Details

Time bar (total: 7.8s)

analyze885.0ms (11.4%)

Algorithm
1×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
0%74.9%25.1%5
0%74.9%25.1%6
0%74.9%25.1%7
6.2%56.2%37.6%8
7.8%53%39.2%9
10.9%45.6%43.4%10
18.3%31.4%50.3%11
19.1%29.5%51.3%12
21.4%24.8%53.8%13
25.8%16.7%57.5%14
Compiler

Compiled 28 to 21 computations (25% saved)

sample41.0ms (0.5%)

Algorithm
1×intervals
Results
24.0ms256×body128valid
4.0ms41×body128invalid
1.0ms18×body128nan
Compiler

Compiled 58 to 44 computations (24.1% saved)

simplify81.0ms (1%)

Algorithm
1×egg-herbie
Rules
703×fma-def_binary64
691×associate-/l*_binary64
673×sub-neg_binary64
568×fma-neg_binary64
439×div-sub_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02132
14332
29931
322330
452930
5101630
6191730
7300130
8339630
9483030
10511030

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
8.7b
Counts
3 → 2
Alt Table
StatusErrorProgram
8.7b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x))
▶8.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
Compiler

Compiled 150 to 107 computations (28.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)
✓0.2b
(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x)
✓0.3b
(fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)
✓8.1b
(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x)

rewrite51.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
42×add-cube-cbrt_binary64
18×add-sqr-sqrt_binary64
16×pow1_binary64
16×add-cbrt-cube_binary64
14×fma-udef_binary64
Counts
4 → 161
Calls

4 calls:

14.0ms
(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x)
12.0ms
(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x)
8.0ms
(fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)
8.0ms
(fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)

series204.0ms (2.6%)

Counts
4 → 84
Calls

4 calls:

74.0ms
(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x)
59.0ms
(fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)
52.0ms
(-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x)
19.0ms
(fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)

simplify158.0ms (2%)

Algorithm
1×egg-herbie
Rules
758×times-frac_binary64
756×fma-def_binary64
412×cancel-sign-sub-inv_binary64
329×fma-neg_binary64
158×sub-neg_binary64
Counts
245 → 418
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02404338
16043924
219713692
349353692
449463692

prune350.0ms (4.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New40612418
Fresh101
Picked101
Done000
Total40812420
Error
2.5b
Counts
420 → 12
Alt Table
StatusErrorProgram
8.8b
(+.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) (sqrt.f64 x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
8.8b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (*.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) (/.f64 1 x)))
8.9b
(+.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) 2) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
14.2b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (/.f64 (fma.f64 z -3202559735019045/1152921504606846976 6004799503160637/72057594037927936) x))
9.1b
(+.f64 (-.f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) 3) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
11.5b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (fma.f64 (/.f64 z x) -3202559735019045/1152921504606846976 (fma.f64 7320129949063637/9223372036854775808 (/.f64 (*.f64 z z) x) (fma.f64 (/.f64 y x) (*.f64 z z) (/.f64 6004799503160637/72057594037927936 x)))))
9.1b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (-.f64 (+.f64 (*.f64 7320129949063637/9223372036854775808 (/.f64 (pow.f64 z 2) x)) (+.f64 (/.f64 (*.f64 y (pow.f64 z 2)) x) (*.f64 6004799503160637/72057594037927936 (/.f64 1 x)))) (*.f64 3202559735019045/1152921504606846976 (/.f64 z x))))
8.8b
(+.f64 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x)) 2) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
9.1b
(+.f64 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x)) 3) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
▶8.7b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
13.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (pow.f64 (sqrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x)) 2))
27.2b
(+.f64 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 2069265617858471/2251799813685248) 3)) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
Compiler

Compiled 8369 to 5337 computations (36.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
0.1b
(fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)
✓0.3b
(fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x))
8.1b
(/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x)

rewrite26.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
12×add-cube-cbrt_binary64
9×fma-udef_binary64
8×add-log-exp_binary64
8×pow1_binary64
8×add-sqr-sqrt_binary64
Counts
2 → 77
Calls

2 calls:

13.0ms
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
9.0ms
(fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x))

series176.0ms (2.3%)

Counts
2 → 48
Calls

2 calls:

121.0ms
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
54.0ms
(fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x))

simplify136.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
695×fma-def_binary64
656×distribute-rgt-in_binary64
294×fma-neg_binary64
237×sub-neg_binary64
156×cancel-sign-sub-inv_binary64
Counts
125 → 218
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01703803
15253686
218843476
346623476
449643476

prune363.0ms (4.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New4564460
Fresh3811
Picked101
Done000
Total46012472
Error
2.5b
Counts
472 → 12
Alt Table
StatusErrorProgram
8.8b
(+.f64 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x)) 2) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
14.2b
(-.f64 (+.f64 2069265617858471/2251799813685248 (fma.f64 x (log.f64 x) (/.f64 6004799503160637/72057594037927936 x))) (fma.f64 1/2 (log.f64 x) (fma.f64 3202559735019045/1152921504606846976 (/.f64 z x) x)))
9.1b
(+.f64 (-.f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) 3) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
11.5b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (fma.f64 (/.f64 z x) -3202559735019045/1152921504606846976 (fma.f64 7320129949063637/9223372036854775808 (/.f64 (*.f64 z z) x) (fma.f64 (/.f64 y x) (*.f64 z z) (/.f64 6004799503160637/72057594037927936 x)))))
8.8b
(+.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) (sqrt.f64 x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
9.1b
(+.f64 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x)) 3) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
▶8.8b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (*.f64 (/.f64 1 x) (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)))
13.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (pow.f64 (sqrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x)) 2))
9.0b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (neg.f64 (/.f64 (-.f64 (*.f64 3202559735019045/1152921504606846976 z) (fma.f64 (*.f64 z z) (+.f64 7320129949063637/9223372036854775808 y) 6004799503160637/72057594037927936)) x)))
27.2b
(+.f64 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 2069265617858471/2251799813685248) 3)) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
14.1b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (/.f64 (fma.f64 z -3202559735019045/1152921504606846976 6004799503160637/72057594037927936) x))
8.9b
(+.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) 2) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
Compiler

Compiled 8659 to 5633 computations (34.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (*.f64 (/.f64 1 x) (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)))
0.1b
(fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)
0.3b
(fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x))
✓8.2b
(*.f64 (/.f64 1 x) (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936))

rewrite33.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
11×fma-udef_binary64
9×pow1_binary64
8×add-log-exp_binary64
Counts
2 → 93
Calls

2 calls:

14.0ms
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (*.f64 (/.f64 1 x) (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)))
13.0ms
(*.f64 (/.f64 1 x) (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936))

series200.0ms (2.6%)

Counts
2 → 72
Calls

2 calls:

125.0ms
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (*.f64 (/.f64 1 x) (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)))
74.0ms
(*.f64 (/.f64 1 x) (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936))

simplify169.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
444×fma-neg_binary64
401×times-frac_binary64
391×cancel-sign-sub-inv_binary64
241×sub-neg_binary64
174×fma-def_binary64
Counts
165 → 295
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02144848
16454605
225184495
346484494
449024494

prune373.0ms (4.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New5641565
Fresh11011
Picked011
Done000
Total56512577
Error
0.0b
Counts
577 → 12
Alt Table
StatusErrorProgram
9.1b
(+.f64 (-.f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) 3) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
11.5b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (fma.f64 (/.f64 z x) -3202559735019045/1152921504606846976 (fma.f64 7320129949063637/9223372036854775808 (/.f64 (*.f64 z z) x) (fma.f64 (/.f64 y x) (*.f64 z z) (/.f64 6004799503160637/72057594037927936 x)))))
8.8b
(+.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) (sqrt.f64 x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
8.8b
(+.f64 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x)) 2) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
9.1b
(+.f64 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x)) 3) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
✓8.8b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (*.f64 (/.f64 1 x) (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)))
13.7b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (pow.f64 (sqrt.f64 (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x)) 2))
9.0b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (neg.f64 (/.f64 (-.f64 (*.f64 3202559735019045/1152921504606846976 z) (fma.f64 (*.f64 z z) (+.f64 7320129949063637/9223372036854775808 y) 6004799503160637/72057594037927936)) x)))
27.2b
(+.f64 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 2069265617858471/2251799813685248) 3)) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
14.1b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (/.f64 (fma.f64 z -3202559735019045/1152921504606846976 6004799503160637/72057594037927936) x))
▶1.9b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (+.f64 (*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976)) (/.f64 6004799503160637/72057594037927936 x)))
8.9b
(+.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) 2) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
Compiler

