Details

Time bar (total: 11.1s)

analyze1.1s (9.8%)

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 (0.3%)

Algorithm
intervals
Results
9.0ms207×body128valid
3.0ms18×body1024valid
2.0ms15×body512valid
1.0ms33×body128invalid
1.0ms12×body256valid
1.0msbody2048valid
Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify257.0ms (2.3%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (87.0ms)

IterNodesCost
0485119
1485119

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 25.8b

Counts
2 → 1
Compiler

Compiled 26 to 22 computations (15.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 (-.f64 y z) (-.f64 t x))
2.2b
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
17.7b
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))

rewrite41.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64_10208 *-un-lft-identity_binary64_10187
13×flip--_binary64_10162 flip3--_binary64_10191
10×add-exp-log_binary64_10222 add-cbrt-cube_binary64_10220
associate-/l/_binary64_10136 frac-times_binary64_10197
add-cube-cbrt_binary64_10219
associate-*l*_binary64_10130 associate-*r*_binary64_10129 associate-/r*_binary64_10133 pow1_binary64_10245 add-log-exp_binary64_10223 times-frac_binary64_10193
associate-*r/_binary64_10131 distribute-lft-out--_binary64_10141 difference-of-squares_binary64_10156 associate-*l/_binary64_10132
associate-/r/_binary64_10135 cbrt-undiv_binary64_10218 sub-neg_binary64_10180 div-exp_binary64_10235 prod-exp_binary64_10233 cbrt-unprod_binary64_10217
frac-2neg_binary64_10198 distribute-lft-out_binary64_10140 +-commutative_binary64_10119 flip3-+_binary64_10190 pow-prod-down_binary64_10255 sum-log_binary64_10275 associate-/l*_binary64_10134 *-commutative_binary64_10120 unswap-sqr_binary64_10155 distribute-rgt-in_binary64_10139 flip-+_binary64_10161 div-inv_binary64_10184 distribute-lft-in_binary64_10138 clear-num_binary64_10186
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))
9.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

series944.0ms (8.5%)

Counts
3 → 9
Calls

3 calls:

499.0ms
(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
368.0ms
(/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))
77.0ms
(*.f64 (-.f64 y z) (-.f64 t x))

simplify62.0ms (0.6%)

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
067421599

prune99.0ms (0.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New751388
Fresh000
Picked011
Done000
Total751489

Merged error: 5.8b

Counts
89 → 14
Compiler

Compiled 2045 to 563 computations (72.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 a z))
0.5b
(cbrt.f64 (-.f64 a z))
1.9b
(*.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))))
10.0b
(+.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)))))

rewrite77.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt_binary64_10208
59×*-un-lft-identity_binary64_10187
52×times-frac_binary64_10193
46×associate-*r*_binary64_10129
37×cbrt-prod_binary64_10215
27×add-cube-cbrt_binary64_10219
25×add-exp-log_binary64_10222
18×cbrt-div_binary64_10216 add-cbrt-cube_binary64_10220
17×associate-*l*_binary64_10130
16×distribute-lft-out--_binary64_10141 difference-of-squares_binary64_10156
10×associate-/r/_binary64_10135
flip--_binary64_10162 flip3--_binary64_10191
prod-exp_binary64_10233 cbrt-unprod_binary64_10217
cbrt-undiv_binary64_10218 div-exp_binary64_10235
unswap-sqr_binary64_10155 pow1_binary64_10245 add-log-exp_binary64_10223
frac-times_binary64_10197
associate-*r/_binary64_10131 associate-*l/_binary64_10132
pow1/3_binary64_10266 div-inv_binary64_10184
+-commutative_binary64_10119 flip3-+_binary64_10190 pow-prod-down_binary64_10255 sum-log_binary64_10275 *-commutative_binary64_10120 flip-+_binary64_10161
Counts
4 → 134
Calls

4 calls:

46.0ms
(*.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))))
4.0ms
(+.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)))))
3.0ms
(cbrt.f64 (-.f64 a z))
3.0ms
(cbrt.f64 (-.f64 a z))

series1.8s (15.9%)

Counts
4 → 12
Calls

4 calls:

763.0ms
(*.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))))
544.0ms
(+.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)))))
230.0ms
(cbrt.f64 (-.f64 a z))
224.0ms
(cbrt.f64 (-.f64 a z))

simplify68.0ms (0.6%)

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
053093930

prune155.0ms (1.4%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1442146
Fresh01212
Picked011
Done011
Total14416160

