Details

Time bar (total: 17.3s)

analyze2.5s (14.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.6%0.4%0
0%99.6%0.4%1
0%99.6%0.4%2
0%99.6%0.4%3
0%99.6%0.4%4
0%99.6%0.4%5
0%99.6%0.4%6
0%99.6%0.4%7
0%99.6%0.4%8
0%99.6%0.4%9
0%99.6%0.4%10
0%99.6%0.4%11
0%99.6%0.4%12
0%99.6%0.4%13
0%99.6%0.4%14
Compiler

Compiled 39 to 24 computations (38.5% saved)

sample3.8s (21.7%)

Results
2.1s11259×body128invalid
1.5s8256×body128valid
Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify35.0ms (0.2%)

Algorithm
egg-herbie
Rules
486×fma-neg_binary64
408×sub-neg_binary64
353×unsub-neg_binary64
284×fma-def_binary64
258×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02443
15941
215541
354839
4192639
5445539
Stop Event
node limit
Counts
1 → 2

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
15.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
15.0b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))))
Compiler

Compiled 137 to 74 computations (46% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 y z) (*.f64 t a))
4.9b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))))
5.8b
(fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))
6.7b
(*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))

series192.0ms (1.1%)

Counts
4 → 312
Calls

4 calls:

99.0ms
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))))
64.0ms
(fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))
20.0ms
(*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))
8.0ms
(-.f64 (*.f64 y z) (*.f64 t a))

rewrite42.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
238×add-sqr-sqrt_binary64
219×log1p-expm1-u_binary64
219×expm1-log1p-u_binary64
218×add-cbrt-cube_binary64
216×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02288
146278
Stop Event
node limit
Counts
4 → 105
Calls

4 calls:

39.0ms
(-.f64 (*.f64 y z) (*.f64 t a))
39.0ms
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))))
39.0ms
(fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c))))
39.0ms
(*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))

simplify133.0ms (0.8%)

Algorithm
egg-herbie
Rules
870×fma-neg_binary64
391×sub-neg_binary64
371×associate--l+_binary64
329×cancel-sign-sub-inv_binary64
199×distribute-rgt-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01717694
16747597
215417516
329507105
Stop Event
node limit
Counts
417 → 205

prune229.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1969205
Fresh000
Picked011
Done000
Total19610206
Error
0.0b
Counts
206 → 10
Alt Table
StatusErrorProgram
44.4b
(*.f64 (-.f64 (*.f64 y x) (*.f64 c b)) z)
29.5b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (*.f64 i (-.f64 (*.f64 a b) (*.f64 j y))))
45.1b
(pow.f64 (sqrt.f64 (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (fma.f64 z c (*.f64 i a)) (*.f64 j (fma.f64 i y (*.f64 t c)))))) 2)
12.0b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (-.f64 (+.f64 (*.f64 i (*.f64 a b)) (*.f64 c (*.f64 t j))) (+.f64 (*.f64 i (*.f64 y j)) (*.f64 c (*.f64 z b)))))
21.3b
(fma.f64 x (+.f64 (fma.f64 y z (neg.f64 (*.f64 (cbrt.f64 (*.f64 t a)) (cbrt.f64 (pow.f64 (*.f64 t a) 2))))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 t a))) (cbrt.f64 (pow.f64 (*.f64 t a) 2)) (*.f64 (cbrt.f64 (*.f64 t a)) (cbrt.f64 (pow.f64 (*.f64 t a) 2))))) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))))
11.9b
(+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (fma.f64 z (-.f64 (*.f64 y x) (*.f64 c b)) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))))
13.1b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 y (*.f64 i j)) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
45.8b
(*.f64 t (-.f64 (*.f64 c j) (*.f64 a x)))
32.8b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (pow.f64 (cbrt.f64 (fma.f64 b (fma.f64 z c (*.f64 i a)) (*.f64 j (fma.f64 i y (*.f64 t c))))) 3))
15.0b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))))
Compiler

Compiled 6731 to 1293 computations (80.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 y x) (*.f64 c b))
4.1b
(fma.f64 z (-.f64 (*.f64 y x) (*.f64 c b)) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x))))
4.7b
(*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))
6.7b
(*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))

series103.0ms (0.6%)

Counts
4 → 220
Calls

4 calls:

55.0ms
(fma.f64 z (-.f64 (*.f64 y x) (*.f64 c b)) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x))))
20.0ms
(*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))
19.0ms
(*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))
8.0ms
(-.f64 (*.f64 y x) (*.f64 c b))

rewrite41.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
255×add-sqr-sqrt_binary64
240×log1p-expm1-u_binary64
240×expm1-log1p-u_binary64
239×add-cbrt-cube_binary64
234×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02262
149962
Stop Event
node limit
Counts
4 → 88
Calls

4 calls:

