Details

Time bar (total: 3.6s)

analyze63.0ms (1.7%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
50%50%0.1%3
50%50%0.1%4
62.4%37.5%0.1%5
62.4%31.2%6.3%6
68.7%21.9%9.5%7
68.7%17.2%14.1%8
71.8%11.7%16.5%9
71.8%9%19.2%10
73.4%6%20.6%11
73.4%4.6%22%12
74.1%3.1%22.8%13
74.1%2.3%23.5%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.9s (54.1%)

Results
737.0ms1521×body2048valid
558.0ms1798×body1024valid
285.0ms3162×body128valid
244.0ms1133×body512valid
96.0ms642×body256valid
12.0ms141×body128invalid
Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess41.0ms (1.1%)

Algorithm
2×egg-herbie
Rules
736×unswap-sqr_binary64
572×associate-*l*_binary64
458×associate-*r*_binary64
278×fma-def_binary64
262×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01012
12212
23012
34812
49812
525612
687512
7391312
022
122
Stop Event
1×unsound
1×node limit
Symmetry

(sort a x)

Compiler

Compiled 8 to 6 computations (25% saved)

simplify19.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
440×unswap-sqr_binary64
329×associate-*l*_binary64
275×associate-+l+_binary64
252×associate-*r*_binary64
201×associate-/l/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
076
1166
2236
3356
4706
51756
65566
723316
Stop Event
1×node limit
Counts
1 → 2

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.0b
(expm1.f64 (*.f64 a x))
Compiler

Compiled 24 to 15 computations (37.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(expm1.f64 (*.f64 a x))

series5.0ms (0.1%)

Counts
1 → 24
Calls

6 calls:

2.0ms
(expm1.f64 (*.f64 a x))
a
0
1.0ms
(expm1.f64 (*.f64 a x))
x
0
0.0ms
(expm1.f64 (*.f64 a x))
a
-inf
0.0ms
(expm1.f64 (*.f64 a x))
a
inf
0.0ms
(expm1.f64 (*.f64 a x))
x
inf

rewrite29.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
405×log1p-expm1-u_binary64
405×expm1-log1p-u_binary64
342×pow1_binary64
285×unpow-prod-down_binary64
236×log-prod_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
1966
211236
Stop Event
1×node limit
Counts
1 → 36

simplify41.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
882×fma-def_binary64
844×distribute-lft-out_binary64
307×*-commutative_binary64
300×unswap-sqr_binary64
172×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
030284
187284
2242278
31040262
43195248
54880248
Stop Event
1×node limit
Counts
60 → 45

prune31.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New41445
Fresh000
Picked011
Done000
Total41546
Error
0.0b
Counts
46 → 5
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (*.f64 a x))
41.8b
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
25.4b
(fma.f64 x (fma.f64 x (*.f64 1/2 (*.f64 a a)) a) (fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4))))
46.6b
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)
▶0.7b
(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2))
Compiler

Compiled 640 to 306 computations (52.2% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
✓0.1b
(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2))
✓0.3b
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2)
✓10.1b
(cbrt.f64 (expm1.f64 (*.f64 a x)))

series223.0ms (6.2%)

Counts
3 → 56
Calls

18 calls:

27.0ms
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2)
x
inf
26.0ms
(cbrt.f64 (expm1.f64 (*.f64 a x)))
a
-inf
25.0ms
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2)
a
inf
25.0ms
(cbrt.f64 (expm1.f64 (*.f64 a x)))
x
-inf
24.0ms
(pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2)
a
-inf

rewrite38.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
595×log1p-expm1-u_binary64
595×expm1-log1p-u_binary64
326×log-prod_binary64
126×expm1-udef_binary64
126×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0925
117825
2175025
Stop Event
1×node limit
Counts
3 → 69

simplify36.0ms (1%)

