Details

Time bar (total: 10.0s)

analyze473.0ms (4.8%)

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%74.9%25.1%5
0%74.9%25.1%6
0%74.9%25.1%7
6.2%56.2%37.6%8
7.8%53%39.2%9
10.9%45.6%43.4%10
18.3%31.4%50.3%11
19.1%29.5%51.3%12
21.4%24.8%53.8%13
25.8%16.7%57.5%14
Compiler

Compiled 25 to 21 computations (16% saved)

sample37.0ms (0.4%)

Algorithm
intervals
Results
19.0ms256×body128valid
4.0ms48×body128invalid
1.0ms20×body128nan
Compiler

Compiled 49 to 44 computations (10.2% saved)

simplify195.0ms (2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (104.0ms)

IterNodesCost
0482336
1482336

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
4.8b
Counts
2 → 1
Compiler

Compiled 48 to 40 computations (16.7% saved)

localize21.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z)
0.0b
(*.f64 (+.f64 y 7320129949063637/9223372036854775808) z)
0.0b
(+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936)
0.0b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x))
0.1b
(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.1b
(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.1b
(*.f64 (-.f64 x 1/2) (log.f64 x))
4.4b
(/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite49.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity_binary64_14059 add-sqr-sqrt_binary64_14081
22×add-cube-cbrt_binary64_14094
18×log-prod_binary64_14145
12×associate--l+_binary64_13996
11×add-log-exp_binary64_14098
10×associate-+l+_binary64_13992
distribute-rgt-in_binary64_14009 distribute-lft-in_binary64_14008 times-frac_binary64_14065
add-cbrt-cube_binary64_14095 add-exp-log_binary64_14097
pow1_binary64_14120
cancel-sign-sub-inv_binary64_14025
associate-*l*_binary64_14000
associate-*r*_binary64_13999
associate-/r*_binary64_14003 associate-/l*_binary64_14004
sum-log_binary64_14150 flip--_binary64_14034 flip-+_binary64_14033 associate-*l/_binary64_14002 associate-/l/_binary64_14006 diff-log_binary64_14151 sub-neg_binary64_14052 flip3-+_binary64_14062 flip3--_binary64_14063
frac-2neg_binary64_14070 prod-exp_binary64_14108 div-exp_binary64_14110 cbrt-unprod_binary64_14092 log-pow_binary64_14148 *-commutative_binary64_13990 distribute-lft-out_binary64_14010 div-inv_binary64_14056 clear-num_binary64_14058 cbrt-undiv_binary64_14093 unswap-sqr_binary64_14027 pow-prod-down_binary64_14130 difference-of-squares_binary64_14028 +-commutative_binary64_13989 distribute-lft-out--_binary64_14011 associate-+l-_binary64_13994
Counts
4 → 102
Calls

8 calls:

12.0ms
(/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
11.0ms
(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
8.0ms
(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
7.0ms
(*.f64 (-.f64 x 1/2) (log.f64 x))
0.0ms
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248) (/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x))

series719.0ms (7.2%)

Counts
4 → 33
Calls

4 calls:

378.0ms
(/.f64 (+.f64 (*.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
135.0ms
(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
130.0ms
(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
76.0ms
(*.f64 (-.f64 x 1/2) (log.f64 x))
Compiler

Compiled 1532 to 1262 computations (17.6% saved)

simplify74.0ms (0.7%)

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049672450
149672450

prune340.0ms (3.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New12015135
Fresh000
Picked101
Done000
Total12115136
Error
0.5b
Counts
136 → 15
Compiler