Compiled 9420 to 6313 computations (33% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976)) (/.f64 6004799503160637/72057594037927936 x))
✓0.0b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (+.f64 (*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976)) (/.f64 6004799503160637/72057594037927936 x)))
0.3b
(fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x))
✓2.3b
(*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976))

rewrite53.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
19×pow1_binary64
17×add-cube-cbrt_binary64
16×add-log-exp_binary64
16×add-sqr-sqrt_binary64
13×fma-udef_binary64
Counts
3 → 138
Calls

3 calls:

16.0ms
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (+.f64 (*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976)) (/.f64 6004799503160637/72057594037927936 x)))
14.0ms
(+.f64 (*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976)) (/.f64 6004799503160637/72057594037927936 x))
13.0ms
(*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976))

series269.0ms (3.5%)

Counts
3 → 108
Calls

3 calls:

126.0ms
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (+.f64 (*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976)) (/.f64 6004799503160637/72057594037927936 x)))
74.0ms
(+.f64 (*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976)) (/.f64 6004799503160637/72057594037927936 x))
68.0ms
(*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976))

simplify184.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
573×times-frac_binary64
429×fma-neg_binary64
233×fma-def_binary64
187×associate-*l*_binary64
169×associate-*r*_binary64
Counts
246 → 440
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02716560
18296303
234296258
352236258

prune402.0ms (5.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New5902592
Fresh4610
Picked011
Done011
Total59410604
Error
0.0b
Counts
604 → 10
Alt Table
StatusErrorProgram
0.9b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (+.f64 (*.f64 (*.f64 z (/.f64 z x)) (+.f64 7320129949063637/9223372036854775808 y)) (/.f64 6004799503160637/72057594037927936 x)))
11.5b
(+.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x) (fma.f64 (/.f64 z x) -3202559735019045/1152921504606846976 (fma.f64 7320129949063637/9223372036854775808 (/.f64 (*.f64 z z) x) (fma.f64 (/.f64 y x) (*.f64 z z) (/.f64 6004799503160637/72057594037927936 x)))))
9.1b
(+.f64 (-.f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) 3) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
8.8b
(+.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) (sqrt.f64 x))) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
9.1b
(+.f64 (pow.f64 (cbrt.f64 (-.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248) x)) 3) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
✓8.8b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (*.f64 (/.f64 1 x) (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936)))
27.2b
(+.f64 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 x) (-.f64 x 1/2) 2069265617858471/2251799813685248) 3)) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
5.5b
(pow.f64 (sqrt.f64 (+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (+.f64 (*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976)) (/.f64 6004799503160637/72057594037927936 x)))) 2)
✓1.9b
(+.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) (-.f64 2069265617858471/2251799813685248 x)) (+.f64 (*.f64 (/.f64 z x) (fma.f64 (+.f64 7320129949063637/9223372036854775808 y) z -3202559735019045/1152921504606846976)) (/.f64 6004799503160637/72057594037927936 x)))
8.9b
(+.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 (-.f64 x 1/2) (log.f64 x) 2069265617858471/2251799813685248)) 2) x) (/.f64 (fma.f64 z (fma.f64 (+.f64 y 7320129949063637/9223372036854775808) z -3202559735019045/1152921504606846976) 6004799503160637/72057594037927936) x))
Compiler

Compiled 10175 to 6210 computations (39% saved)

regimes2.0s (26.2%)

Accuracy

Total 0.7b remaining (92.8%)

Threshold costs 0.7b (92.8%)

Compiler

Compiled 43704 to 31154 computations (28.7% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01934
12934
23534
33734
43834
53734

end1.0ms (0%)

Compiler

Compiled 26 to 18 computations (30.8% saved)

sample1.5s (19.5%)

Algorithm
1×intervals
Results
732.0ms8000×body128valid
117.0ms1280×body128invalid
57.0ms723×body128nan
Compiler

Compiled 347 to 247 computations (28.8% saved)

Profiling

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