Details

Time bar (total: 8.2s)

analyze40.0ms (0.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
75%25%0%5
87.5%12.5%0%6
93.7%6.2%0%7
96.8%3.1%0%8
98.4%1.6%0%9
99.2%0.8%0%10
99.6%0.4%0%11
99.8%0.2%0%12
99.9%0.1%0%13
99.9%0.1%0.1%14
Compiler

Compiled 17 to 14 computations (17.6% saved)

sample31.0ms (0.4%)

Algorithm
intervals
Results
8.0ms132×body128valid
7.0ms43×body1024valid
7.0ms57×body512valid
2.0ms24×body256valid
Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify20.0ms (0.3%)

Algorithm
egg-herbie
Rules
127×fma-neg_binary64
82×fma-def_binary64
41×cancel-sign-sub-inv_binary64
41×sub-neg_binary64
28×distribute-rgt-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
12222
23822
36122
410922
518622
624622
729622
834822
936822
1034422

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
10.5b
Counts
2 → 1
Alt Table
StatusErrorProgram
10.5b
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
Compiler

Compiled 48 to 39 computations (18.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 1 (-.f64 x 1))
0.0b
(/.f64 1 (+.f64 x 1))
0.0b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.4b
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite933.0ms (11.4%)

Algorithm
rewrite-expression-head
Error
9.6b
Rules
757×*-un-lft-identity_binary64
733×times-frac_binary64
558×add-sqr-sqrt_binary64
508×add-cube-cbrt_binary64
468×prod-diff_binary64
Counts
4 → 668
Calls

4 calls:

55.0ms
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
24.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms
(/.f64 1 (-.f64 x 1))
4.0ms
(/.f64 1 (+.f64 x 1))
Compiler

Compiled 24496 to 18897 computations (22.9% saved)

series69.0ms (0.8%)

Error
0.1b
Counts
4 → 48
Calls

4 calls:

14.0ms
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
11.0ms
(/.f64 1 (+.f64 x 1))
9.0ms
(/.f64 1 (-.f64 x 1))
9.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
Compiler

Compiled 1486 to 1208 computations (18.7% saved)

simplify422.0ms (5.2%)

Algorithm
egg-herbie
Rules
932×fma-neg_binary64
457×times-frac_binary64
236×fma-def_binary64
186×sub-neg_binary64
176×exp-prod_binary64
Counts
716 → 669
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
041919278
198913709
225199843
343499843
448159843

prune267.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New6654669
Fresh000
Picked011
Done000
Total6655670
Error
0.0b
Counts
670 → 5
Alt Table
StatusErrorProgram
33.1b
(+.f64 (fma.f64 (/.f64 1 (-.f64 (*.f64 x x) (*.f64 1 1))) (-.f64 x 1) (neg.f64 (*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) 1)))) (/.f64 1 (+.f64 x -1)))
28.6b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
10.5b
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
11.0b
(*.f64 (*.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))))
28.0b
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
Compiler

Compiled 8880 to 7076 computations (20.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))))
2.4b
(+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))
2.4b
(+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))
2.4b
(+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))

rewrite699.0ms (8.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
636×*-un-lft-identity_binary64
361×distribute-lft-out_binary64
168×times-frac_binary64
164×cbrt-prod_binary64
98×div-inv_binary64
Counts
4 → 266
Calls

4 calls:

82.0ms
(*.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))))
45.0ms
(+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))
28.0ms
(+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))
27.0ms
(+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))
Compiler

Compiled 11408 to 9350 computations (18% saved)

series277.0ms (3.4%)

Error
0.0b
Counts
4 → 45
Calls

4 calls:

56.0ms
(*.f64 (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))))
44.0ms
(+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))
42.0ms
(+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))
40.0ms
(+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))
Compiler

Compiled 4137 to 3500 computations (15.4% saved)

simplify629.0ms (7.7%)

