Details

Time bar (total: 6.5s)

analyze295.0ms (4.6%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14
Compiler

Compiled 30 to 24 computations (20% saved)

sample35.0ms (0.5%)

Algorithm
1×intervals
Results
15.0ms247×body128valid
9.0ms277×pre128true
1.0ms21×body128nan
1.0ms9×body256valid
Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify67.0ms (1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
092724
192724

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 29.1b

Counts
2 → 1
Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.2b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.2b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
29.1b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite38.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
13×*-un-lft-identity_binary64
9×add-exp-log_binary64 add-cbrt-cube_binary64
8×add-log-exp_binary64
7×add-cube-cbrt_binary64
6×difference-of-squares_binary64 associate-/l*_binary64 times-frac_binary64 sqrt-prod_binary64
5×pow1_binary64
4×flip3--_binary64 flip--_binary64
3×distribute-lft-out--_binary64
2×associate-/l/_binary64 sub-neg_binary64 diff-log_binary64 cbrt-undiv_binary64 div-exp_binary64 sqrt-div_binary64
1×associate-/r*_binary64 pow1/2_binary64 cbrt-unprod_binary64 sqrt-pow1_binary64 div-sub_binary64 rem-sqrt-square_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 div-inv_binary64
Counts
4 → 70
Calls

4 calls:

12.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
11.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

series528.0ms (8.1%)

Counts
4 → 12
Calls

4 calls:

203.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
134.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
126.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
64.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify97.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
048841963
148841963

prune96.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh000
Picked101
Done000
Total80383

Merged error: 0.4b

Counts
83 → 3
Compiler

Compiled 1953 to 1159 computations (40.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.2b
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))
0.2b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.3b
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

rewrite52.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
45×add-exp-log_binary64 add-cbrt-cube_binary64
22×times-frac_binary64
20×*-un-lft-identity_binary64
17×cbrt-undiv_binary64 div-exp_binary64
13×cbrt-unprod_binary64 prod-exp_binary64
11×associate-/l*_binary64
10×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
8×add-log-exp_binary64
6×associate-/r/_binary64
5×associate-/r*_binary64 distribute-lft-out_binary64
4×flip3-+_binary64 pow1_binary64 div-inv_binary64 flip-+_binary64
2×clear-num_binary64 frac-2neg_binary64
1×associate-/l/_binary64 sub-neg_binary64 flip3--_binary64 diff-log_binary64 +-commutative_binary64 flip--_binary64 sum-log_binary64
Counts
4 → 98
Calls

4 calls:

18.0ms
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))
12.0ms
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
6.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

series898.0ms (13.9%)

Counts
4 → 12
Calls

4 calls:

384.0ms
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
302.0ms
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))
136.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
76.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify72.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049233030
149233030

prune173.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1019110
Fresh202
Picked101
Done000
Total1049113

Merged error: 0.0b

Counts
113 → 9
Compiler

Compiled 3363 to 2078 computations (38.2% saved)

localize34.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 c (*.f64 (*.f64 a 4) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.3b
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (+.f64 (*.f64 -64 (pow.f64 (*.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (*.f64 c (*.f64 (*.f64 a 4) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))))
0.4b
(/.f64 (+.f64 (*.f64 -64 (pow.f64 (*.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (*.f64 c (*.f64 (*.f64 a 4) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
0.7b
(pow.f64 (*.f64 a c) 3)

rewrite74.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
27×add-exp-log_binary64 add-cbrt-cube_binary64
20×*-un-lft-identity_binary64
16×pow1_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64
13×times-frac_binary64
10×cbrt-unprod_binary64 prod-exp_binary64
7×pow-prod-down_binary64 associate-/r*_binary64
4×flip3-+_binary64 add-log-exp_binary64 cbrt-undiv_binary64 associate-*r/_binary64 distribute-lft-in_binary64 associate-/r/_binary64 distribute-rgt-in_binary64 associate-/l*_binary64 div-exp_binary64 flip-+_binary64
3×pow-unpow_binary64 associate-*l*_binary64
2×associate-/l/_binary64 distribute-lft-out_binary64 pow-pow_binary64 clear-num_binary64 rem-cube-cbrt_binary64 frac-2neg_binary64 div-inv_binary64 pow-exp_binary64
1×pow-to-exp_binary64 associate-*r*_binary64 sqr-pow_binary64 unpow-prod-down_binary64 cube-prod_binary64 unpow3_binary64 *-commutative_binary64 cube-mult_binary64
Counts
4 → 107
Calls

4 calls:

22.0ms
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (+.f64 (*.f64 -64 (pow.f64 (*.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (*.f64 c (*.f64 (*.f64 a 4) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))))
14.0ms
(/.f64 (+.f64 (*.f64 -64 (pow.f64 (*.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (*.f64 c (*.f64 (*.f64 a 4) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
12.0ms
(*.f64 c (*.f64 (*.f64 a 4) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
4.0ms
(pow.f64 (*.f64 a c) 3)

series1.1s (16.4%)

Counts
4 → 12
Calls

4 calls:

577.0ms
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (+.f64 (*.f64 -64 (pow.f64 (*.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (*.f64 c (*.f64 (*.f64 a 4) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))))
284.0ms
(/.f64 (+.f64 (*.f64 -64 (pow.f64 (*.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (*.f64 c (*.f64 (*.f64 a 4) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
133.0ms
(*.f64 c (*.f64 (*.f64 a 4) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
70.0ms
(pow.f64 (*.f64 a c) 3)

simplify91.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049954770
149954770

prune329.0ms (5.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1190119
Fresh088
Picked011
Done000
Total1199128

Merged error: 0.0b

Counts
128 → 9
Compiler

Compiled 6827 to 4408 computations (35.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
0.2b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.2b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
0.3b
(*.f64 (*.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))

rewrite44.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
37×*-un-lft-identity_binary64
24×times-frac_binary64
21×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
18×associate-*r*_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
9×pow1_binary64
8×add-log-exp_binary64 distribute-lft-out_binary64
6×cbrt-unprod_binary64 prod-exp_binary64
4×associate-/r*_binary64 associate-/r/_binary64
3×pow-prod-down_binary64 flip3-+_binary64 cbrt-undiv_binary64 associate-/l*_binary64 div-exp_binary64 flip-+_binary64
2×div-inv_binary64
1×sub-neg_binary64 flip3--_binary64 diff-log_binary64 associate-*r/_binary64 associate-*l*_binary64 clear-num_binary64 frac-2neg_binary64 +-commutative_binary64 flip--_binary64 sum-log_binary64 *-commutative_binary64
Counts
4 → 94
Calls

4 calls:

14.0ms
(*.f64 (*.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
9.0ms
(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
6.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

series799.0ms (12.3%)

Counts
4 → 12
Calls

4 calls:

377.0ms
(*.f64 (*.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
223.0ms
(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
133.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
66.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

simplify76.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049402605
149402605

prune134.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1042106
Fresh257
Picked101
Done011
Total1078115

Merged error: 0b

Counts
115 → 8
Compiler

Compiled 2726 to 1721 computations (36.9% saved)

regimes80.0ms (1.2%)

Compiler

Compiled 1008 to 723 computations (28.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04466
14466

end0.0ms (0%)

sample1.4s (20.9%)

Algorithm
1×intervals
Results
460.0ms7694×body128valid
285.0ms8854×pre128true
49.0ms854×body128nan
35.0ms306×body256valid
Compiler

Compiled 408 to 295 computations (27.7% saved)

Profiling

Loading profile data...