64
Counts
4 → 111
Calls

4 calls:

34.0ms
(+.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 b b) (*.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
11.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
11.0ms
(*.f64 (*.f64 b b) (*.f64 a a))
10.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))

series325.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

143.0ms
(+.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 b b) (*.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a)))))
79.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
52.0ms
(*.f64 (*.f64 b b) (*.f64 a a))
51.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))

simplify158.0ms (0.1%)

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (109.0ms)

IterNodesCost
049364589
149364589

prune306.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1221123
Fresh022
Picked011
Done000
Total1224126

Merged error: 0b

Counts
126 → 4
Compiler

Compiled 6549 to 3842 computations (41.3% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (*.f64 b b) (+.f64 3 a))
0.4b
(*.f64 (*.f64 b b) (+.f64 3 a))
8.8b
(sqrt.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (+.f64 3 a)) (-.f64 (*.f64 a a) (pow.f64 a 3))))))
8.8b
(sqrt.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (+.f64 3 a)) (-.f64 (*.f64 a a) (pow.f64 a 3))))))

rewrite45.0ms (0%)

Algorithm
rewrite-expression-head
Rules
16×pow1_binary64
14×add-exp-log_binary64 add-cbrt-cube_binary64
12×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
associate-*r*_binary64 add-cube-cbrt_binary64
pow-prod-down_binary64 cbrt-unprod_binary64 prod-exp_binary64 sqrt-prod_binary64
flip3-+_binary64 add-log-exp_binary64 associate-*r/_binary64 insert-posit16 flip-+_binary64 sqrt-div_binary64
pow1/2_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 associate-*l*_binary64 distribute-rgt-in_binary64 sqrt-pow1_binary64 unswap-sqr_binary64 rem-sqrt-square_binary64 *-commutative_binary64
Counts
4 → 82
Calls

4 calls:

12.0ms
(sqrt.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (+.f64 3 a)) (-.f64 (*.f64 a a) (pow.f64 a 3))))))
11.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
10.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
10.0ms
(sqrt.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (+.f64 3 a)) (-.f64 (*.f64 a a) (pow.f64 a 3))))))

series402.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

152.0ms
(sqrt.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (+.f64 3 a)) (-.f64 (*.f64 a a) (pow.f64 a 3))))))
148.0ms
(sqrt.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 b b) (+.f64 3 a)) (-.f64 (*.f64 a a) (pow.f64 a 3))))))
54.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
48.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))

simplify129.0ms (0.1%)

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (96.0ms)

IterNodesCost
052132456

prune260.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New94094
Fresh022
Picked011
Done011
Total94498

Merged error: 0b

Counts
98 → 4
Compiler

Compiled 6408 to 3267 computations (49% saved)

localize43.0ms (0%)

Local error

Found 4 expressions with local error:

2.2b
(*.f64 (pow.f64 b 4) (pow.f64 a 4))
2.2b
(*.f64 (+.f64 (pow.f64 a 3) 27) (*.f64 (*.f64 b b) (+.f64 a 1)))
4.9b
(+.f64 (*.f64 (*.f64 (+.f64 9 (*.f64 a (-.f64 a 3))) (+.f64 a 1)) (-.f64 (*.f64 (*.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (*.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (*.f64 (+.f64 (*.f64 a (*.f64 (-.f64 a (pow.f64 a 3)) (+.f64 9 (*.f64 a (-.f64 a 3))))) (*.f64 (+.f64 (pow.f64 a 3) 27) (*.f64 (*.f64 b b) (+.f64 a 1)))) (*.f64 4 (-.f64 (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))))
39.6b
(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 9 (*.f64 a (-.f64 a 3))) (+.f64 a 1)) (-.f64 (*.f64 (*.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (*.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (*.f64 (+.f64 (*.f64 a (*.f64 (-.f64 a (pow.f64 a 3)) (+.f64 9 (*.f64 a (-.f64 a 3))))) (*.f64 (+.f64 (pow.f64 a 3) 27) (*.f64 (*.f64 b b) (+.f64 a 1)))) (*.f64 4 (-.f64 (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))) (*.f64 (*.f64 (+.f64 9 (*.f64 a (-.f64 a 3))) (+.f64 a 1)) (-.f64 (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))

rewrite5.5s (3.7%)

