Details

Time bar (total: 2.9s)

analyze2.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.0s (35.2%)

Results
816.0ms8256×body128valid
Compiler

Compiled 44 to 28 computations (36.4% saved)

simplify86.0ms (2.9%)

Algorithm
egg-herbie
Rules
649×fma-neg_binary64
504×div-sub_binary64
481×fma-def_binary64
326×times-frac_binary64
174×associate-/l/_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11310
22110
33710
46410
511310
621610
741510
875410
9118310
10153710
11161210
12165710
13168410
14169410
15170210
16170210
17160010

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
62.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
62.0b
(/.f64 (-.f64 x lo) (-.f64 hi lo))
Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
62.0b
(/.f64 (-.f64 x lo) (-.f64 hi lo))

series17.0ms (0.6%)

Counts
1 → 36
Calls

1 calls:

17.0ms
(/.f64 (-.f64 x lo) (-.f64 hi lo))

rewrite11.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity_binary64
37×add-sqr-sqrt_binary64
25×times-frac_binary64
13×add-cube-cbrt_binary64
12×distribute-lft-out--_binary64
Counts
1 → 54
Calls

1 calls:

7.0ms
(/.f64 (-.f64 x lo) (-.f64 hi lo))

simplify79.0ms (2.7%)

Algorithm
egg-herbie
Rules
810×fma-neg_binary64
418×fma-def_binary64
402×associate--l+_binary64
279×cancel-sign-sub-inv_binary64
264×times-frac_binary64
Counts
90 → 84
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01622093
14362033
213581879
346431879
453461879

prune41.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New81384
Fresh000
Picked101
Done000
Total82385
Error
51.2b
Counts
85 → 3
Alt Table
StatusErrorProgram
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
57.6b
(-.f64 (+.f64 1 (+.f64 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
Compiler

Compiled 1853 to 655 computations (64.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))
0.7b
(pow.f64 (/.f64 lo hi) 3)
1.4b
(+.f64 (/.f64 lo hi) 1)
1.4b
(-.f64 -1 (/.f64 lo hi))

series39.0ms (1.3%)

Counts
4 → 96
Calls

4 calls:

15.0ms
(*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))
14.0ms
(pow.f64 (/.f64 lo hi) 3)
5.0ms
(+.f64 (/.f64 lo hi) 1)
5.0ms
(-.f64 -1 (/.f64 lo hi))

rewrite58.0ms (2%)

Algorithm
rewrite-expression-head
Rules
173×add-sqr-sqrt_binary64
164×*-un-lft-identity_binary64
158×add-cube-cbrt_binary64
147×times-frac_binary64
117×prod-diff_binary64
Counts
4 → 293
Calls

4 calls:

15.0ms
(*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))
6.0ms
(-.f64 -1 (/.f64 lo hi))
5.0ms
(+.f64 (/.f64 lo hi) 1)
3.0ms
(pow.f64 (/.f64 lo hi) 3)

simplify185.0ms (6.3%)

Algorithm
egg-herbie
Rules
621×fma-neg_binary64
480×associate-*l*_binary64
444×associate-*r*_binary64
380×log-prod_binary64
293×*-commutative_binary64
Counts
389 → 340
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04107239
111255197
232834476
342784476
448464476

prune236.0ms (8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3328340
Fresh022
Picked101
Done000
Total33310343
Error
50.6b
Counts
343 → 10
Alt Table
StatusErrorProgram
52.4b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (/.f64 (*.f64 lo (-.f64 1 (pow.f64 (/.f64 lo hi) 2))) (*.f64 hi (+.f64 -1 (/.f64 lo hi))))) (pow.f64 (/.f64 lo hi) 3)))
57.6b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (neg.f64 (pow.f64 (/.f64 lo hi) 2))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 lo (/.f64 (-.f64 -1 (/.f64 lo hi)) hi))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (+.f64 -1 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (*.f64 (cbrt.f64 hi) (cbrt.f64 hi)))) (/.f64 (cbrt.f64 lo) (cbrt.f64 hi)))))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (*.f64 (pow.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (sqrt.f64 hi)) 3) (pow.f64 (/.f64 (cbrt.f64 lo) (sqrt.f64 hi)) 3))))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (*.f64 (pow.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (*.f64 (cbrt.f64 hi) (cbrt.f64 hi))) 3) (pow.f64 (/.f64 (cbrt.f64 lo) (cbrt.f64 hi)) 3))))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (+.f64 (*.f64 -1 (/.f64 lo hi)) (*.f64 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (*.f64 (cbrt.f64 hi) (cbrt.f64 hi)))) (/.f64 (cbrt.f64 lo) (cbrt.f64 hi))) (/.f64 lo hi)))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (+.f64 -1 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) 1)) (/.f64 (cbrt.f64 lo) hi))))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
57.6b
(-.f64 (+.f64 1 (+.f64 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
Compiler

Compiled 17853 to 6114 computations (65.8% saved)

localize20.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(*.f64 (cbrt.f64 lo) (cbrt.f64 lo))
0.7b
(pow.f64 (/.f64 lo hi) 3)
1.4b
(+.f64 -1 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) 1)) (/.f64 (cbrt.f64 lo) hi)))
1.4b
(+.f64 (/.f64 lo hi) 1)

series53.0ms (1.8%)

Counts
2 → 36
Calls

2 calls:

40.0ms
(*.f64 (cbrt.f64 lo) (cbrt.f64 lo))
14.0ms
(+.f64 -1 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) 1)) (/.f64 (cbrt.f64 lo) hi)))

rewrite11.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64
16×cbrt-prod_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
pow1_binary64
Counts
2 → 59
Calls

2 calls:

4.0ms
(*.f64 (cbrt.f64 lo) (cbrt.f64 lo))
2.0ms
(+.f64 -1 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) 1)) (/.f64 (cbrt.f64 lo) hi)))

simplify92.0ms (3.1%)

Algorithm
egg-herbie
Rules
735×fma-def_binary64
477×fma-neg_binary64
267×unsub-neg_binary64
262×associate-*l/_binary64
246×unswap-sqr_binary64
Counts
95 → 87
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0831103
1195760
2606720
32342704
44146626
54913626
64893626

prune108.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1682170
Fresh369
Picked101
Done000
Total1728180
Error
50.6b
Counts
180 → 8
Alt Table
StatusErrorProgram
52.4b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (/.f64 (*.f64 lo (-.f64 1 (pow.f64 (/.f64 lo hi) 2))) (*.f64 hi (+.f64 -1 (/.f64 lo hi))))) (pow.f64 (/.f64 lo hi) 3)))
57.6b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (neg.f64 (pow.f64 (/.f64 lo hi) 2))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (+.f64 -1 (*.f64 (neg.f64 (/.f64 (expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)))) 1)) (/.f64 (cbrt.f64 lo) hi))))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (*.f64 (pow.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (*.f64 (cbrt.f64 hi) (cbrt.f64 hi))) 3) (pow.f64 (/.f64 (cbrt.f64 lo) (cbrt.f64 hi)) 3))))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (+.f64 -1 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) 1)) (/.f64 (cbrt.f64 lo) hi))))) (*.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 lo hi) 3)) (cbrt.f64 (pow.f64 (/.f64 lo hi) 3))) (cbrt.f64 (pow.f64 (/.f64 lo hi) 3)))))
51.9b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
57.6b
(-.f64 (+.f64 1 (+.f64 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 lo (/.f64 (-.f64 -1 (/.f64 lo hi)) hi))) (pow.f64 (/.f64 lo hi) 3)))
Compiler

Compiled 8669 to 3395 computations (60.8% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(pow.f64 (/.f64 lo hi) 3)
1.4b
(+.f64 (/.f64 lo hi) 1)
1.4b
(-.f64 -1 (/.f64 lo hi))
2.9b
(*.f64 lo (/.f64 (-.f64 -1 (/.f64 lo hi)) hi))

series16.0ms (0.5%)

Counts
1 → 24
Calls

1 calls:

16.0ms
(*.f64 lo (/.f64 (-.f64 -1 (/.f64 lo hi)) hi))

rewrite13.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt_binary64
22×associate-*r*_binary64
22×times-frac_binary64
18×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
Counts
1 → 43
Calls

1 calls:

10.0ms
(*.f64 lo (/.f64 (-.f64 -1 (/.f64 lo hi)) hi))

simplify77.0ms (2.6%)

Algorithm
egg-herbie
Rules
446×div-sub_binary64
356×associate-*l*_binary64
291×fma-def_binary64
270×associate-*r*_binary64
255×associate-/l*_binary64
Counts
67 → 59
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0971162
12261081
2752981
32636981
44149977
55440977

prune134.0ms (4.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2232225
Fresh077
Picked101
Done000
Total2249233
Error
50.6b
Counts
233 → 9
Alt Table
StatusErrorProgram
52.4b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (/.f64 (*.f64 lo (-.f64 1 (pow.f64 (/.f64 lo hi) 2))) (*.f64 hi (+.f64 -1 (/.f64 lo hi))))) (pow.f64 (/.f64 lo hi) 3)))
57.6b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (neg.f64 (pow.f64 (/.f64 lo hi) 2))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (+.f64 -1 (*.f64 (neg.f64 (/.f64 (expm1.f64 (log1p.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)))) 1)) (/.f64 (cbrt.f64 lo) hi))))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (-.f64 -1 (/.f64 lo hi)))) (*.f64 (pow.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (*.f64 (cbrt.f64 hi) (cbrt.f64 hi))) 3) (pow.f64 (/.f64 (cbrt.f64 lo) (cbrt.f64 hi)) 3))))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (/.f64 lo hi) (+.f64 -1 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) 1)) (/.f64 (cbrt.f64 lo) hi))))) (*.f64 (*.f64 (cbrt.f64 (pow.f64 (/.f64 lo hi) 3)) (cbrt.f64 (pow.f64 (/.f64 lo hi) 3))) (cbrt.f64 (pow.f64 (/.f64 lo hi) 3)))))
57.6b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 lo (/.f64 (neg.f64 (/.f64 lo hi)) hi))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(+.f64 (/.f64 x hi) (-.f64 (fma.f64 (/.f64 x hi) (*.f64 (+.f64 (/.f64 lo hi) 1) (/.f64 lo hi)) (*.f64 (*.f64 (cbrt.f64 lo) (cbrt.f64 lo)) (*.f64 (cbrt.f64 lo) (/.f64 (-.f64 -1 (/.f64 lo hi)) hi)))) (pow.f64 (/.f64 lo hi) 3)))
51.9b
(-.f64 (+.f64 1 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
57.6b
(-.f64 (+.f64 1 (+.f64 (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)) (pow.f64 (/.f64 hi lo) 3))) (+.f64 (/.f64 x lo) (*.f64 (/.f64 x lo) (*.f64 (+.f64 1 (/.f64 hi lo)) (/.f64 hi lo)))))
Compiler

Compiled 10262 to 3954 computations (61.5% saved)

regimes400.0ms (13.6%)

Accuracy

Total 1.3b remaining (2.4%)

Threshold costs 0b (0%)

Counts
83 → 1
Compiler

Compiled 14806 to 7000 computations (52.7% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01544
12144
23044
33644
44044
54144
64144

end186.0ms (6.3%)

Compiler

Compiled 445 to 219 computations (50.8% saved)

Profiling

Loading profile data...