Algorithm
egg-herbie
Rules
817×fma-def_binary64
473×distribute-rgt-in_binary64
411×distribute-lft-in_binary64
351×times-frac_binary64
257×fma-neg_binary64
Counts
311 → 215
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
025214678
162113996
2177311560
3496311560
4504411560

prune332.0ms (4.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2141215
Fresh033
Picked101
Done011
Total2155220
Error
0.0b
Counts
220 → 5
Alt Table
StatusErrorProgram
33.1b
(+.f64 (fma.f64 (/.f64 1 (-.f64 (*.f64 x x) (*.f64 1 1))) (-.f64 x 1) (neg.f64 (*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) 1)))) (/.f64 1 (+.f64 x -1)))
47.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 (+.f64 x -1) (+.f64 (pow.f64 (/.f64 -2 x) 3) (pow.f64 (/.f64 1 (+.f64 x 1)) 3)) (+.f64 (/.f64 (/.f64 4 x) x) (/.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (+.f64 x 1)))) (*.f64 (+.f64 x -1) (+.f64 (/.f64 (/.f64 4 x) x) (/.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (+.f64 x 1)))))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))))
28.6b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
10.5b
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
28.0b
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
Compiler

Compiled 6695 to 5392 computations (19.5% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
0.0b
(/.f64 2 (pow.f64 x 7))
0.1b
(/.f64 2 (pow.f64 x 5))
0.1b
(/.f64 2 (pow.f64 x 3))

rewrite496.0ms (6.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
108×times-frac_binary64
92×*-un-lft-identity_binary64
78×add-sqr-sqrt_binary64
78×add-cube-cbrt_binary64
45×unpow-prod-down_binary64
Counts
4 → 210
Calls

4 calls:

117.0ms
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
13.0ms
(/.f64 2 (pow.f64 x 3))
7.0ms
(/.f64 2 (pow.f64 x 7))
7.0ms
(/.f64 2 (pow.f64 x 5))
Compiler

Compiled 4955 to 4089 computations (17.5% saved)

series46.0ms (0.6%)

Error
0.0b
Counts
4 → 18
Calls

4 calls:

21.0ms
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
9.0ms
(/.f64 2 (pow.f64 x 7))
6.0ms
(/.f64 2 (pow.f64 x 5))
6.0ms
(/.f64 2 (pow.f64 x 3))
Compiler

Compiled 615 to 522 computations (15.1% saved)

simplify142.0ms (1.7%)

Algorithm
egg-herbie
Rules
680×fma-def_binary64
379×distribute-rgt-in_binary64
260×fma-neg_binary64
223×cancel-sign-sub-inv_binary64
205×unswap-sqr_binary64
Counts
228 → 116
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02903403
15993333
221183235
347553235
450003235

prune82.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1142116
Fresh033
Picked011
Done011
Total1147121
Error
0.0b
Counts
121 → 7
Alt Table
StatusErrorProgram
28.0b
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
28.1b
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (/.f64 2 (pow.f64 x 7))))
33.1b
(+.f64 (fma.f64 (/.f64 1 (-.f64 (*.f64 x x) (*.f64 1 1))) (-.f64 x 1) (neg.f64 (*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) 1)))) (/.f64 1 (+.f64 x -1)))
47.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 (+.f64 x -1) (+.f64 (pow.f64 (/.f64 -2 x) 3) (pow.f64 (/.f64 1 (+.f64 x 1)) 3)) (+.f64 (/.f64 (/.f64 4 x) x) (/.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (+.f64 x 1)))) (*.f64 (+.f64 x -1) (+.f64 (/.f64 (/.f64 4 x) x) (/.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (+.f64 x 1)))))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))))
28.6b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
10.5b
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
28.1b
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3))) (/.f64 2 (pow.f64 x 7))))
Compiler

