Details

Time bar (total: 7.6s)

analyze1.3s (16.6%)

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
2.3%97.4%0.2%9
4.7%95.1%0.2%10
12.7%87.1%0.2%11
15.9%83.9%0.2%12
24.9%74.9%0.2%13
33.2%66.5%0.2%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample26.0ms (0.3%)

Algorithm
intervals
Results
11.0ms256×body128valid
1.0ms16×body128invalid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify124.0ms (1.6%)

Algorithm
egg-herbie
Rules
1691×fma-neg_binary64
841×div-sub_binary64
807×distribute-rgt-in_binary64
769×fma-def_binary64
504×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01116
11916
24014
38214
416614
529714
664314
7155114
8311114
9306414
10315314
11315214
12317014
13320114
14549414

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.6b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
11.9b
(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 z t) (-.f64 z a))
0.5b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

rewrite29.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
20×add-cube-cbrt_binary64
10×add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
add-sqr-sqrt_binary64
Counts
2 → 87
Calls

2 calls:

17.0ms
(/.f64 (-.f64 z t) (-.f64 z a))
9.0ms
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series102.0ms (1.3%)

Counts
2 → 96
Calls

2 calls:

73.0ms
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
28.0ms
(/.f64 (-.f64 z t) (-.f64 z a))

simplify146.0ms (1.9%)

Algorithm
egg-herbie
Rules
576×cancel-sign-sub-inv_binary64
359×sub-neg_binary64
291×fma-neg_binary64
181×times-frac_binary64
174×div-sub_binary64
Counts
183 → 294
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02774179
17724102
229683951
344503621
451093621

prune139.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2886294
Fresh101
Picked011
Done000
Total2897296
Error
0.0b
Counts
296 → 7
Alt Table
StatusErrorProgram
1.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
11.9b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (-.f64 z a)) x) (/.f64 (*.f64 y t) (-.f64 z a)))
33.5b
(/.f64 (-.f64 (*.f64 y (*.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 2) y)) (*.f64 x x)) (-.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) x))
1.2b
(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (cbrt.f64 (-.f64 z a))) x)
0.6b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
0.9b
(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 3) x)
0.6b
(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
Compiler

Compiled 4158 to 1328 computations (68.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 z a) (-.f64 z t))
0.1b
(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1)
0.5b
(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)

rewrite45.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
28×add-cube-cbrt_binary64
13×add-cbrt-cube_binary64
12×add-exp-log_binary64
12×add-sqr-sqrt_binary64
11×pow1_binary64
Counts
3 → 130
Calls

3 calls:

15.0ms
(/.f64 (-.f64 z a) (-.f64 z t))
12.0ms
(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
11.0ms
(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1)

series255.0ms (3.3%)

Counts
3 → 132
Calls

3 calls:

159.0ms
(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
66.0ms
(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1)
29.0ms
(/.f64 (-.f64 z a) (-.f64 z t))

simplify160.0ms (2.1%)

Algorithm
egg-herbie
Rules
671×associate-/l*_binary64
555×associate-/r*_binary64
217×fma-def_binary64
203×+-commutative_binary64
195×sub-neg_binary64
Counts
262 → 438
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
06488912
120118515
250298515

prune296.0ms (3.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New4362438
Fresh235
Picked011
Done011
Total4387445
Error
0b
Counts
445 → 7
Alt Table
StatusErrorProgram
1.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
11.9b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (-.f64 z a)) x) (/.f64 (*.f64 y t) (-.f64 z a)))
0.6b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
4.7b
(fma.f64 y (*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2)) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
33.5b
(/.f64 (-.f64 (*.f64 y (*.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 2) y)) (*.f64 x x)) (-.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) x))
25.5b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (-.f64 z a)) (+.f64 (/.f64 (*.f64 y (*.f64 a t)) (pow.f64 (-.f64 z a) 2)) x)) (/.f64 (*.f64 y (*.f64 t z)) (pow.f64 (-.f64 z a) 2)))
0.6b
(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
Compiler

