Details

Time bar (total: 7.5s)

analyze2.0s (26.9%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
1.6%98.1%0.3%13
2.3%97.4%0.3%14
Compiler

Compiled 24 to 18 computations (25% saved)

sample1.7s (23.4%)

Results
1.2s8256×body128valid
480.0ms3054×body128invalid
Compiler

Compiled 48 to 36 computations (25% saved)

preprocess65.0ms (0.9%)

Algorithm
2×egg-herbie
Rules
506×distribute-rgt-neg-in_binary64
439×fma-neg_binary64
406×distribute-lft-neg-in_binary64
398×cancel-sign-sub-inv_binary64
306×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
092400
1324368
21141336
32788336
43992336
066
166
Stop Event
1×unsound
1×node limit
Symmetry

(sort y z t)

(sort a b)

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify55.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
698×fma-neg_binary64
641×fma-def_binary64
211×cancel-sign-sub-inv_binary64
172×distribute-rgt-neg-in_binary64
157×unsub-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01825
13923
212321
342321
490821
5146321
6215521
7254721
8301921
9313421
10313821
11313821
12313821
Stop Event
1×saturated
Counts
1 → 2

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
2.9b
(fma.f64 x 2 (fma.f64 y (*.f64 z (*.f64 t -9)) (*.f64 a (*.f64 27 b))))
▶2.7b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))
Compiler

Compiled 126 to 90 computations (28.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t))
✓0.2b
(*.f64 (*.f64 y 9) z)
✓0.2b
(*.f64 (*.f64 a 27) b)
✓5.4b
(*.f64 (*.f64 (*.f64 y 9) z) t)

series36.0ms (0.5%)

Counts
4 → 132
Calls

33 calls:

3.0ms
(*.f64 (*.f64 (*.f64 y 9) z) t)
y
0
2.0ms
(*.f64 (*.f64 y 9) z)
z
inf
1.0ms
(-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t))
x
inf
1.0ms
(-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t))
x
-inf
1.0ms
(*.f64 (*.f64 (*.f64 y 9) z) t)
y
inf

rewrite72.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
318×log1p-udef_binary64
177×add-sqr-sqrt_binary64
169×log1p-expm1-u_binary64
169×expm1-log1p-u_binary64
168×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01740
136540
2453240
Stop Event
1×node limit
Counts
4 → 94

simplify106.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
760×fma-def_binary64
290×fma-neg_binary64
132×distribute-rgt-neg-in_binary64
131×cancel-sign-sub-inv_binary64
92×associate-*l*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0211362
1441290
21071290
32651290
44581290
56391290
68401290
710861290
813141290
919851290
1022381290
1122681290
1222681290
Stop Event
1×saturated
Counts
226 → 105

prune126.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New987105
Fresh011
Picked101
Done000
Total998107
Error
0.0b
Counts
107 → 8
Alt Table
StatusErrorProgram
2.7b
(+.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) (*.f64 (*.f64 a 27) b))
2.9b
(fma.f64 x 2 (fma.f64 y (*.f64 z (*.f64 t -9)) (*.f64 a (*.f64 27 b))))
30.6b
(+.f64 (*.f64 z (*.f64 t (*.f64 y -9))) (*.f64 (*.f64 a 27) b))
▶2.7b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 27 (*.f64 a b)))
2.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 9 (*.f64 y (*.f64 t z)))) (*.f64 (*.f64 a 27) b))
2.9b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 y 9) (neg.f64 (*.f64 z t)))) (*.f64 (*.f64 a 27) b))
12.7b
(+.f64 (+.f64 (-.f64 (*.f64 x 2) (*.f64 y (*.f64 9 (*.f64 z t)))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 y (*.f64 9 (*.f64 z t))))) (cbrt.f64 (pow.f64 (*.f64 y (*.f64 9 (*.f64 z t))) 2)) (*.f64 y (*.f64 9 (*.f64 z t))))) (*.f64 (*.f64 a 27) b))
29.1b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (pow.f64 (sqrt.f64 (*.f64 a (*.f64 27 b))) 2))
Compiler

Compiled 3136 to 1987 computations (36.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t))
0.2b
(*.f64 (*.f64 y 9) z)
✓0.3b
(*.f64 27 (*.f64 a b))
5.4b
(*.f64 (*.f64 (*.f64 y 9) z) t)

series4.0ms (0.1%)

Counts
1 → 0
Calls

6 calls:

1.0ms
(*.f64 27 (*.f64 a b))
a
0
1.0ms
(*.f64 27 (*.f64 a b))
b
inf
1.0ms
(*.f64 27 (*.f64 a b))
b
-inf
1.0ms
(*.f64 27 (*.f64 a b))
a
inf
1.0ms
(*.f64 27 (*.f64 a b))
a
-inf

rewrite35.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
512×log1p-expm1-u_binary64
512×expm1-log1p-u_binary64
386×unpow-prod-down_binary64
299×log-prod_binary64
153×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
11217
214057
Stop Event
1×node limit
Counts
1 → 17

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
17 → 17

prune133.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1023105
Fresh347
Picked101
Done000
Total1067113
Error
0.0b
Counts
113 → 7
Alt Table
StatusErrorProgram
2.9b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 9 (*.f64 y (*.f64 t z)))) (*.f64 27 (*.f64 a b)))
2.9b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 y 9) (neg.f64 (*.f64 z t)))) (*.f64 (*.f64 a 27) b))
2.9b
(fma.f64 x 2 (fma.f64 y (*.f64 z (*.f64 t -9)) (*.f64 a (*.f64 27 b))))
30.6b
(+.f64 (*.f64 z (*.f64 t (*.f64 y -9))) (*.f64 27 (*.f64 a b)))
▶2.7b
(+.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) (*.f64 27 (*.f64 a b)))
12.7b
(+.f64 (+.f64 (-.f64 (*.f64 x 2) (*.f64 y (*.f64 9 (*.f64 z t)))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 y (*.f64 9 (*.f64 z t))))) (cbrt.f64 (pow.f64 (*.f64 y (*.f64 9 (*.f64 z t))) 2)) (*.f64 y (*.f64 9 (*.f64 z t))))) (*.f64 (*.f64 a 27) b))
29.1b
(+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (pow.f64 (sqrt.f64 (*.f64 a (*.f64 27 b))) 2))
Compiler

Compiled 3112 to 1874 computations (39.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) (*.f64 27 (*.f64 a b)))
✓0.2b
(*.f64 y (*.f64 z -9))
0.3b
(*.f64 27 (*.f64 a b))
✓3.2b
(fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x))

series48.0ms (0.6%)

Counts
3 → 144
Calls

36 calls:

3.0ms
(+.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) (*.f64 27 (*.f64 a b)))
t
0
2.0ms
(fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x))
x
0
2.0ms
(+.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) (*.f64 27 (*.f64 a b)))
x
0
2.0ms
(fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x))
x
-inf
2.0ms
(+.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) (*.f64 27 (*.f64 a b)))
t
inf

rewrite66.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
314×expm1-udef_binary64
314×log1p-udef_binary64
176×add-sqr-sqrt_binary64
166×log1p-expm1-u_binary64
166×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01744
135342
2435342
Stop Event
1×node limit
Counts
3 → 76

simplify176.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
738×fma-def_binary64
699×fma-neg_binary64
297×cancel-sign-sub-inv_binary64
180×distribute-rgt-neg-in_binary64
119×unsub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0242256
1552070
21382070
33662070
47092070
510932070
615742070
721722070
826382070
929432070
1032622070
1132962070
1232962070
1332962070
Stop Event
1×saturated
Counts
220 → 90

prune121.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1052107
Fresh246
Picked011
Done000
Total1077114
Error
0.0b
Counts
114 → 7
Alt Table
StatusErrorProgram
2.9b
(fma.f64 x 2 (fma.f64 y (*.f64 z (*.f64 t -9)) (*.f64 a (*.f64 27 b))))
30.6b
(+.f64 (*.f64 z (*.f64 t (*.f64 y -9))) (*.f64 27 (*.f64 a b)))
✓2.7b
(+.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) (*.f64 27 (*.f64 a b)))
2.9b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 y 9) (neg.f64 (*.f64 z t)))) (*.f64 (*.f64 a 27) b))
▶2.9b
(fma.f64 (*.f64 y (*.f64 t z)) -9 (fma.f64 27 (*.f64 a b) (*.f64 2 x)))
12.7b
(+.f64 (+.f64 (-.f64 (*.f64 x 2) (*.f64 y (*.f64 9 (*.f64 z t)))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 y (*.f64 9 (*.f64 z t))))) (cbrt.f64 (pow.f64 (*.f64 y (*.f64 9 (*.f64 z t))) 2)) (*.f64 y (*.f64 9 (*.f64 z t))))) (*.f64 (*.f64 a 27) b))
33.4b
(/.f64 (-.f64 (pow.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) 2) (*.f64 (pow.f64 (*.f64 a b) 2) 729)) (+.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) (*.f64 -27 (*.f64 a b))))
Compiler

