Details

Time bar (total: 7.8s)

analyze223.0ms (2.8%)

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 32 to 20 computations (37.5% saved)

sample25.0ms (0.3%)

Algorithm
intervals
Results
16.0ms256×body128valid
Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify78.0ms (1%)

Algorithm
egg-herbie
Rules
705×unsub-neg_binary64
556×cancel-sign-sub-inv_binary64
344×+-commutative_binary64
342×distribute-rgt-in_binary64
317×sub-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01943
15543
215043
338943
4108343
5223343
6433643
7472443
8493043

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
0.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.2b
(-.f64 (+.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))))) 1)
Compiler

Compiled 93 to 57 computations (38.7% saved)

localize19.0ms (0.2%)

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)))))
0.0b
(*.f64 (*.f64 a a) (-.f64 1 a))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
0.6b
(*.f64 (*.f64 b b) (+.f64 3 a))

rewrite181.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
15×pow1_binary64 add-exp-log_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
14×add-cbrt-cube_binary64
10×add-cube-cbrt_binary64 associate-*r*_binary64
pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 cancel-sign-sub-inv_binary64
associate-*r/_binary64
Counts
4 → 87
Calls

4 calls:

12.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
9.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
9.0ms
(+.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)))))
5.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
Compiler

Compiled 3141 to 1575 computations (49.9% saved)

series235.0ms (3%)

Error
0.0b
Counts
4 → 54
Calls

4 calls:

92.0ms
(+.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)))))
55.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
24.0ms
(*.f64 (*.f64 b b) (+.f64 3 a))
16.0ms
(*.f64 (*.f64 a a) (-.f64 1 a))
Compiler

Compiled 3039 to 2229 computations (26.7% saved)

simplify183.0ms (2.3%)

Algorithm
egg-herbie
Rules
532×associate-+l+_binary64
343×associate-+r+_binary64
267×associate-*l*_binary64
226×exp-prod_binary64
217×associate-*r*_binary64 +-commutative_binary64
Counts
141 → 116
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02152929
15852614
218682518
342532514
449482514
549992514
649422514

prune115.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1133116
Fresh000
Picked101
Done000
Total1143117
Error
0.0b
Counts
117 → 3
Alt Table
StatusErrorProgram
39.0b
(-.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) 3)) (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3))) (-.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2)))))) 1)
14.5b
(-.f64 (+.f64 (*.f64 (pow.f64 a 3) (+.f64 a -4)) (*.f64 (*.f64 a a) (+.f64 (*.f64 2 (*.f64 b b)) 4))) 1)
0.0b
(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a))))) (+.f64 (pow.f64 a 4) (*.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3)))))) 1)
Compiler

Compiled 2548 to 1358 computations (46.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (*.f64 a a) (pow.f64 a 3))
0.0b
(+.f64 (pow.f64 a 4) (*.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3))))
0.0b
(*.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3)))
1.0b
(*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a)))))

rewrite276.0ms (3.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
60×cancel-sign-sub-inv_binary64
31×add-sqr-sqrt_binary64
27×distribute-rgt-in_binary64 distribute-lft-in_binary64
26×associate-+r+_binary64
22×add-cube-cbrt_binary64 *-un-lft-identity_binary64
Counts
4 → 141
Calls

4 calls:

12.0ms
(*.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3)))
10.0ms
(-.f64 (*.f64 a a) (pow.f64 a 3))
8.0ms
(+.f64 (pow.f64 a 4) (*.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3))))
8.0ms
(*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a)))))
Compiler

Compiled 5026 to 3391 computations (32.5% saved)

series145.0ms (1.8%)

Error
0.0b
Counts
4 → 31
Calls

4 calls:

44.0ms
(*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a)))))
29.0ms
(+.f64 (pow.f64 a 4) (*.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3))))
21.0ms
(*.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3)))
19.0ms
(-.f64 (*.f64 a a) (pow.f64 a 3))
Compiler

Compiled 2091 to 1608 computations (23.1% saved)

simplify162.0ms (2.1%)

Algorithm
egg-herbie
Rules
701×exp-prod_binary64
432×cancel-sign-sub-inv_binary64
309×associate-*l*_binary64
297×associate-*r*_binary64
292×distribute-rgt-out_binary64
Counts
172 → 143
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02122833
15222584
221032569
342692545
449522545
549512545

prune142.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1421143
Fresh112
Picked011
Done000
Total1433146
Error
0.0b
Counts
146 → 3
Alt Table
StatusErrorProgram
39.0b
(-.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) 3)) (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3))) (-.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2)))))) 1)
0.5b
(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a))))) (*.f64 (pow.f64 a 3) (+.f64 a -4)))) 1)
0.0b
(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a))))) (+.f64 (pow.f64 a 4) (*.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3)))))) 1)
Compiler