Algorithm
1×egg-herbie
Rules
900×fma-def_binary64
846×distribute-lft-out_binary64
320×unswap-sqr_binary64
316×*-commutative_binary64
180×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
034588
1101588
2271582
31120566
43417552
Stop Event
1×node limit
Counts
125 → 80

prune110.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1980198
Fresh033
Picked011
Done011
Total1985203
Error
0.0b
Counts
203 → 5
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (*.f64 a x))
41.8b
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
▶25.4b
(fma.f64 x (fma.f64 x (*.f64 1/2 (*.f64 a a)) a) (fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4))))
46.6b
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)
✓0.7b
(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2))
Compiler

Compiled 3709 to 1427 computations (61.5% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(pow.f64 (*.f64 a x) 3)
✓0.2b
(fma.f64 x (fma.f64 x (*.f64 1/2 (*.f64 a a)) a) (fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓5.0b
(fma.f64 x (*.f64 1/2 (*.f64 a a)) a)
✓13.8b
(fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4)))

series65.0ms (1.8%)

Counts
4 → 96
Calls

24 calls:

9.0ms
(fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4)))
x
0
5.0ms
(pow.f64 (*.f64 a x) 3)
a
inf
4.0ms
(fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4)))
a
-inf
4.0ms
(fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4)))
x
-inf
4.0ms
(fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4)))
a
inf

rewrite65.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
303×prod-diff_binary64
286×log1p-udef_binary64
164×add-sqr-sqrt_binary64
163×log1p-expm1-u_binary64
163×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01772
136172
2400572
Stop Event
1×node limit
Counts
4 → 97

simplify66.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
1298×distribute-lft-out_binary64
849×fma-def_binary64
316×*-commutative_binary64
304×unswap-sqr_binary64
183×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0341734
1971698
22601664
310491626
430811368
545971368
Stop Event
1×node limit
Counts
193 → 119

prune102.0ms (2.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1190119
Fresh022
Picked011
Done022
Total1195124
Error
0.0b
Counts
124 → 5
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (*.f64 a x))
▶41.8b
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
✓25.4b
(fma.f64 x (fma.f64 x (*.f64 1/2 (*.f64 a a)) a) (fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4))))
46.6b
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)
✓0.7b
(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2))
Compiler

Compiled 3565 to 1961 computations (45% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(expm1.f64 (*.f64 a x))
✓1.1b
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
✓9.8b
(log.f64 (expm1.f64 (*.f64 a x)))

series356.0ms (9.9%)

Counts
2 → 48
Calls

12 calls:

103.0ms
(log.f64 (expm1.f64 (*.f64 a x)))
x
-inf
92.0ms
(log.f64 (expm1.f64 (*.f64 a x)))
x
inf
79.0ms
(log.f64 (expm1.f64 (*.f64 a x)))
a
-inf
72.0ms
(log.f64 (expm1.f64 (*.f64 a x)))
a
inf
3.0ms
(log.f64 (expm1.f64 (*.f64 a x)))
a
0

rewrite39.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
467×log1p-expm1-u_binary64
467×expm1-log1p-u_binary64
325×unpow-prod-down_binary64
274×log-prod_binary64
144×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
111714
2130814
Stop Event
1×node limit
Counts
2 → 86

simplify48.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
641×fma-neg_binary64
415×*-commutative_binary64
370×cancel-sign-sub-inv_binary64
300×unswap-sqr_binary64
228×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
043608
1128600
2382590
31687578
44381558
Stop Event
1×node limit
Counts
134 → 103

prune105.0ms (2.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

PrunedKeptTotal
New1480148
Fresh011
Picked011
Done033
Total1485153
Error
0.0b
Counts
153 → 5
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (*.f64 a x))
✓41.8b
(exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))
✓25.4b
(fma.f64 x (fma.f64 x (*.f64 1/2 (*.f64 a a)) a) (fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4))))
46.6b
(pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)
✓0.7b
(*.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2))
Compiler

Compiled 2117 to 883 computations (58.3% saved)

regimes65.0ms (1.8%)

Accuracy

Total 0.0b remaining (30.9%)

Threshold costs 0.0b (30.9%)

Counts
14 → 1
Compiler

Compiled 1015 to 644 computations (36.6% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
Stop Event
1×saturated

end68.0ms (1.9%)

Stop Event
1×fuel
Remove

(sort a x)

Compiler

Compiled 89 to 58 computations (34.8% saved)

Profiling

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