Details

Time bar (total: 6.5s)

analyze502.0ms (7.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
18.7%81.1%0.1%7
21.8%78%0.1%8
21.8%78%0.1%9
49.1%50.7%0.1%10
52.7%47.2%0.1%11
52.7%47.2%0.1%12
71.7%28.2%0.1%13
74.1%25.8%0.1%14
Compiler

Compiled 22 to 19 computations (13.6% saved)

sample23.0ms (0.3%)

Algorithm
intervals
Results
12.0ms256×body128valid
Compiler

Compiled 43 to 40 computations (7% saved)

simplify109.0ms (1.7%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (14.0ms)

IterNodesCost
045331
145331

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
19.4b
Counts
2 → 1
Compiler

Compiled 42 to 36 computations (14.3% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
0.0b
(+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248)))
0.0b
(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
0.0b
(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
0.0b
(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
0.1b
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
3.4b
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
18.7b
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))

rewrite52.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64_11353
15×add-exp-log_binary64_11369 add-cbrt-cube_binary64_11367
14×*-un-lft-identity_binary64_11331
12×add-cube-cbrt_binary64_11366
10×pow1_binary64_11392 associate-*l*_binary64_11272
associate-*r*_binary64_11271
flip3-+_binary64_11334 flip-+_binary64_11305
cbrt-unprod_binary64_11364 add-log-exp_binary64_11370 associate-*l/_binary64_11274 prod-exp_binary64_11380 associate-*r/_binary64_11273
*-commutative_binary64_11262 unswap-sqr_binary64_11299 associate-/r*_binary64_11275 pow-prod-down_binary64_11402 times-frac_binary64_11337
div-exp_binary64_11382 associate-/l/_binary64_11278 cbrt-undiv_binary64_11365 associate-/r/_binary64_11277
distribute-lft-in_binary64_11280 associate-/l*_binary64_11276 div-inv_binary64_11328 frac-2neg_binary64_11342 distribute-lft-out_binary64_11282 distribute-rgt-in_binary64_11281 clear-num_binary64_11330
Counts
4 → 88
Calls

8 calls:

18.0ms
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
12.0ms
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
8.0ms
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
7.0ms
(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
0.0ms
(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)

series446.0ms (6.9%)

Counts
4 → 39
Calls

4 calls:

198.0ms
(/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984)) (+.f64 (*.f64 (+.f64 z 1692356830115869/281474976710656) z) 7544303578448747/2251799813685248))
155.0ms
(*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z) 5029535718965825/18014398509481984))
50.0ms
(*.f64 (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992) z)
43.0ms
(*.f64 (+.f64 z 1692356830115869/281474976710656) z)
Compiler

Compiled 1136 to 982 computations (13.6% saved)

simplify109.0ms (1.7%)

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
049202207
149202207

prune215.0ms (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1225127
Fresh000
Picked101
Done000
Total1235128
Error
0.0b
Counts
128 → 5
Compiler

Compiled 3303 to 2405 computations (27.2% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 x (*.f64 y 4992947066835229/72057594037927936))
0.0b
(+.f64 x (*.f64 y 4992947066835229/72057594037927936))

rewrite4.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-log-exp_binary64_11370
add-exp-log_binary64_11369 +-commutative_binary64_11261 pow1_binary64_11392 sum-log_binary64_11422 *-un-lft-identity_binary64_11331 add-cube-cbrt_binary64_11366 add-sqr-sqrt_binary64_11353 add-cbrt-cube_binary64_11367 flip3-+_binary64_11334 flip-+_binary64_11305
Counts
1 → 11
Calls

2 calls:

3.0ms
(+.f64 x (*.f64 y 4992947066835229/72057594037927936))
0.0ms
(+.f64 x (*.f64 y 4992947066835229/72057594037927936))

series56.0ms (0.9%)

Counts
1 → 12
Calls

1 calls:

56.0ms
(+.f64 x (*.f64 y 4992947066835229/72057594037927936))
Compiler

Compiled 72 to 96 computations (-33.3% saved)

simplify103.0ms (1.6%)

Algorithm
egg-herbie
Counts
23 → 23
Iterations

Useful iterations: 0 (94.0ms)

IterNodesCost
04833193
14833193

prune24.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New22123
Fresh044
Picked011
Done000
Total22628
Error
0b
Counts
28 → 6
Compiler

Compiled 304 to 227 computations (25.3% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.0b
(*.f64 z (+.f64 z 1692356830115869/281474976710656))
0.0b
(+.f64 x (*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
0.0b
(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
0.0b
(+.f64 x (*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
0.1b
(*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
0.1b
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
14.9b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))

rewrite58.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64_11353
22×*-un-lft-identity_binary64_11331 add-cube-cbrt_binary64_11366
19×times-frac_binary64_11337
18×associate-*r*_binary64_11271
13×add-exp-log_binary64_11369 add-cbrt-cube_binary64_11367
pow1_binary64_11392
add-log-exp_binary64_11370 associate-*l*_binary64_11272
flip3-+_binary64_11334 flip-+_binary64_11305
associate-/r/_binary64_11277
cbrt-unprod_binary64_11364 associate-/l*_binary64_11276 unswap-sqr_binary64_11299 associate-/r*_binary64_11275 prod-exp_binary64_11380 associate-*r/_binary64_11273
*-commutative_binary64_11262 div-exp_binary64_11382 associate-/l/_binary64_11278 div-inv_binary64_11328 cbrt-undiv_binary64_11365 pow-prod-down_binary64_11402
+-commutative_binary64_11261 distribute-lft-in_binary64_11280 sum-log_binary64_11422 frac-2neg_binary64_11342 distribute-rgt-in_binary64_11281 clear-num_binary64_11330
Counts
4 → 98
Calls