Compiled 3070 to 2088 computations (32% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a))))) (*.f64 (pow.f64 a 3) (+.f64 a -4))))
0.0b
(*.f64 a (+.f64 4 (*.f64 2 a)))
0.1b
(*.f64 (pow.f64 a 3) (+.f64 a -4))
1.0b
(*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a)))))

rewrite198.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
21×add-sqr-sqrt_binary64
16×add-exp-log_binary64 associate-*l*_binary64
15×*-un-lft-identity_binary64
13×add-cbrt-cube_binary64
11×pow1_binary64 add-cube-cbrt_binary64
Counts
4 → 95
Calls

4 calls:

12.0ms
(+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a))))) (*.f64 (pow.f64 a 3) (+.f64 a -4))))
8.0ms
(*.f64 (pow.f64 a 3) (+.f64 a -4))
8.0ms
(*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a)))))
6.0ms
(*.f64 a (+.f64 4 (*.f64 2 a)))
Compiler

Compiled 3162 to 2264 computations (28.4% saved)

series193.0ms (2.5%)

Error
0.0b
Counts
4 → 43
Calls

4 calls:

82.0ms
(+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a))))) (*.f64 (pow.f64 a 3) (+.f64 a -4))))
44.0ms
(*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a)))))
16.0ms
(*.f64 (pow.f64 a 3) (+.f64 a -4))
16.0ms
(*.f64 a (+.f64 4 (*.f64 2 a)))
Compiler

Compiled 2231 to 1764 computations (20.9% saved)

simplify135.0ms (1.7%)

Algorithm
egg-herbie
Rules
557×exp-prod_binary64
426×associate-*l*_binary64
371×associate-*r*_binary64
339×cancel-sign-sub-inv_binary64
262×unswap-sqr_binary64
Counts
138 → 109
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02193048
16172622
227412616
345282592
449512592

prune125.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1090109
Fresh011
Picked011
Done011
Total1093112
Error
0.0b
Counts
112 → 3
Alt Table
StatusErrorProgram
39.0b
(-.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) 3)) (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3))) (-.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2)))))) 1)
0.5b
(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a))))) (*.f64 (pow.f64 a 3) (+.f64 a -4)))) 1)
0.0b
(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a))))) (+.f64 (pow.f64 a 4) (*.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3)))))) 1)
Compiler

Compiled 2474 to 1729 computations (30.1% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b
(*.f64 (+.f64 a 3) (*.f64 b b))
2.6b
(+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) 3))
5.6b
(+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3))) (-.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2)))))
45.4b
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) 3)) (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3))) (-.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2))))))

rewrite380.0ms (4.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
48×distribute-rgt-in_binary64 distribute-lft-in_binary64
44×associate-+r+_binary64
34×*-un-lft-identity_binary64
32×cancel-sign-sub-inv_binary64
23×add-sqr-sqrt_binary64
Counts
4 → 124
Calls

4 calls:

19.0ms
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) 3)) (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3))) (-.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2))))))
15.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3))) (-.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2)))))
11.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) 3))
8.0ms
(*.f64 (+.f64 a 3) (*.f64 b b))
Compiler

Compiled 14334 to 7029 computations (51% saved)

series2.1s (26.5%)

Error
0.0b
Counts
4 → 58
Calls

4 calls:

1.6s
(/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) 3)) (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3))) (-.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2))))))
146.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3))) (-.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2)))))
81.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) 3))
37.0ms
(*.f64 (+.f64 a 3) (*.f64 b b))
Compiler

Compiled 20084 to 15413 computations (23.3% saved)

simplify318.0ms (4.1%)

Algorithm
egg-herbie
Rules
461×associate-/l*_binary64
436×times-frac_binary64
232×+-commutative_binary64
225×*-commutative_binary64
181×associate-+r+_binary64
Counts
182 → 155
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
080921214
1232120095
2511420095

prune411.0ms (5.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1550155
Fresh000
Picked011
Done022
Total1553158
Error
0.0b
Counts
158 → 3
Alt Table
StatusErrorProgram
39.0b
(-.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 6) (pow.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) 3)) (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3))) (-.f64 (*.f64 4 (+.f64 (*.f64 (+.f64 a 3) (*.f64 b b)) (-.f64 (*.f64 a a) (pow.f64 a 3)))) (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) 2)))))) 1)
0.5b
(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a))))) (*.f64 (pow.f64 a 3) (+.f64 a -4)))) 1)
0.0b
(-.f64 (+.f64 (pow.f64 b 4) (+.f64 (*.f64 (*.f64 b b) (+.f64 12 (*.f64 a (+.f64 4 (*.f64 2 a))))) (+.f64 (pow.f64 a 4) (*.f64 4 (-.f64 (*.f64 a a) (pow.f64 a 3)))))) 1)
Compiler

Compiled 18528 to 10683 computations (42.3% saved)

regimes1.2s (15.6%)

Accuracy

Total 0.0b remaining (32.2%)

Threshold costs 0.0b (32.2%)

Compiler

Compiled 23162 to 15296 computations (34% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
1-exp_binary64 neg-mul-1_binary64 neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02555
14255
24655
34855
44955
54755

end1.0ms (0%)

Compiler

Compiled 39 to 29 computations (25.6% saved)

sample914.0ms (11.7%)

Algorithm
intervals
Results
516.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 226 to 146 computations (35.4% saved)

Profiling

Loading profile data...