Details

Time bar (total: 7.3s)

analyze1.4s (19.1%)

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
1.8%98%0.2%10
7.7%92.1%0.2%11
10.4%89.4%0.2%12
12.2%87.6%0.2%13
21.8%77.8%0.4%14
Compiler

Compiled 14 to 12 computations (14.3% saved)

sample29.0ms (0.4%)

Algorithm
intervals
Results
8.0ms208×body80valid
2.0ms20×body320valid
2.0ms49×body80invalid
2.0ms11×body640valid
1.0msbody1280valid
1.0ms10×body160valid
Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify134.0ms (1.8%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (120.0ms)

IterNodesCost
0489419
1489419

prune12.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.8b

Counts
2 → 1
Compiler

Compiled 26 to 22 computations (15.4% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 (-.f64 y z) (-.f64 t x))
2.5b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
18.5b
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite35.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
13×flip3--_binary64 flip--_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64
associate-/l/_binary64 frac-times_binary64
add-cube-cbrt_binary64
associate-/r*_binary64 add-log-exp_binary64 pow1_binary64 associate-*r*_binary64 associate-*l*_binary64 times-frac_binary64
associate-*r/_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 associate-*l/_binary64
sub-neg_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 associate-/r/_binary64 prod-exp_binary64 div-exp_binary64
pow-prod-down_binary64 flip3-+_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
3 → 79
Calls

3 calls:

14.0ms
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
10.0ms
(*.f64 (-.f64 y z) (-.f64 t x))
8.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

series128.0ms (1.7%)

Counts
3 → 9
Calls

3 calls:

64.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
54.0ms
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
10.0ms
(*.f64 (-.f64 y z) (-.f64 t x))

simplify80.0ms (1.1%)

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
060391597

prune99.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New771188
Fresh000
Picked011
Done000
Total771289

Merged error: 3.3b

Counts
89 → 12
Compiler

Compiled 1931 to 532 computations (72.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 a z))
0.5b
(cbrt.f64 (-.f64 a z))
2.5b
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
8.1b
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

rewrite64.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt_binary64
59×*-un-lft-identity_binary64
52×times-frac_binary64
46×associate-*r*_binary64
37×cbrt-prod_binary64
27×add-cube-cbrt_binary64
25×add-exp-log_binary64
18×cbrt-div_binary64 add-cbrt-cube_binary64
17×associate-*l*_binary64
16×difference-of-squares_binary64 distribute-lft-out--_binary64
10×associate-/r/_binary64
flip3--_binary64 flip--_binary64
cbrt-unprod_binary64 prod-exp_binary64
cbrt-undiv_binary64 div-exp_binary64
add-log-exp_binary64 pow1_binary64 unswap-sqr_binary64
frac-times_binary64
associate-*r/_binary64 associate-*l/_binary64
pow1/3_binary64 div-inv_binary64
pow-prod-down_binary64 flip3-+_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 134
Calls

4 calls:

36.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
6.0ms
(cbrt.f64 (-.f64 a z))
5.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
4.0ms
(cbrt.f64 (-.f64 a z))

series237.0ms (3.2%)

Counts
4 → 12
Calls

4 calls:

100.0ms
(+.f64 x (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
74.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
37.0ms
(cbrt.f64 (-.f64 a z))
25.0ms
(cbrt.f64 (-.f64 a z))

simplify116.0ms (1.6%)

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
052943936

prune212.0ms (2.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1406146
Fresh3710
Picked101
Done011
Total14414158

Merged error: 3.3b

Counts
158 → 14
Compiler

Compiled 4732 to 898 computations (81% saved)

localize48.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))
0.7b
(*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
0.8b
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))
10.1b
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

rewrite206.0ms (2.8%)