Compiled 2014 to 1640 computations (18.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 2 (pow.f64 x 5))
0.1b
(/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3)))
0.6b
(/.f64 2 (*.f64 x x))
40.5b
(cbrt.f64 (pow.f64 x 3))

rewrite292.0ms (3.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
177×times-frac_binary64
108×cbrt-prod_binary64
89×*-un-lft-identity_binary64
89×add-sqr-sqrt_binary64
89×add-cube-cbrt_binary64
Counts
4 → 239
Calls

4 calls:

9.0ms
(/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3)))
9.0ms
(/.f64 2 (*.f64 x x))
3.0ms
(/.f64 2 (pow.f64 x 5))
2.0ms
(cbrt.f64 (pow.f64 x 3))
Compiler

Compiled 6440 to 4755 computations (26.2% saved)

series39.0ms (0.5%)

Error
0.0b
Counts
4 → 12
Calls

4 calls:

14.0ms
(/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3)))
7.0ms
(cbrt.f64 (pow.f64 x 3))
7.0ms
(/.f64 2 (pow.f64 x 5))
6.0ms
(/.f64 2 (*.f64 x x))
Compiler

Compiled 645 to 516 computations (20% saved)

simplify170.0ms (2.1%)

Algorithm
egg-herbie
Rules
563×associate-/l*_binary64
524×associate-/r/_binary64
488×associate-*l/_binary64
366×associate-*r/_binary64
291×unswap-sqr_binary64
Counts
251 → 193
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03044255
14554114
215003955
345083955
449693955

prune110.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1921193
Fresh044
Picked011
Done022
Total1928200
Error
0.0b
Counts
200 → 8
Alt Table
StatusErrorProgram
28.1b
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (*.f64 (sqrt.f64 (/.f64 2 (*.f64 x x))) (/.f64 (sqrt.f64 (/.f64 2 (*.f64 x x))) x)) (/.f64 2 (pow.f64 x 7))))
33.1b
(+.f64 (fma.f64 (/.f64 1 (-.f64 (*.f64 x x) (*.f64 1 1))) (-.f64 x 1) (neg.f64 (*.f64 (/.f64 (sqrt.f64 2) x) (/.f64 (sqrt.f64 2) 1)))) (/.f64 1 (+.f64 x -1)))
28.0b
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))))
28.1b
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (/.f64 2 (pow.f64 x 7))))
47.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 (+.f64 x -1) (+.f64 (pow.f64 (/.f64 -2 x) 3) (pow.f64 (/.f64 1 (+.f64 x 1)) 3)) (+.f64 (/.f64 (/.f64 4 x) x) (/.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (+.f64 x 1)))) (*.f64 (+.f64 x -1) (+.f64 (/.f64 (/.f64 4 x) x) (/.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (+.f64 x 1)))))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1))))) (cbrt.f64 (+.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (/.f64 1 (+.f64 x -1)))))
28.6b
(/.f64 (*.f64 (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1))) (+.f64 (*.f64 (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x 1))) (+.f64 x -1)) 1)) (*.f64 (+.f64 x -1) (+.f64 (/.f64 2 x) (/.f64 1 (+.f64 x 1)))))
10.5b
(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
28.1b
(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3))) (/.f64 2 (pow.f64 x 7))))
Compiler

Compiled 2578 to 1878 computations (27.2% saved)

regimes1.7s (21.3%)

Accuracy

Total 0.3b remaining (90.4%)

Threshold costs 0.3b (90.4%)

Compiler

Compiled 15234 to 12196 computations (19.9% saved)

bsearch13.0ms (0.2%)

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
13×+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
distribute-rgt-neg-in_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
044145
166145
282145
394145
498145
599145
696145

end2.0ms (0%)

Compiler

Compiled 98 to 78 computations (20.4% saved)

sample1.3s (15.4%)

Algorithm
intervals
Results
307.0ms4366×body128valid
241.0ms1309×body1024valid
209.0ms1540×body512valid
73.0ms785×body256valid
0.0msbody128invalid
Compiler

Compiled 389 to 311 computations (20.1% saved)

Profiling

Loading profile data...