Merged error: 5.8b

Counts
160 → 16
Compiler

Compiled 4781 to 898 computations (81.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (-.f64 a z))
0.5b
(cbrt.f64 (-.f64 a z))
1.7b
(*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
10.0b
(+.f64 x (*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))

rewrite127.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt_binary64_10208
98×times-frac_binary64_10193
84×cbrt-prod_binary64_10215
74×*-un-lft-identity_binary64_10187
69×add-exp-log_binary64_10222
61×associate-*r*_binary64_10129
44×cbrt-div_binary64_10216
42×add-cbrt-cube_binary64_10220
36×add-cube-cbrt_binary64_10219
29×associate-*l*_binary64_10130
27×cbrt-undiv_binary64_10218 div-exp_binary64_10235
24×prod-exp_binary64_10233 cbrt-unprod_binary64_10217
19×distribute-lft-out--_binary64_10141 difference-of-squares_binary64_10156
18×associate-/r/_binary64_10135
15×flip--_binary64_10162 flip3--_binary64_10191
12×unswap-sqr_binary64_10155
frac-times_binary64_10197
pow1_binary64_10245 add-log-exp_binary64_10223
associate-*r/_binary64_10131 associate-*l/_binary64_10132
div-inv_binary64_10184
pow1/3_binary64_10266
+-commutative_binary64_10119 flip3-+_binary64_10190 pow-prod-down_binary64_10255 sum-log_binary64_10275 *-commutative_binary64_10120 flip-+_binary64_10161
Counts
4 → 183
Calls

4 calls:

78.0ms
(*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
5.0ms
(+.f64 x (*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
4.0ms
(cbrt.f64 (-.f64 a z))
3.0ms
(cbrt.f64 (-.f64 a z))

series1.7s (15.6%)

Counts
4 → 12
Calls

4 calls:

759.0ms
(*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z)))))
537.0ms
(+.f64 x (*.f64 (/.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 a z))) (cbrt.f64 (cbrt.f64 (-.f64 a z))))) (/.f64 (-.f64 t x) (cbrt.f64 (cbrt.f64 (-.f64 a z))))))
220.0ms
(cbrt.f64 (-.f64 a z))
214.0ms
(cbrt.f64 (-.f64 a z))

simplify143.0ms (1.3%)

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
049717805
149717805

prune262.0ms (2.4%)

Pruning

16 alts after pruning (13 fresh and 3 done)

PrunedKeptTotal
New1932195
Fresh21113
Picked011
Done022
Total19516211

Merged error: 5.8b

Counts
211 → 16
Compiler

Compiled 8461 to 1817 computations (78.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
2.0b
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
2.0b
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
11.7b
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))

rewrite78.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
213×cbrt-prod_binary64_10215
139×add-sqr-sqrt_binary64_10208 *-un-lft-identity_binary64_10187
120×times-frac_binary64_10193
61×add-cube-cbrt_binary64_10219
39×distribute-lft-out--_binary64_10141 difference-of-squares_binary64_10156
cbrt-div_binary64_10216
associate-/r/_binary64_10135 add-log-exp_binary64_10223
add-exp-log_binary64_10222 pow1_binary64_10245 add-cbrt-cube_binary64_10220
pow1/3_binary64_10266 flip--_binary64_10162 flip3--_binary64_10191 div-inv_binary64_10184
+-commutative_binary64_10119 flip3-+_binary64_10190 sum-log_binary64_10275 flip-+_binary64_10161
Counts
4 → 176
Calls

4 calls:

11.0ms
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
10.0ms
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
10.0ms
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
5.0ms
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))

series2.2s (20.3%)

Counts
4 → 12
Calls

4 calls:

577.0ms
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
576.0ms
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
565.0ms
(cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
527.0ms
(+.f64 x (*.f64 (*.f64 (/.f64 (-.f64 y z) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))) (cbrt.f64 (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))))

simplify102.0ms (0.9%)

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
050566025

prune239.0ms (2.2%)

Pruning

17 alts after pruning (13 fresh and 4 done)

PrunedKeptTotal
New1871188
Fresh01212
Picked011
Done033
Total18717204

Merged error: 5.8b

Counts
204 → 17
Compiler

Compiled 10410 to 1242 computations (88.1% saved)

regimes303.0ms (2.7%)

Compiler

Compiled 2864 to 1536 computations (46.4% saved)

bsearch2.0ms (0%)

Compiler

Compiled 13 to 11 computations (15.4% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
096163
196163

end0.0ms (0%)

sample1.2s (10.7%)

Algorithm
intervals
Results
302.0ms6694×body128valid
61.0ms401×body1024valid
59.0ms483×body512valid
54.0ms1211×body128invalid
32.0ms361×body256valid
12.0ms61×body2048valid
Compiler

Compiled 614 to 306 computations (50.2% saved)

Profiling

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