Compiled 10084 to 4098 computations (59.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))
0.5b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
0.5b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
0.5b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cube-cbrt_binary64
add-sqr-sqrt_binary64
pow1/3_binary64
log1p-expm1-u_binary64
expm1-log1p-u_binary64
Counts
1 → 30
Calls

1 calls:

9.0ms
(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))

series570.0ms (7.5%)

Counts
1 → 60
Calls

1 calls:

569.0ms
(cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))

simplify248.0ms (3.3%)

Algorithm
egg-herbie
Rules
466×*-commutative_binary64
235×+-commutative_binary64
211×fma-def_binary64
208×associate-*r*_binary64
182×associate-+r+_binary64
Counts
90 → 151
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0104213584
1387312971
2510312971

prune389.0ms (5.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New122201222
Fresh044
Picked011
Done022
Total122271229
Error
0b
Counts
1229 → 7
Alt Table
StatusErrorProgram
1.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
11.9b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (-.f64 z a)) x) (/.f64 (*.f64 y t) (-.f64 z a)))
0.6b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
4.7b
(fma.f64 y (*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2)) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
33.5b
(/.f64 (-.f64 (*.f64 y (*.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 2) y)) (*.f64 x x)) (-.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) x))
25.5b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (-.f64 z a)) (+.f64 (/.f64 (*.f64 y (*.f64 a t)) (pow.f64 (-.f64 z a) 2)) x)) (/.f64 (*.f64 y (*.f64 t z)) (pow.f64 (-.f64 z a) 2)))
0.6b
(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
Compiler

Compiled 29685 to 10435 computations (64.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2)
0.5b
(fma.f64 y (*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2)) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
3.0b
(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))
10.7b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2))

rewrite61.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
27×add-cube-cbrt_binary64
16×add-sqr-sqrt_binary64
12×log1p-expm1-u_binary64
12×expm1-log1p-u_binary64
11×pow1_binary64
Counts
4 → 136
Calls

4 calls:

19.0ms
(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2)
17.0ms
(cbrt.f64 (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2))
9.0ms
(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))
9.0ms
(fma.f64 y (*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2)) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)

series653.0ms (8.6%)

Counts
4 → 168
Calls

4 calls:

286.0ms
(cbrt.f64 (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2))
152.0ms
(pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2)
129.0ms
(cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))
83.0ms
(fma.f64 y (*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2)) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)

simplify245.0ms (3.2%)

Algorithm
egg-herbie
Rules
547×*-commutative_binary64
298×fma-def_binary64
288×associate-+r+_binary64
173×associate-*r*_binary64
172×associate-*r/_binary64
Counts
304 → 475
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0152419316
1503219316

prune603.0ms (7.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New4750475
Fresh033
Picked011
Done033
Total4757482
Error
0b
Counts
482 → 7
Alt Table
StatusErrorProgram
1.8b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
11.9b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (-.f64 z a)) x) (/.f64 (*.f64 y t) (-.f64 z a)))
0.6b
(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
4.7b
(fma.f64 y (*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -2)) (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
33.5b
(/.f64 (-.f64 (*.f64 y (*.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 2) y)) (*.f64 x x)) (-.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) x))
25.5b
(-.f64 (+.f64 (/.f64 (*.f64 y z) (-.f64 z a)) (+.f64 (/.f64 (*.f64 y (*.f64 a t)) (pow.f64 (-.f64 z a) 2)) x)) (/.f64 (*.f64 y (*.f64 t z)) (pow.f64 (-.f64 z a) 2)))
0.6b
(fma.f64 y (pow.f64 (/.f64 (-.f64 z a) (-.f64 z t)) -1) x)
Compiler

Compiled 26097 to 13995 computations (46.4% saved)

regimes913.0ms (12%)

Accuracy

Total 1.2b remaining (98.5%)

Threshold costs 0b (0%)

Compiler

Compiled 18853 to 10621 computations (43.7% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01120
11520
22520
33120
43520
53620
63620

end0.0ms (0%)

Compiler

Compiled 19 to 10 computations (47.4% saved)

sample1.3s (17%)

Algorithm
intervals
Results
526.0ms7999×body128valid
43.0ms693×body128invalid
0.0msbody256valid
Compiler

Compiled 234 to 123 computations (47.4% saved)

Profiling

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