8 calls:

18.0ms
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
15.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
7.0ms
(*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
4.0ms
(+.f64 x (*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
0.0ms
(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)

series1.1s (17%)

Counts
4 → 57
Calls

4 calls:

801.0ms
(+.f64 x (*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
201.0ms
(*.f64 y (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
54.0ms
(*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992))
45.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
Compiler

Compiled 1617 to 1399 computations (13.5% saved)

simplify102.0ms (1.6%)

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049264256
149264256

prune217.0ms (3.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1541155
Fresh134
Picked011
Done011
Total1556161
Error
0b
Counts
161 → 6
Compiler

Compiled 4361 to 3177 computations (27.1% saved)

localize18.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))))
0.0b
(*.f64 z (+.f64 z 1692356830115869/281474976710656))
0.0b
(*.f64 z (+.f64 z 1692356830115869/281474976710656))
0.0b
(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)
6.2b
(*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
14.2b
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
14.2b
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
14.3b
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))

rewrite91.0ms (1.4%)

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt_binary64_11353
66×times-frac_binary64_11337
47×*-un-lft-identity_binary64_11331 add-cube-cbrt_binary64_11366
42×sqrt-prod_binary64_11347
24×associate-*r*_binary64_11271 associate-*l*_binary64_11272
18×add-exp-log_binary64_11369 add-cbrt-cube_binary64_11367
10×sqrt-div_binary64_11348
unswap-sqr_binary64_11299
pow1_binary64_11392
associate-/r/_binary64_11277 associate-/r*_binary64_11275 flip3-+_binary64_11334 flip-+_binary64_11305
div-exp_binary64_11382 cbrt-undiv_binary64_11365
cbrt-unprod_binary64_11364 add-log-exp_binary64_11370 prod-exp_binary64_11380
associate-/l*_binary64_11276 div-inv_binary64_11328
associate-/l/_binary64_11278 sqrt-pow1_binary64_11349 pow1/2_binary64_11411 rem-sqrt-square_binary64_11344
*-commutative_binary64_11262 frac-2neg_binary64_11342 associate-*l/_binary64_11274 frac-times_binary64_11341 associate-*r/_binary64_11273 pow-prod-down_binary64_11402 clear-num_binary64_11330
Counts
4 → 150
Calls

8 calls:

38.0ms
(*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
19.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
6.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
6.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
0.0ms
(+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)

series381.0ms (5.9%)

Counts
4 → 45
Calls

4 calls:

207.0ms
(*.f64 (/.f64 y (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))) (/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))))
78.0ms
(/.f64 (+.f64 (*.f64 z (+.f64 (*.f64 z 4992947066835229/72057594037927936) 4429125951667411/9007199254740992)) 5029535718965825/18014398509481984) (sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248)))
49.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
46.0ms
(sqrt.f64 (+.f64 (*.f64 z (+.f64 z 1692356830115869/281474976710656)) 7544303578448747/2251799813685248))
Compiler

Compiled 1464 to 1279 computations (12.6% saved)

simplify116.0ms (1.8%)

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
055396773

prune430.0ms (6.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1950195
Fresh033
Picked011
Done022
Total1956201
Error
0b
Counts
201 → 6
Compiler

Compiled 7741 to 5840 computations (24.6% saved)

simplify17.0ms (0.3%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0314865
1314865

regimes299.0ms (4.6%)

Compiler

Compiled 1755 to 1530 computations (12.8% saved)

bsearch38.0ms (0.6%)

Steps
ItersRangePoint
10
9.416312076425774e-09
48.680051193511154
48.17602907496802
5
-2.5431286576031824e+36
-9.84199984016058e+35
-9.990746456204017e+35
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes89.0ms (1.4%)

Compiler

Compiled 213 to 252 computations (-18.3% saved)

bsearch46.0ms (0.7%)

Steps
ItersRangePoint
10
9.416312076425774e-09
48.680051193511154
5.0434340818853745
9
-170.40489543807897
-0.0018941511781248729
-5.411826093399547
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes84.0ms (1.3%)

Compiler

Compiled 168 to 213 computations (-26.8% saved)

bsearch45.0ms (0.7%)

Steps
ItersRangePoint
10
9.416312076425774e-09
48.680051193511154
5.0434340818853745
9
-170.40489543807897
-0.0018941511781248729
-5.411826093399547
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes67.0ms (1%)

Compiler

Compiled 57 to 114 computations (-100% saved)

bsearch42.0ms (0.6%)

Steps
ItersRangePoint
10
9.416312076425774e-09
48.680051193511154
5.9254727893358545
9
-170.40489543807897
-0.0018941511781248729
-5.411826093399547
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes36.0ms (0.5%)

Compiler

Compiled 42 to 96 computations (-128.6% saved)

bsearch0.0ms (0%)

regimes75.0ms (1.2%)

Compiler

Compiled 27 to 78 computations (-188.9% saved)

bsearch31.0ms (0.5%)

Steps
ItersRangePoint
8
4.583625185151487e-54
4.447742780684361e-50
3.632870605740012e-53
7
-1.3382909013199293e-50
-1.0690345876117488e-52
-3.0864478654520087e-51
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0.5%)

Compiler

Compiled 18 to 63 computations (-250% saved)

bsearch0.0ms (0%)

regimes26.0ms (0.4%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch0.0ms (0%)

regimes23.0ms (0.4%)

Accuracy

Total 0.3b remaining (99.3%)

Threshold costs 0.3b (99.3%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 147 to 125 computations (15% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0106196
1106196

end0.0ms (0%)

sample1.3s (20.3%)

Algorithm
intervals
Results
399.0ms8000×body128valid
Compiler

Compiled 805 to 692 computations (14% saved)

Pareto

0.6978137772484342

Profiling

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