Compiled 4546 to 3052 computations (32.9% saved)

localize21.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.0b
(+.f64 (+.f64 (/.f64 6004799503160637/72057594037927936 x) (*.f64 (/.f64 (*.f64 z z) x) (+.f64 y 7320129949063637/9223372036854775808))) (*.f64 (/.f64 z x) -3202559735019045/1152921504606846976))
0.0b
(+.f64 (/.f64 6004799503160637/72057594037927936 x) (*.f64 (/.f64 (*.f64 z z) x) (+.f64 y 7320129949063637/9223372036854775808)))
0.0b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248) (+.f64 (+.f64 (/.f64 6004799503160637/72057594037927936 x) (*.f64 (/.f64 (*.f64 z z) x) (+.f64 y 7320129949063637/9223372036854775808))) (*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)))
0.1b
(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b
(*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)
3.1b
(*.f64 (/.f64 (*.f64 z z) x) (+.f64 y 7320129949063637/9223372036854775808))
7.7b
(/.f64 (*.f64 z z) x)

rewrite45.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt_binary64_14081
25×add-cbrt-cube_binary64_14095 *-un-lft-identity_binary64_14059 associate-*l*_binary64_14000 add-exp-log_binary64_14097
21×add-cube-cbrt_binary64_14094
17×times-frac_binary64_14065
11×associate-*r*_binary64_13999 pow1_binary64_14120
prod-exp_binary64_14108 cbrt-unprod_binary64_14092
log-prod_binary64_14145
div-exp_binary64_14110 cbrt-undiv_binary64_14093 unswap-sqr_binary64_14027
add-log-exp_binary64_14098 distribute-rgt-in_binary64_14009 associate-*l/_binary64_14002 distribute-lft-in_binary64_14008
*-commutative_binary64_13990 div-inv_binary64_14056 associate-/r*_binary64_14003 pow-prod-down_binary64_14130
frac-times_binary64_14069 flip-+_binary64_14033 associate-*r/_binary64_14001 flip3-+_binary64_14062
frac-2neg_binary64_14070 flip--_binary64_14034 log-pow_binary64_14148 distribute-lft-out_binary64_14010 clear-num_binary64_14058 difference-of-squares_binary64_14028 distribute-lft-out--_binary64_14011 flip3--_binary64_14063 associate-/l*_binary64_14004
Counts
4 → 117
Calls

8 calls:

12.0ms
(*.f64 (/.f64 (*.f64 z z) x) (+.f64 y 7320129949063637/9223372036854775808))
8.0ms
(*.f64 (-.f64 x 1/2) (log.f64 x))
7.0ms
(*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)
5.0ms
(/.f64 (*.f64 z z) x)
0.0ms
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248) (+.f64 (+.f64 (/.f64 6004799503160637/72057594037927936 x) (*.f64 (/.f64 (*.f64 z z) x) (+.f64 y 7320129949063637/9223372036854775808))) (*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)))

series395.0ms (4%)

Counts
4 → 29
Calls

4 calls:

179.0ms
(*.f64 (/.f64 (*.f64 z z) x) (+.f64 y 7320129949063637/9223372036854775808))
80.0ms
(*.f64 (-.f64 x 1/2) (log.f64 x))
73.0ms
(/.f64 (*.f64 z z) x)
62.0ms
(*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)
Compiler

Compiled 1676 to 1316 computations (21.5% saved)

simplify71.0ms (0.7%)

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049711727
149711727

prune249.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1433146
Fresh41014
Picked101
Done000
Total14813161
Error
0.0b
Counts
161 → 13
Compiler

Compiled 5417 to 3051 computations (43.7% saved)

localize21.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.0b
(+.f64 (+.f64 (/.f64 6004799503160637/72057594037927936 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808))) (*.f64 (/.f64 z x) -3202559735019045/1152921504606846976))
0.0b
(+.f64 (/.f64 6004799503160637/72057594037927936 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808)))
0.0b
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248) (+.f64 (+.f64 (/.f64 6004799503160637/72057594037927936 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808))) (*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)))
0.1b
(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b
(*.f64 z (/.f64 z x))
0.2b
(*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)
3.1b
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808))