Algorithm
rewrite-expression-head
Rules
163×cbrt-prod_binary64
144×add-exp-log_binary64
110×associate-*r*_binary64
105×add-sqr-sqrt_binary64
104×times-frac_binary64
95×*-un-lft-identity_binary64
70×add-cbrt-cube_binary64
65×cbrt-unprod_binary64 prod-exp_binary64
56×cbrt-div_binary64
55×add-cube-cbrt_binary64
46×cbrt-undiv_binary64 div-exp_binary64
20×difference-of-squares_binary64 distribute-lft-out--_binary64
19×flip3--_binary64 flip--_binary64
18×associate-/r/_binary64 associate-*l*_binary64 frac-times_binary64
12×associate-*l/_binary64
11×pow1_binary64
10×associate-*r/_binary64
add-log-exp_binary64 unswap-sqr_binary64
pow-prod-down_binary64
div-inv_binary64
*-commutative_binary64
flip3-+_binary64 pow1/3_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64
Counts
4 → 249
Calls

4 calls:

76.0ms
(*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
63.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))
19.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))
11.0ms
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

series420.0ms (5.7%)

Counts
4 → 12
Calls

4 calls:

211.0ms
(*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))))
108.0ms
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
68.0ms
(*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
33.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))

simplify183.0ms (2.5%)

Algorithm
egg-herbie
Counts
261 → 261
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0503816145

prune271.0ms (3.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2574261
Fresh4812
Picked101
Done011
Total26213275

Merged error: 3.3b

Counts
275 → 13
Compiler

Compiled 14816 to 2161 computations (85.4% saved)

localize32.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 t x))
0.6b
(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))
0.7b
(*.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
8.6b
(+.f64 x (*.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

rewrite111.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
288×add-exp-log_binary64
165×cbrt-prod_binary64
148×cbrt-unprod_binary64 prod-exp_binary64
104×add-cbrt-cube_binary64
94×associate-*r*_binary64
92×*-un-lft-identity_binary64 cbrt-undiv_binary64 add-sqr-sqrt_binary64 div-exp_binary64
88×times-frac_binary64
52×add-cube-cbrt_binary64
26×cbrt-div_binary64
21×frac-times_binary64
20×difference-of-squares_binary64 distribute-lft-out--_binary64
15×associate-*l/_binary64
13×pow1_binary64 associate-*r/_binary64
flip3--_binary64 flip--_binary64
pow-prod-down_binary64 add-log-exp_binary64
pow1/3_binary64 associate-/r/_binary64
flip3-+_binary64 associate-*l*_binary64 div-inv_binary64 +-commutative_binary64 flip-+_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 252
Calls

4 calls:

70.0ms
(*.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
10.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))
7.0ms
(+.f64 x (*.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
3.0ms
(cbrt.f64 (-.f64 t x))

series192.0ms (2.6%)

Counts
4 → 12
Calls

4 calls:

69.0ms
(*.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
64.0ms
(+.f64 x (*.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (cbrt.f64 (-.f64 a z))) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
34.0ms
(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))
25.0ms
(cbrt.f64 (-.f64 t x))

simplify237.0ms (3.2%)

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
0500120285

prune155.0ms (2.1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New2631264
Fresh01111
Picked011
Done011
Total26314277

Merged error: 3.3b

Counts
277 → 14
Compiler

Compiled 16830 to 1475 computations (91.2% saved)

regimes610.0ms (8.3%)

Compiler

Compiled 3144 to 1596 computations (49.2% saved)

bsearch89.0ms (1.2%)

Steps
ItersRangePoint
8
2.3542111825163664e+188
4.2796275971846994e+192
5.623859092829061e+189
8
-2.4338734444855465e+112
-3.2865750821796655e+108
-2.0363509759686045e+110
9
-2.938522547506897e+216
-7.808719703674719e+207
-6.569825719871904e+210
8
-9.818578761893817e+250
-2.4609590677187412e+247
-4.2800453603295935e+247
Compiler

Compiled 1 to 5 computations (-400% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0103137
1103137

end0.0ms (0%)

sample2.2s (29.9%)

Algorithm
intervals
Results
257.0ms6547×body80valid
72.0ms478×body640valid
48.0ms256×body1280valid
43.0ms416×body320valid
42.0ms1182×body80invalid
20.0ms283×body160valid
4.0ms20×body2560valid
Compiler

Compiled 658 to 334 computations (49.2% saved)

Profiling

Loading profile data...