Algorithm
rewrite-expression-head
Rules
32752×associate-*r/_binary64
28080×frac-times_binary64
20384×frac-add_binary64
18614×flip3-+_binary64 flip-+_binary64
14040×associate-*l/_binary64
10837×flip3--_binary64 flip--_binary64
5202×associate-/l/_binary64
34×add-exp-log_binary64
26×associate-/r/_binary64
24×add-cbrt-cube_binary64
23×add-sqr-sqrt_binary64
18×prod-exp_binary64
13×*-un-lft-identity_binary64 pow1_binary64
12×unpow-prod-down_binary64
11×add-cube-cbrt_binary64 associate-*l*_binary64
10×cbrt-unprod_binary64
distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64
associate-*r*_binary64 sqr-pow_binary64
pow-prod-down_binary64
pow-to-exp_binary64 add-log-exp_binary64 sub-neg_binary64 pow-exp_binary64
insert-posit16 associate-+r+_binary64
cbrt-undiv_binary64 associate-/l*_binary64 times-frac_binary64 div-exp_binary64
associate-+l+_binary64 *-commutative_binary64
associate-/r*_binary64 distribute-lft-out_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 10548
Calls

4 calls:

623.0ms
(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 9 (*.f64 a (-.f64 a 3))) (+.f64 a 1)) (-.f64 (*.f64 (*.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (*.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (*.f64 (+.f64 (*.f64 a (*.f64 (-.f64 a (pow.f64 a 3)) (+.f64 9 (*.f64 a (-.f64 a 3))))) (*.f64 (+.f64 (pow.f64 a 3) 27) (*.f64 (*.f64 b b) (+.f64 a 1)))) (*.f64 4 (-.f64 (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))) (*.f64 (*.f64 (+.f64 9 (*.f64 a (-.f64 a 3))) (+.f64 a 1)) (-.f64 (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
385.0ms
(+.f64 (*.f64 (*.f64 (+.f64 9 (*.f64 a (-.f64 a 3))) (+.f64 a 1)) (-.f64 (*.f64 (*.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (*.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (*.f64 (+.f64 (*.f64 a (*.f64 (-.f64 a (pow.f64 a 3)) (+.f64 9 (*.f64 a (-.f64 a 3))))) (*.f64 (+.f64 (pow.f64 a 3) 27) (*.f64 (*.f64 b b) (+.f64 a 1)))) (*.f64 4 (-.f64 (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))))
20.0ms
(*.f64 (+.f64 (pow.f64 a 3) 27) (*.f64 (*.f64 b b) (+.f64 a 1)))
9.0ms
(*.f64 (pow.f64 b 4) (pow.f64 a 4))

series2.0s (1.3%)

Counts
4 → 12
Calls

4 calls:

1.2s
(+.f64 (*.f64 (*.f64 (+.f64 9 (*.f64 a (-.f64 a 3))) (+.f64 a 1)) (-.f64 (*.f64 (*.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (*.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (*.f64 (+.f64 (*.f64 a (*.f64 (-.f64 a (pow.f64 a 3)) (+.f64 9 (*.f64 a (-.f64 a 3))))) (*.f64 (+.f64 (pow.f64 a 3) 27) (*.f64 (*.f64 b b) (+.f64 a 1)))) (*.f64 4 (-.f64 (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))))
670.0ms
(/.f64 (+.f64 (*.f64 (*.f64 (+.f64 9 (*.f64 a (-.f64 a 3))) (+.f64 a 1)) (-.f64 (*.f64 (*.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (*.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (*.f64 (+.f64 (*.f64 a (*.f64 (-.f64 a (pow.f64 a 3)) (+.f64 9 (*.f64 a (-.f64 a 3))))) (*.f64 (+.f64 (pow.f64 a 3) 27) (*.f64 (*.f64 b b) (+.f64 a 1)))) (*.f64 4 (-.f64 (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))) (*.f64 (*.f64 (+.f64 9 (*.f64 a (-.f64 a 3))) (+.f64 a 1)) (-.f64 (*.f64 (*.f64 (*.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
98.0ms
(*.f64 (pow.f64 b 4) (pow.f64 a 4))
84.0ms
(*.f64 (+.f64 (pow.f64 a 3) 27) (*.f64 (*.f64 b b) (+.f64 a 1)))

simplify22.8s (15.2%)

Algorithm
egg-herbie
Counts
10560 → 10560
Iterations

Useful iterations: 0 (584.0ms)

IterNodesCost
0270523975867

prune2.0min (78.1%)

Profiling

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