38.0ms
(-.f64 (*.f64 y x) (*.f64 c b))
38.0ms
(fma.f64 z (-.f64 (*.f64 y x) (*.f64 c b)) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x))))
38.0ms
(*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))
38.0ms
(*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))

simplify262.0ms (1.5%)

Algorithm
egg-herbie
Rules
1699×fma-neg_binary64
805×fma-def_binary64
339×sub-neg_binary64
262×unsub-neg_binary64
235×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0873877
12963788
27023716
315423572
430023572
539803572
643823572
745993572
846753572
946873572
1046893572
1147993572
1248433572
1348433572
Stop Event
node limit
Counts
308 → 140

prune155.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1373140
Fresh448
Picked101
Done011
Total1428150
Error
0.0b
Counts
150 → 8
Alt Table
StatusErrorProgram
12.0b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (-.f64 (+.f64 (*.f64 i (*.f64 a b)) (*.f64 c (*.f64 t j))) (+.f64 (*.f64 i (*.f64 y j)) (*.f64 c (*.f64 z b)))))
21.5b
(+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (fma.f64 z (-.f64 (*.f64 y x) (*.f64 c b)) (*.f64 t (*.f64 x (neg.f64 a)))))
45.1b
(pow.f64 (sqrt.f64 (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (fma.f64 z c (*.f64 i a)) (*.f64 j (fma.f64 i y (*.f64 t c)))))) 2)
13.1b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 y (*.f64 i j)) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
45.8b
(*.f64 t (-.f64 (*.f64 c j) (*.f64 a x)))
24.8b
(+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (fma.f64 z (/.f64 (-.f64 (pow.f64 (*.f64 y x) 2) (pow.f64 (*.f64 c b) 2)) (fma.f64 y x (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))))
12.5b
(+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 y x (neg.f64 (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x))))) 3))
15.0b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))))
Compiler

Compiled 4949 to 1022 computations (79.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.4b
(*.f64 i (*.f64 a b))
4.9b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (-.f64 (+.f64 (*.f64 i (*.f64 a b)) (*.f64 c (*.f64 t j))) (+.f64 (*.f64 i (*.f64 y j)) (*.f64 c (*.f64 z b)))))
5.6b
(*.f64 i (*.f64 y j))
6.9b
(*.f64 c (*.f64 t j))

series130.0ms (0.8%)

Counts
4 → 140
Calls

4 calls:

103.0ms
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (-.f64 (+.f64 (*.f64 i (*.f64 a b)) (*.f64 c (*.f64 t j))) (+.f64 (*.f64 i (*.f64 y j)) (*.f64 c (*.f64 z b)))))
10.0ms
(*.f64 i (*.f64 a b))
9.0ms
(*.f64 c (*.f64 t j))
8.0ms
(*.f64 i (*.f64 y j))

rewrite36.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
272×log1p-expm1-u_binary64
272×expm1-log1p-u_binary64
271×add-cbrt-cube_binary64
264×add-log-exp_binary64
263×add-cube-cbrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02564
156064
Stop Event
node limit
Counts
4 → 52
Calls

4 calls:

35.0ms
(*.f64 i (*.f64 a b))
35.0ms
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (-.f64 (+.f64 (*.f64 i (*.f64 a b)) (*.f64 c (*.f64 t j))) (+.f64 (*.f64 i (*.f64 y j)) (*.f64 c (*.f64 z b)))))
35.0ms
(*.f64 i (*.f64 y j))
35.0ms
(*.f64 c (*.f64 t j))

simplify86.0ms (0.5%)

Algorithm
egg-herbie
Rules
752×fma-neg_binary64
740×fma-def_binary64
414×cancel-sign-sub-inv_binary64
350×associate--l+_binary64
325×sub-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01194292
14404292
212304202
333204013
Stop Event
node limit
Counts
192 → 111

prune89.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1092111
Fresh336
Picked011
Done011
Total1127119
Error
0.0b
Counts
119 → 7
Alt Table
StatusErrorProgram
29.0b
(fma.f64 z (-.f64 (*.f64 y x) (*.f64 b c)) (*.f64 t (-.f64 (*.f64 j c) (*.f64 a x))))
12.5b
(+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 y x (neg.f64 (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x))))) 3))
12.0b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (-.f64 (+.f64 (*.f64 i (*.f64 a b)) (*.f64 c (*.f64 t j))) (+.f64 (*.f64 i (*.f64 y j)) (*.f64 c (*.f64 z b)))))
13.1b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 y (*.f64 i j)) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
35.0b
(pow.f64 (sqrt.f64 (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (-.f64 (fma.f64 i (*.f64 a b) (*.f64 (*.f64 c t) j)) (fma.f64 c (*.f64 z b) (*.f64 i (*.f64 j y)))))) 2)
24.8b
(+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (fma.f64 z (/.f64 (-.f64 (pow.f64 (*.f64 y x) 2) (pow.f64 (*.f64 c b) 2)) (fma.f64 y x (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))))
15.0b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))))
Compiler