Compiled 2801 to 1765 computations (37% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(fma.f64 (*.f64 y (*.f64 t z)) -9 (fma.f64 27 (*.f64 a b) (*.f64 2 x)))
✓0.1b
(fma.f64 27 (*.f64 a b) (*.f64 2 x))
✓6.9b
(*.f64 y (*.f64 t z))

series58.0ms (0.8%)

Counts
3 → 108
Calls

36 calls:

9.0ms
(fma.f64 27 (*.f64 a b) (*.f64 2 x))
x
inf
6.0ms
(fma.f64 (*.f64 y (*.f64 t z)) -9 (fma.f64 27 (*.f64 a b) (*.f64 2 x)))
x
-inf
3.0ms
(fma.f64 (*.f64 y (*.f64 t z)) -9 (fma.f64 27 (*.f64 a b) (*.f64 2 x)))
x
inf
2.0ms
(fma.f64 (*.f64 y (*.f64 t z)) -9 (fma.f64 27 (*.f64 a b) (*.f64 2 x)))
z
-inf
2.0ms
(fma.f64 (*.f64 y (*.f64 t z)) -9 (fma.f64 27 (*.f64 a b) (*.f64 2 x)))
y
-inf

rewrite58.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
286×expm1-udef_binary64
286×log1p-udef_binary64
189×prod-diff_binary64
160×add-sqr-sqrt_binary64
148×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01639
132139
2370339
Stop Event
1×node limit
Counts
3 → 62

simplify136.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
710×fma-def_binary64
685×fma-neg_binary64
295×cancel-sign-sub-inv_binary64
178×distribute-rgt-neg-in_binary64
119×unsub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0221770
1501656
21311656
33741656
47171656
510991656
615511656
721331656
825971656
929021656
1032211656
1132551656
1232551656
1332551656
Stop Event
1×saturated
Counts
170 → 73

prune77.0ms (1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New71273
Fresh235
Picked011
Done011
Total73780
Error
0.0b
Counts
80 → 7
Alt Table
StatusErrorProgram
33.4b
(/.f64 (-.f64 (pow.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) 2) (*.f64 (pow.f64 (*.f64 a b) 2) 729)) (+.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) (*.f64 -27 (*.f64 a b))))
25.0b
(fma.f64 z (*.f64 t (*.f64 y -9)) (*.f64 2 x))
2.9b
(fma.f64 x 2 (fma.f64 y (*.f64 z (*.f64 t -9)) (*.f64 a (*.f64 27 b))))
✓2.7b
(+.f64 (fma.f64 t (*.f64 y (*.f64 z -9)) (*.f64 2 x)) (*.f64 27 (*.f64 a b)))
2.9b
(+.f64 (fma.f64 x 2 (*.f64 (*.f64 y 9) (neg.f64 (*.f64 z t)))) (*.f64 (*.f64 a 27) b))
✓2.9b
(fma.f64 (*.f64 y (*.f64 t z)) -9 (fma.f64 27 (*.f64 a b) (*.f64 2 x)))
2.6b
(fma.f64 (pow.f64 (*.f64 (*.f64 y z) t) 1) -9 (fma.f64 27 (*.f64 a b) (*.f64 2 x)))
Compiler

Compiled 1602 to 846 computations (47.2% saved)

regimes1.5s (20.1%)

Accuracy

Total 0.5b remaining (96.9%)

Threshold costs 0.5b (96.9%)

Counts
68 → 2
Compiler

Compiled 27174 to 19729 computations (27.4% saved)

bsearch7.0ms (0.1%)

Algorithm
1×binary-search
Calls

1 calls:

5.0ms
z
Steps
ItersPointRange
4.469489406442574e-111
∈ [
8.790981101733973e-113
, 
2.1245702504901676e-109
]
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
6×*-commutative_binary64
1×1-exp_binary64
1×unpow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02548
13448
Stop Event
1×saturated

end768.0ms (10.3%)

Stop Event
1×fuel
Remove

(sort a b)

Compiler

Compiled 489 to 330 computations (32.5% saved)

Profiling

Loading profile data...