Details

Time bar (total: 4.4s)

analyze123.0ms (2.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
0%50%50%4
0%50%50%5
6.2%31.2%62.5%6
9.4%28.1%62.5%7
14%17.2%68.8%8
14.8%16.4%68.8%9
17.6%9.8%72.7%10
18.1%8.8%73.1%11
19.6%5.2%75.2%12
20%4.5%75.5%13
20.7%2.7%76.6%14
Compiler

Compiled 23 to 20 computations (13% saved)

sample1.4s (32%)

Results
1.1s8256×body128valid
68.0ms559×body128invalid
Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify99.0ms (2.3%)

Algorithm
egg-herbie
Rules
1035×fma-def_binary64
742×fma-neg_binary64
189×distribute-rgt-in_binary64
173×cancel-sign-sub-inv_binary64
156×distribute-lft-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01524
13221
27519
316819
435819
567819
690119
7144619
8191419
9187319
10191619
11191519
12191219
13246519
14246519
15232119

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.1b
(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
Compiler

Compiled 109 to 91 computations (16.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 a 9 -3)
0.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
0.1b
(sqrt.f64 (fma.f64 a 9 -3))
0.2b
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

series56.0ms (1.3%)

Counts
4 → 50
Calls

4 calls:

26.0ms
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
22.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
6.0ms
(sqrt.f64 (fma.f64 a 9 -3))
1.0ms
(fma.f64 a 9 -3)

rewrite76.0ms (1.7%)

Algorithm
batch-egg-rewrite
Rules
492×prod-diff_binary64
237×log1p-udef_binary64
135×add-sqr-sqrt_binary64
132×log1p-expm1-u_binary64
132×expm1-log1p-u_binary64
Counts
4 → 131
Calls

4 calls:

71.0ms
(fma.f64 a 9 -3)
71.0ms
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
71.0ms
(sqrt.f64 (fma.f64 a 9 -3))
71.0ms
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01341
128640
2348140
3483740
000
100

simplify74.0ms (1.7%)

Algorithm
egg-herbie
Rules
689×fma-neg_binary64
397×associate-+l+_binary64
381×fma-def_binary64
282×associate-/l*_binary64
276×times-frac_binary64
Counts
181 → 167
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01001065
13201019
21084867
34794849
45374849

prune295.0ms (6.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1607167
Fresh101
Picked101
Done000
Total1627169
Error
0.0b
Counts
169 → 7
Alt Table
StatusErrorProgram
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
24.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) 2)))
9.4b
(pow.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))) 2)
1.4b
(pow.f64 (cbrt.f64 (*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))) 3)
0.1b
(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))
0.1b
(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
Compiler

Compiled 3687 to 2872 computations (22.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 a 9 -3)
0.1b
(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
0.1b
(fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)
0.1b
(pow.f64 (fma.f64 a 9 -3) -1/2)

series174.0ms (4%)

Counts
3 → 60
Calls

3 calls:

100.0ms
(fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)
69.0ms
(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
4.0ms
(pow.f64 (fma.f64 a 9 -3) -1/2)

rewrite54.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
503×log-prod_binary64
225×expm1-udef_binary64
225×log1p-udef_binary64
184×log-pow_binary64
129×add-sqr-sqrt_binary64
Counts
3 → 79
Calls

3 calls:

52.0ms
(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
52.0ms
(fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)
52.0ms
(pow.f64 (fma.f64 a 9 -3) -1/2)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01338
127538
2293338
3478138
000
100

simplify101.0ms (2.3%)

Algorithm
egg-herbie
Rules
362×associate-*l*_binary64
352×times-frac_binary64
342×associate-*r*_binary64
251×sub-neg_binary64
237×fma-neg_binary64
Counts
139 → 161
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01772271
15462155
216881801
347461519
449751519

prune426.0ms (9.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1940194
Fresh066
Picked011
Done000
Total1947201
Error
0.0b
Counts
201 → 7
Alt Table
StatusErrorProgram
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
24.1b
(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) 2)))
9.4b
(pow.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))) 2)
1.4b
(pow.f64 (cbrt.f64 (*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))) 3)
0.1b
(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3))
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2))))
0.1b
(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
Compiler

Compiled 4646 to 3724 computations (19.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
0.2b
(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
0.3b
(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
0.3b
(/.f64 1 (fma.f64 9 a -3))

series108.0ms (2.5%)

Counts
4 → 36
Calls

4 calls:

72.0ms
(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
26.0ms
(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
7.0ms
(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
2.0ms
(/.f64 1 (fma.f64 9 a -3))

rewrite74.0ms (1.7%)

Algorithm
batch-egg-rewrite
Rules
546×log-prod_binary64
227×expm1-udef_binary64
227×log1p-udef_binary64
209×prod-diff_binary64
194×log-pow_binary64
Counts
4 → 148
Calls