rewrite46.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt_binary64_14081
29×*-un-lft-identity_binary64_14059
25×add-cbrt-cube_binary64_14095 add-cube-cbrt_binary64_14094 add-exp-log_binary64_14097
24×associate-*r*_binary64_13999
22×associate-*l*_binary64_14000
20×times-frac_binary64_14065
16×pow1_binary64_14120
10×prod-exp_binary64_14108 cbrt-unprod_binary64_14092
associate-*r/_binary64_14001 pow-prod-down_binary64_14130 log-prod_binary64_14145
unswap-sqr_binary64_14027
add-log-exp_binary64_14098 distribute-rgt-in_binary64_14009 associate-*l/_binary64_14002 distribute-lft-in_binary64_14008 *-commutative_binary64_13990
div-exp_binary64_14110 cbrt-undiv_binary64_14093
frac-times_binary64_14069 flip-+_binary64_14033 div-inv_binary64_14056 flip3-+_binary64_14062
flip--_binary64_14034 log-pow_binary64_14148 distribute-lft-out_binary64_14010 difference-of-squares_binary64_14028 distribute-lft-out--_binary64_14011 flip3--_binary64_14063
Counts
4 → 121
Calls

8 calls:

10.0ms
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808))
7.0ms
(*.f64 (-.f64 x 1/2) (log.f64 x))
7.0ms
(*.f64 z (/.f64 z x))
7.0ms
(*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)
0.0ms
(+.f64 (+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248) (+.f64 (+.f64 (/.f64 6004799503160637/72057594037927936 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808))) (*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)))

series385.0ms (3.9%)

Counts
4 → 29
Calls

4 calls:

178.0ms
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808))
76.0ms
(*.f64 (-.f64 x 1/2) (log.f64 x))
71.0ms
(*.f64 z (/.f64 z x))
60.0ms
(*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)
Compiler

Compiled 1676 to 1296 computations (22.7% saved)

simplify72.0ms (0.7%)

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049541719
149541719

prune272.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1473150
Fresh21012
Picked101
Done000
Total15013163
Error
0.0b
Counts
163 → 13
Compiler

Compiled 5586 to 3113 computations (44.3% saved)

localize27.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (/.f64 6004799503160637/72057594037927936 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808)))
0.0b
(+.f64 (+.f64 (-.f64 (+.f64 (*.f64 (-.f64 x 1/2) (*.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x)))) x) 2069265617858471/2251799813685248) (+.f64 (+.f64 (/.f64 6004799503160637/72057594037927936 x) (*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808))) (*.f64 (/.f64 z x) -3202559735019045/1152921504606846976)))
0.0b
(log.f64 (cbrt.f64 x))
0.0b
(log.f64 (cbrt.f64 x))
0.3b
(+.f64 (*.f64 (-.f64 x 1/2) (*.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
0.5b
(cbrt.f64 x)
0.5b
(cbrt.f64 x)
3.1b
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808))

rewrite47.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
36×log-prod_binary64_14145
31×distribute-rgt-in_binary64_14009 distribute-lft-in_binary64_14008
24×cbrt-prod_binary64_14090 associate-+l+_binary64_13992
21×*-un-lft-identity_binary64_14059
19×add-cube-cbrt_binary64_14094 add-sqr-sqrt_binary64_14081
13×add-cbrt-cube_binary64_14095 add-exp-log_binary64_14097
12×associate-+r+_binary64_13991
associate-*l/_binary64_14002 pow1_binary64_14120
add-log-exp_binary64_14098
prod-exp_binary64_14108 cbrt-unprod_binary64_14092 associate-*r/_binary64_14001
associate-*r*_binary64_13999 flip--_binary64_14034 frac-add_binary64_14067 flip3--_binary64_14063
flip-+_binary64_14033 pow-prod-down_binary64_14130 flip3-+_binary64_14062
frac-times_binary64_14069 distribute-lft-out_binary64_14010 pow1/3_binary64_14141
sum-log_binary64_14150 div-exp_binary64_14110 *-commutative_binary64_13990 cbrt-undiv_binary64_14093 +-commutative_binary64_13989 associate-*l*_binary64_14000
Counts
4 → 102
Calls

8 calls:

16.0ms
(+.f64 (*.f64 (-.f64 x 1/2) (*.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
13.0ms
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
0.0ms
(log.f64 (cbrt.f64 x))

series580.0ms (5.8%)

Counts
4 → 23
Calls

4 calls:

248.0ms
(+.f64 (*.f64 (-.f64 x 1/2) (*.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
184.0ms
(*.f64 (*.f64 z (/.f64 z x)) (+.f64 y 7320129949063637/9223372036854775808))
74.0ms
(cbrt.f64 x)
74.0ms
(cbrt.f64 x)
Compiler

Compiled 1745 to 1332 computations (23.7% saved)

simplify59.0ms (0.6%)

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
052851863

prune240.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1232125
Fresh3912
Picked101
Done000
Total12711138
Error
0.0b
Counts
138 → 11
Compiler

Compiled 5527 to 3039 computations (45% saved)

simplify51.0ms (0.5%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (10.0ms)

IterNodesCost
06433109
16433109

regimes558.0ms (5.6%)

Compiler

Compiled 8168 to 6380 computations (21.9% saved)

bsearch0.0ms (0%)

regimes129.0ms (1.3%)

Compiler

Compiled 1352 to 1148 computations (15.1% saved)

bsearch0.0ms (0%)

regimes215.0ms (2.2%)

Compiler

Compiled 1469 to 1273 computations (13.3% saved)

bsearch1.0ms (0%)

Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes209.0ms (2.1%)

Compiler

Compiled 1357 to 1189 computations (12.4% saved)

bsearch1.0ms (0%)

Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes175.0ms (1.8%)

Compiler

Compiled 1217 to 1084 computations (10.9% saved)

bsearch40.0ms (0.4%)

Steps
ItersRangePoint
9
8.284618348521768e+111
1.086063905650908e+117
1.2228625266445235e+116
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes129.0ms (1.3%)

Compiler

Compiled 896 to 812 computations (9.4% saved)

bsearch19.0ms (0.2%)

Steps
ItersRangePoint
5
3.865984058620325e+136
1.2463260213552496e+137
6.616024221671603e+136
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes121.0ms (1.2%)

Compiler

Compiled 792 to 728 computations (8.1% saved)

bsearch19.0ms (0.2%)

Steps
ItersRangePoint
5
3.865984058620325e+136
1.2463260213552496e+137
5.884474440997912e+136
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes181.0ms (1.8%)

Compiler

Compiled 595 to 579 computations (2.7% saved)

bsearch73.0ms (0.7%)

Steps
ItersRangePoint
8
8.720555477392201e+201
3.8556711614538083e+205
1.531059835466683e+202
9
1.0101183495137219e-10
0.0002105607146670681
0.00020805856612656504
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes138.0ms (1.4%)

Compiler

Compiled 275 to 309 computations (-12.4% saved)

bsearch67.0ms (0.7%)

Steps
ItersRangePoint
8
8.720555477392201e+201
3.8556711614538083e+205
1.2522505983322424e+202
9
1.0101183495137219e-10
0.0002105607146670681
0.00020805856612656504
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes87.0ms (0.9%)

Compiler

Compiled 111 to 135 computations (-21.6% saved)

bsearch283.0ms (2.8%)

Steps
ItersRangePoint
10
9.830814924810537e+148
2.4592521300044376e+160
1.3502924843869215e+154
6
1.4124727831446974e-38
6.950249310698864e-38
2.0605854833901066e-38
8
-1.2117235356410474e-22
-6.221408505385352e-26
-8.976890746316297e-23
9
-1.37440234011368e+85
-7.388778223149884e+79
-1.3611053783285396e+85
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes31.0ms (0.3%)

Compiler

Compiled 57 to 93 computations (-63.2% saved)

bsearch0.0ms (0%)

regimes26.0ms (0.3%)

Accuracy

Total 0.4b remaining (96.8%)

Threshold costs 0.4b (96.8%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch22.0ms (0.2%)

Compiler

Compiled 627 to 433 computations (30.9% saved)

simplify15.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0198835
1198835

end0.0ms (0%)

sample2.9s (29.4%)

Algorithm
intervals
Results
611.0ms8000×body128valid
87.0ms1176×body128invalid
52.0ms752×body128nan
Compiler

Compiled 2646 to 2031 computations (23.2% saved)

Pareto

0.004107451119992796

Profiling

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