Details

Time bar (total: 5.8s)

analyze259.0ms (4.5%)

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)

sample37.0ms (0.6%)

Algorithm
1×intervals
Results
10.0ms104×body256valid
8.0ms290×pre128true
8.0ms152×body128valid
2.0ms34×body128nan
Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify238.0ms (4.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
092724
192724

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 44.4b

Counts
2 → 1
Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
39.0b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite39.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64_101
14×*-un-lft-identity_binary64_79
9×add-exp-log_binary64_117 add-cbrt-cube_binary64_115
8×add-cube-cbrt_binary64_114 add-log-exp_binary64_118
6×sqrt-prod_binary64_95 times-frac_binary64_85 associate-/l*_binary64_24 difference-of-squares_binary64_48
5×pow1_binary64_140
4×flip--_binary64_54 flip3--_binary64_83 cancel-sign-sub-inv_binary64_45
3×distribute-lft-out--_binary64_31
2×cbrt-undiv_binary64_113 div-exp_binary64_130 sqrt-div_binary64_96 diff-log_binary64_171 associate-/l/_binary64_26 sub-neg_binary64_72
1×associate-/r*_binary64_23 div-sub_binary64_84 div-inv_binary64_76 cbrt-unprod_binary64_112 prod-exp_binary64_128 rem-sqrt-square_binary64_92 sqrt-pow1_binary64_97 clear-num_binary64_78 pow1/2_binary64_159 frac-2neg_binary64_90
Counts
4 → 74
Calls

4 calls:

13.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
9.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series552.0ms (9.5%)

Counts
4 → 12
Calls

4 calls:

225.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
139.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
124.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
64.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify69.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
050311979

prune201.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New80686
Fresh000
Picked011
Done000
Total80787

Merged error: 0.2b

Counts
87 → 7
Compiler

Compiled 4016 to 2662 computations (33.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.3b
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))
0.4b
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

rewrite56.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
45×add-exp-log_binary64_117 add-cbrt-cube_binary64_115
22×times-frac_binary64_85
20×*-un-lft-identity_binary64_79
17×cbrt-undiv_binary64_113 div-exp_binary64_130
13×cbrt-unprod_binary64_112 prod-exp_binary64_128
11×associate-/l*_binary64_24
10×add-cube-cbrt_binary64_114 add-sqr-sqrt_binary64_101
8×add-log-exp_binary64_118
6×associate-/r/_binary64_25
5×associate-/r*_binary64_23 distribute-lft-out_binary64_30
4×flip-+_binary64_53 div-inv_binary64_76 flip3-+_binary64_82 pow1_binary64_140
2×clear-num_binary64_78 frac-2neg_binary64_90
1×sum-log_binary64_170 +-commutative_binary64_9 flip--_binary64_54 diff-log_binary64_171 flip3--_binary64_83 cancel-sign-sub-inv_binary64_45 associate-/l/_binary64_26 sub-neg_binary64_72
Counts
4 → 99
Calls

4 calls:

17.0ms
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))
13.0ms
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
7.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

series926.0ms (16%)

Counts
4 → 12
Calls

4 calls:

398.0ms
(/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
323.0ms
(/.f64 (/.f64 (*.f64 a (*.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 a 2))
134.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
70.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify77.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049603037
149603037

prune423.0ms (7.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1047111
Fresh505
Picked101
Done101
Total1117118

Merged error: 0b

Counts
118 → 7
Compiler

Compiled 8881 to 6103 computations (31.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
0.1b
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
0.1b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

rewrite32.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
24×*-un-lft-identity_binary64_79
15×add-sqr-sqrt_binary64_101
14×add-cube-cbrt_binary64_114
12×times-frac_binary64_85
8×add-log-exp_binary64_118
6×add-exp-log_binary64_117 add-cbrt-cube_binary64_115
5×distribute-lft-out_binary64_30 pow1_binary64_140
4×associate-/r*_binary64_23
3×sqrt-prod_binary64_95 associate-/l*_binary64_24
2×flip-+_binary64_53 flip--_binary64_54 associate-/r/_binary64_25 sqrt-div_binary64_96 flip3--_binary64_83 flip3-+_binary64_82
1×cbrt-undiv_binary64_113 div-exp_binary64_130 div-inv_binary64_76 sum-log_binary64_170 +-commutative_binary64_9 rem-sqrt-square_binary64_92 sqrt-pow1_binary64_97 diff-log_binary64_171 clear-num_binary64_78 pow1/2_binary64_159 cancel-sign-sub-inv_binary64_45 sub-neg_binary64_72 frac-2neg_binary64_90
Counts
4 → 72
Calls

4 calls:

9.0ms
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
7.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))

series689.0ms (11.9%)

Counts
4 → 12
Calls

4 calls:

347.0ms
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
146.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
128.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
67.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

simplify69.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
050871969

prune198.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New81384
Fresh336
Picked101
Done000
Total85691

Merged error: 0b

Counts
91 → 6
Compiler

Compiled 4083 to 2846 computations (30.3% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b
(+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
0.2b
(*.f64 c (*.f64 (*.f64 c a) 16))
0.3b
(*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))
0.5b
(/.f64 (-.f64 (pow.f64 b 4) (*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))

rewrite49.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
29×add-exp-log_binary64_117 add-cbrt-cube_binary64_115
27×pow1_binary64_140
16×cbrt-unprod_binary64_112 prod-exp_binary64_128 pow-prod-down_binary64_150
14×add-cube-cbrt_binary64_114 add-sqr-sqrt_binary64_101 *-un-lft-identity_binary64_79
9×times-frac_binary64_85
6×associate-*l*_binary64_20 add-log-exp_binary64_118
3×associate-/r*_binary64_23 associate-/l*_binary64_24
2×flip-+_binary64_53 associate-/r/_binary64_25 *-commutative_binary64_10 associate-/l/_binary64_26 flip3-+_binary64_82 associate-*r*_binary64_19
1×cbrt-undiv_binary64_113 div-exp_binary64_130 div-sub_binary64_84 div-inv_binary64_76 sum-log_binary64_170 +-commutative_binary64_9 flip--_binary64_54 clear-num_binary64_78 flip3--_binary64_83 frac-2neg_binary64_90
Counts
4 → 88
Calls

4 calls:

12.0ms
(/.f64 (-.f64 (pow.f64 b 4) (*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
12.0ms
(*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))
8.0ms
(*.f64 c (*.f64 (*.f64 c a) 16))
5.0ms
(+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))

series282.0ms (4.9%)

Counts
4 → 12
Calls

4 calls:

146.0ms
(/.f64 (-.f64 (pow.f64 b 4) (*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
56.0ms
(+.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
49.0ms
(*.f64 a (*.f64 c (*.f64 (*.f64 c a) 16)))
31.0ms
(*.f64 c (*.f64 (*.f64 c a) 16))

simplify67.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049782422
149782422

prune172.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1000100
Fresh055
Picked011
Done000
Total1006106

Merged error: 0b

Counts
106 → 6
Compiler

Compiled 4064 to 2446 computations (39.8% saved)

regimes48.0ms (0.8%)

Compiler

Compiled 423 to 348 computations (17.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09645
19645

end0.0ms (0%)

sample1.2s (21.3%)

Algorithm
1×intervals
Results
275.0ms2886×body256valid
267.0ms8930×pre128true
256.0ms5112×body128valid
42.0ms930×body128nan
0.0ms2×body512valid
Compiler

Compiled 199 to 159 computations (20.1% saved)

Profiling

Loading profile data...