Details

Time bar (total: 8.5s)

analyze1.9s (22.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
0%99.8%0.2%11
0%99.8%0.2%12
0%99.8%0.2%13
0%99.8%0.2%14
Compiler

Compiled 19 to 14 computations (26.3% saved)

sample2.9s (33.7%)

Symmetry

(sort x y)

(sort z t)

Results
1.3s8256×body128valid
1.3s1653×body8192exit
248.0ms1626×body128invalid
Compiler

Compiled 37 to 27 computations (27% saved)

simplify211.0ms (2.5%)

Algorithm
egg-herbie
Rules
2966×fma-def_binary64
757×fma-neg_binary64
541×cancel-sign-sub-inv_binary64
473×associate-/l/_binary64
472×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01419
13117
210317
331817
479417
5152617
6205417
7228117
8297517
9354017
10395417
11415817
12409717
13410817
14411817
15446217
16453117
17453617
18453617
19647417

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
7.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
7.6b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
Compiler

Compiled 100 to 69 computations (31% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
0.2b
(*.f64 (*.f64 z 9) t)
7.0b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))

series57.0ms (0.7%)

Counts
3 → 132
Calls

3 calls:

40.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
12.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))
5.0ms
(*.f64 (*.f64 z 9) t)

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
3 → 62
Calls

3 calls:

6.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
4.0ms
(*.f64 (*.f64 z 9) t)
4.0ms
(-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

simplify97.0ms (1.1%)

Algorithm
egg-herbie
Rules
470×fma-def_binary64
445×*-commutative_binary64
325×div-sub_binary64
307×associate-/l*_binary64
287×fma-neg_binary64
Counts
194 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01482790
13962561
215062551
341282551
452472551

prune122.0ms (1.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New10312115
Fresh011
Picked011
Done000
Total10314117
Error
7.1b
Counts
117 → 14
Alt Table
StatusErrorProgram
31.1b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
36.8b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2)) (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))) (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))))
7.6b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
33.2b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
32.5b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
22.5b
(expm1.f64 (log1p.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
31.1b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
8.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) a) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) 2))
33.3b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
26.7b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (fma.f64 t (*.f64 z 9) (*.f64 y x))))
34.7b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (sqrt.f64 (*.f64 (*.f64 z 9) t)) (sqrt.f64 (*.f64 (*.f64 z 9) t)))) (*.f64 a 2))
8.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
Compiler

Compiled 2985 to 1736 computations (41.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
0.2b
(*.f64 z (*.f64 9 t))
7.0b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))

series58.0ms (0.7%)

Counts
3 → 132
Calls

3 calls:

41.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
12.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
5.0ms
(*.f64 z (*.f64 9 t))

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube_binary64
13×add-exp-log_binary64
pow1_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
Counts
3 → 62
Calls

3 calls:

5.0ms
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
4.0ms
(-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t)))
4.0ms
(*.f64 z (*.f64 9 t))

simplify96.0ms (1.1%)

Algorithm
egg-herbie
Rules
423×fma-def_binary64
421×*-commutative_binary64
320×div-sub_binary64
286×associate-/l*_binary64
251×fma-neg_binary64
Counts
194 → 115
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01462786
13882556
213912549
338852549
449522549

prune156.0ms (1.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1141115
Fresh21012
Picked011
Done011
Total11613129
Error
7.1b
Counts
129 → 13
Alt Table
StatusErrorProgram
7.6b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
33.2b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
32.5b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
22.5b
(expm1.f64 (log1p.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
30.7b
(/.f64 (/.f64 (fma.f64 y (*.f64 y (*.f64 x x)) (*.f64 (*.f64 (*.f64 t z) (*.f64 t z)) -81)) (fma.f64 z (*.f64 t 9) (*.f64 y x))) (*.f64 a 2))
8.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
31.1b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
8.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) a) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) 2))
33.3b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
31.1b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
26.7b
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 (*.f64 z 9) t) (*.f64 (*.f64 z 9) t))) (*.f64 (*.f64 a 2) (fma.f64 t (*.f64 z 9) (*.f64 y x))))
Compiler

Compiled 2900 to 1666 computations (42.6% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
7.0b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series54.0ms (0.6%)

Counts
2 → 108
Calls

2 calls:

42.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
12.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
2 → 44
Calls

2 calls:

5.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
0.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

simplify109.0ms (1.3%)