4 calls:

71.0ms
(sqrt.f64 (/.f64 1 (fma.f64 9 a -3)))
71.0ms
(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3)) -1/3)
71.0ms
(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (+.f64 a -1/3))
71.0ms
(/.f64 1 (fma.f64 9 a -3))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01354
127846
2311046
3554046
000
100

simplify57.0ms (1.3%)

Algorithm
egg-herbie
Rules
782×fma-neg_binary64
635×fma-def_binary64
457×times-frac_binary64
317×associate-/l*_binary64
204×associate-*l*_binary64
Counts
184 → 190
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01321003
1414851
21335772
34839766
45464766

prune219.0ms (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1873190
Fresh415
Picked101
Done011
Total1925197
Error
0b
Counts
197 → 5
Alt Table
StatusErrorProgram
22.1b
(+.f64 a (fma.f64 rand (cbrt.f64 (pow.f64 (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 9 a -3))) 3)) -1/3))
0.1b
(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (expm1.f64 (log1p.f64 (pow.f64 (fma.f64 9 a -3) -1/2))) (+.f64 a -1/3)) -1/3))
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
0.1b
(+.f64 a (fma.f64 rand (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 9 a -3))) -1/3))
Compiler

Compiled 4611 to 3571 computations (22.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 9 a -3)
0.1b
(pow.f64 (fma.f64 9 a -3) -1/2)
0.2b
(fma.f64 rand (*.f64 (expm1.f64 (log1p.f64 (pow.f64 (fma.f64 9 a -3) -1/2))) (+.f64 a -1/3)) -1/3)
0.3b
(*.f64 (expm1.f64 (log1p.f64 (pow.f64 (fma.f64 9 a -3) -1/2))) (+.f64 a -1/3))

series44.0ms (1%)

Counts
4 → 44
Calls

4 calls:

28.0ms
(fma.f64 rand (*.f64 (expm1.f64 (log1p.f64 (pow.f64 (fma.f64 9 a -3) -1/2))) (+.f64 a -1/3)) -1/3)
9.0ms
(*.f64 (expm1.f64 (log1p.f64 (pow.f64 (fma.f64 9 a -3) -1/2))) (+.f64 a -1/3))
5.0ms
(pow.f64 (fma.f64 9 a -3) -1/2)
1.0ms
(fma.f64 9 a -3)

rewrite115.0ms (2.6%)

Algorithm
batch-egg-rewrite
Rules
273×prod-diff_binary64
238×expm1-udef_binary64
238×log1p-udef_binary64
225×fma-udef_binary64
199×log-pow_binary64
Counts
4 → 123
Calls

4 calls:

113.0ms
(fma.f64 9 a -3)
113.0ms
(pow.f64 (fma.f64 9 a -3) -1/2)
113.0ms
(fma.f64 rand (*.f64 (expm1.f64 (log1p.f64 (pow.f64 (fma.f64 9 a -3) -1/2))) (+.f64 a -1/3)) -1/3)
113.0ms
(*.f64 (expm1.f64 (log1p.f64 (pow.f64 (fma.f64 9 a -3) -1/2))) (+.f64 a -1/3))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01445
128545
2316745
3494045
4495845
5482645
000
100

simplify60.0ms (1.4%)

Algorithm
egg-herbie
Rules
588×fma-def_binary64
581×fma-neg_binary64
449×times-frac_binary64
307×associate-/l*_binary64
298×associate-+l+_binary64
Counts
167 → 171
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01311221
13891050
21181933
34609927
45077927

prune197.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1710171
Fresh033
Picked011
Done011
Total1715176
Error
0b
Counts
176 → 5
Alt Table
StatusErrorProgram
22.1b
(+.f64 a (fma.f64 rand (cbrt.f64 (pow.f64 (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 9 a -3))) 3)) -1/3))
0.1b
(*.f64 (-.f64 a 1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))
0.1b
(+.f64 a (fma.f64 rand (*.f64 (expm1.f64 (log1p.f64 (pow.f64 (fma.f64 9 a -3) -1/2))) (+.f64 a -1/3)) -1/3))
0.2b
(*.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))
0.1b
(+.f64 a (fma.f64 rand (/.f64 (+.f64 a -1/3) (sqrt.f64 (fma.f64 9 a -3))) -1/3))
Compiler

Compiled 4485 to 3542 computations (21% saved)

regimes487.0ms (11.1%)

Accuracy

Total 0.1b remaining (72.9%)

Threshold costs 0.1b (72.9%)

Counts
117 → 1
Compiler

Compiled 8306 to 6630 computations (20.2% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01525
11825
21825

end98.0ms (2.2%)

Compiler

Compiled 124 to 98 computations (21% saved)

Profiling

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