Details

Time bar (total: 3.1s)

analyze10.0ms (0.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
50%50%0%5
81.2%18.7%0%6
100%0%0%7
Compiler

Compiled 175 to 47 computations (73.1% saved)

sample121.0ms (4%)

Algorithm
1×intervals
Results
42.0ms256×body128valid
Compiler

Compiled 350 to 94 computations (73.1% saved)

simplify64.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
755×unswap-sqr_binary64
705×fma-def_binary64
691×distribute-rgt-out_binary64
576×+-commutative_binary64
488×*-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
046256
1133150
2549101
3242790
4370584
5452984
6487484
7588784

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
26.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶26.1b
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
Compiler

Compiled 356 to 182 computations (48.9% saved)

localize32.0ms (1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))
✓0.4b
(fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))
✓13.5b
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
✓25.6b
(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1)))))))

series61.0ms (2%)

Counts
4 → 48
Calls

4 calls:

43.0ms
(fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))
7.0ms
(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1)))))))
6.0ms
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
4.0ms
(fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))

rewrite19.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
25×add-sqr-sqrt_binary64
20×*-un-lft-identity_binary64
20×add-cube-cbrt_binary64
19×times-frac_binary64
13×associate-*r*_binary64
Counts
4 → 83
Calls

4 calls:

6.0ms
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
2.0ms
(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1)))))))
0.0ms
(fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))
0.0ms
(fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))

simplify226.0ms (7.4%)

Algorithm
1×egg-herbie
Rules
553×associate-*l*_binary64
514×fma-def_binary64
239×distribute-rgt-in_binary64
236×associate-*r/_binary64
233×distribute-lft-in_binary64
Counts
131 → 202
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02248641
15067686
214537678
348037678
449837678

prune491.0ms (16%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2002202
Fresh000
Picked011
Done000
Total2003203
Error
0b
Counts
203 → 3
Alt Table
StatusErrorProgram
▶28.0b
(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)
✓26.1b
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
35.6b
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
Compiler

Compiled 15811 to 11761 computations (25.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)

series3.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

3.0ms
(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)

rewrite1.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
1×*-un-lft-identity_binary64
1×add-sqr-sqrt_binary64
1×add-cube-cbrt_binary64
1×add-cbrt-cube_binary64
1×add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

0.0ms
(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)

simplify64.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
435×neg-mul-1_binary64
394×associate-*l*_binary64
372×associate-*r*_binary64
317×distribute-rgt-out_binary64
261×exp-prod_binary64
Counts
22 → 16
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
020232
135197
287197
3323197
41659197
54536197
65201197

prune10.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New16016
Fresh011
Picked011
Done011
Total16319
Error
0b
Counts
19 → 3
Alt Table
StatusErrorProgram
✓28.0b
(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)
✓26.1b
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
▶35.6b
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
Compiler

Compiled 236 to 176 computations (25.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
✓0.3b
(/.f64 600041/2386628 (pow.f64 x 3))

series6.0ms (0.2%)

Counts
2 → 12
Calls

2 calls:

3.0ms
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
3.0ms
(/.f64 600041/2386628 (pow.f64 x 3))

rewrite32.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
47×times-frac_binary64
40×*-un-lft-identity_binary64
34×add-sqr-sqrt_binary64
34×add-cube-cbrt_binary64
13×fma-def_binary64
Counts
2 → 96
Calls

2 calls:

22.0ms
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
4.0ms
(/.f64 600041/2386628 (pow.f64 x 3))

simplify74.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
683×associate-*l*_binary64
353×associate-/l*_binary64
342×associate-*r/_binary64
342×associate-*l/_binary64
272×associate-/l/_binary64
Counts
108 → 112
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01291319
12421280
29651242
347061242
449471242

prune81.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1120112
Fresh000
Picked011
Done022
Total1123115
Error
0b
Counts
115 → 3
Alt Table
StatusErrorProgram
✓28.0b
(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)
✓26.1b
(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
✓35.6b
(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
Compiler

Compiled 1899 to 1471 computations (22.5% saved)

regimes68.0ms (2.2%)

Accuracy

Total 0.0b remaining (40.7%)

Threshold costs 0.0b (40.7%)

Counts
14 → 3
Compiler

Compiled 1038 to 444 computations (57.2% saved)

bsearch57.0ms (1.9%)

Steps
ItersRangePoint
7
43.40882916655068
1130017288.4631581
51844.40466253649
7
-677162096.5929486
-7501276.721265695
-14037549.39208479
Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
3×*-commutative_binary64
1×+-commutative_binary64
1×1-exp_binary64
1×if-if-or-not_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
054117
163117
262117

end3.0ms (0.1%)

Compiler

Compiled 83 to 64 computations (22.9% saved)

sample1.6s (52.9%)

Algorithm
1×intervals
Results
1.3s8000×body128valid
Compiler

Compiled 337 to 171 computations (49.3% saved)

Profiling

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