Algorithm
egg-herbie
Rules
937×fma-def_binary64
487×associate-*l*_binary64
418×associate-*r*_binary64
225×associate-*r/_binary64
211×associate-*l/_binary64
Counts
152 → 88
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01082547
12482243
28122243
332062242
449372242
550192242

prune102.0ms (1.2%)

Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New85388
Fresh1910
Picked011
Done022
Total8615101
Error
7.1b
Counts
101 → 15
Alt Table
StatusErrorProgram
31.1b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
8.0b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
7.6b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
33.2b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) a) (/.f64 (sqrt.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x))) 2))
32.5b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
22.5b
(expm1.f64 (log1p.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
30.7b
(/.f64 (/.f64 (fma.f64 y (*.f64 y (*.f64 x x)) (*.f64 (*.f64 (*.f64 t z) (*.f64 t z)) -81)) (fma.f64 z (*.f64 t 9) (*.f64 y x))) (*.f64 a 2))
8.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2)))) (cbrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
31.1b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
8.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))
8.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) a) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) 2))
33.3b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
8.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
Compiler

Compiled 2361 to 1316 computations (44.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
0.4b
(/.f64 (sqrt.f64 1/2) a)
0.4b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1))
7.0b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))

series135.0ms (1.6%)

Counts
3 → 108
Calls

3 calls:

106.0ms
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
23.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1))
5.0ms
(/.f64 (sqrt.f64 1/2) a)

rewrite33.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
58×times-frac_binary64
57×add-sqr-sqrt_binary64
47×*-un-lft-identity_binary64
45×add-cube-cbrt_binary64
44×associate-*r*_binary64
Counts
3 → 140
Calls

3 calls:

10.0ms
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
8.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1))
3.0ms
(/.f64 (sqrt.f64 1/2) a)

simplify146.0ms (1.7%)

Algorithm
egg-herbie
Rules
772×fma-def_binary64
582×times-frac_binary64
408×*-commutative_binary64
289×associate-/l/_binary64
262×distribute-rgt-in_binary64
Counts
248 → 197
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01844969
14064213
215424213
344304213
452154213

prune229.0ms (2.7%)

Pruning

17 alts after pruning (13 fresh and 4 done)

PrunedKeptTotal
New2155220
Fresh3811
Picked011
Done033
Total21817235
Error
7.1b
Counts
235 → 17
Alt Table
StatusErrorProgram
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
8.0b
(/.f64 (*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (sqrt.f64 1/2)) (sqrt.f64 1/2)) (*.f64 1 a))
31.1b
(*.f64 -9/2 (/.f64 (*.f64 t z) a))
8.0b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) 1)) (/.f64 (sqrt.f64 1/2) a))
7.6b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
31.4b
(*.f64 -9 (/.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 t z)) a))
8.4b
(*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (fma.f64 (*.f64 t z) -9 (*.f64 y x))) (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) a)) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a)))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) a)))
8.4b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 (sqrt.f64 1/2) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/2) (cbrt.f64 a)))
33.7b
(/.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) (*.f64 y x)) a)
32.5b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))) (sqrt.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
22.5b
(expm1.f64 (log1p.f64 (/.f64 (fma.f64 t (*.f64 z -9) (*.f64 y x)) (*.f64 a 2))))
31.1b
(/.f64 (*.f64 -9 (*.f64 t z)) (*.f64 a 2))
8.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)))) a) (/.f64 (cbrt.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))) 2))
33.3b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
7.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 z (*.f64 9 t))) (*.f64 a 2))
33.4b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (fma.f64 (*.f64 t z) -9 (*.f64 y x)))) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (fma.f64 (*.f64 t z) -9 (*.f64 y x))))) (/.f64 (sqrt.f64 1/2) a))
30.7b
(/.f64 (/.f64 (fma.f64 y (*.f64 y (*.f64 x x)) (*.f64 (*.f64 (*.f64 t z) (*.f64 t z)) -81)) (fma.f64 z (*.f64 t 9) (*.f64 y x))) (*.f64 a 2))
Compiler

Compiled 5912 to 3817 computations (35.4% saved)

regimes1.8s (20.9%)

Accuracy

Total 0.5b remaining (6%)

Threshold costs 0.5b (6%)

Counts
110 → 1
Compiler

Compiled 37609 to 26563 computations (29.4% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01317
11517
21517

end281.0ms (3.3%)

Remove

(sort x y)

Compiler

Compiled 528 to 376 computations (28.8% saved)

Profiling

Loading profile data...