Compiled 3432 to 721 computations (79% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.8b
(cbrt.f64 (fma.f64 z (fma.f64 y x (neg.f64 (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))))
4.1b
(fma.f64 z (fma.f64 y x (neg.f64 (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x))))
4.7b
(*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))
6.7b
(*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))

series180.0ms (1%)

Counts
2 → 128
Calls

2 calls:

126.0ms
(cbrt.f64 (fma.f64 z (fma.f64 y x (neg.f64 (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))))
54.0ms
(fma.f64 z (fma.f64 y x (neg.f64 (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x))))

rewrite40.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
196×add-sqr-sqrt_binary64
181×add-cbrt-cube_binary64
181×log1p-expm1-u_binary64
181×expm1-log1p-u_binary64
178×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01854
138250
Stop Event
node limit
Counts
2 → 47
Calls

2 calls:

38.0ms
(cbrt.f64 (fma.f64 z (fma.f64 y x (neg.f64 (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))))
38.0ms
(fma.f64 z (fma.f64 y x (neg.f64 (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x))))

simplify133.0ms (0.8%)

Algorithm
egg-herbie
Rules
589×*-commutative_binary64
471×fma-def_binary64
308×sub-neg_binary64
253×fma-neg_binary64
203×+-commutative_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05009679
118368723
244878723
Stop Event
node limit
Counts
175 → 154

prune213.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1981199
Fresh044
Picked011
Done022
Total1988206
Error
0.0b
Counts
206 → 8
Alt Table
StatusErrorProgram
29.0b
(fma.f64 z (-.f64 (*.f64 y x) (*.f64 b c)) (*.f64 t (-.f64 (*.f64 j c) (*.f64 a x))))
12.5b
(+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (pow.f64 (cbrt.f64 (fma.f64 z (fma.f64 y x (neg.f64 (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x))))) 3))
12.0b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (-.f64 (+.f64 (*.f64 i (*.f64 a b)) (*.f64 c (*.f64 t j))) (+.f64 (*.f64 i (*.f64 y j)) (*.f64 c (*.f64 z b)))))
13.1b
(-.f64 (+.f64 (*.f64 a (*.f64 i b)) (+.f64 (*.f64 c (*.f64 t j)) (*.f64 y (*.f64 z x)))) (+.f64 (*.f64 y (*.f64 i j)) (+.f64 (*.f64 c (*.f64 b z)) (*.f64 a (*.f64 t x)))))
35.0b
(pow.f64 (sqrt.f64 (fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (-.f64 (fma.f64 i (*.f64 a b) (*.f64 (*.f64 c t) j)) (fma.f64 c (*.f64 z b) (*.f64 i (*.f64 j y)))))) 2)
24.8b
(+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (fma.f64 z (/.f64 (-.f64 (pow.f64 (*.f64 y x) 2) (pow.f64 (*.f64 c b) 2)) (fma.f64 y x (*.f64 c b))) (*.f64 a (-.f64 (*.f64 i b) (*.f64 t x)))))
39.2b
(+.f64 (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))) (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 z (fma.f64 y x (*.f64 c b)) (*.f64 a (-.f64 (*.f64 b i) (*.f64 x t)))) 2)) 1/3) (cbrt.f64 (cbrt.f64 (fma.f64 z (fma.f64 y x (*.f64 c b)) (*.f64 a (-.f64 (*.f64 b i) (*.f64 x t))))))) 3))
15.0b
(fma.f64 x (-.f64 (*.f64 y z) (*.f64 t a)) (fma.f64 b (fma.f64 z (neg.f64 c) (*.f64 a i)) (*.f64 j (fma.f64 i (neg.f64 y) (*.f64 t c)))))
Compiler

Compiled 13446 to 4261 computations (68.3% saved)

regimes8.5s (49.5%)

Accuracy

Total 2.7b remaining (96.9%)

Threshold costs 0b (0%)

Counts
242 → 3
Compiler

Compiled 79756 to 49898 computations (37.4% saved)

bsearch14.0ms (0.1%)

Compiler

Compiled 38 to 23 computations (39.5% saved)

simplify38.0ms (0.2%)

Algorithm
egg-herbie
Rules
226×distribute-rgt-neg-in_binary64
200×cancel-sign-sub-inv_binary64
150×distribute-lft-neg-in_binary64
145×neg-sub0_binary64
145×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
065231
1135231
2204231
3253231
4320231
5365231
6418231
7544231
8668231
9789231
10948231
111172231
121391231
131571231
141667231
151715231
161733231
171737231
Stop Event
saturated

end185.0ms (1.1%)

Compiler

Compiled 671 to 319 computations (52.5% saved)

Profiling

Loading profile data...