Details

Time bar (total: 2.1min)

analyze539.0ms (0.4%)

Algorithm
1×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
18.7%81.1%0.1%6
26.5%67.1%6.4%7
35.1%58.5%6.4%8
41.3%49.9%8.7%9
46.4%40.2%13.4%10
50.8%34.2%15%11
55.2%26.7%18.1%12
57.4%22%20.6%13
59.8%17.9%22.3%14
Compiler

Compiled 39 to 27 computations (30.8% saved)

sample57.0ms (0%)

Algorithm
1×intervals
Results
39.0ms256×body128valid
2.0ms17×body128nan
2.0ms13×body128invalid
Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify466.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (369.0ms)

IterNodesCost
0421954
1421954

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
19.6b
Counts
2 → 2
Compiler

Compiled 36 to 25 computations (30.6% saved)

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)
0.1b
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
2.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite25.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64_100
9×*-un-lft-identity_binary64_78
8×add-log-exp_binary64_117
7×sqrt-prod_binary64_94 add-cube-cbrt_binary64_113
6×pow1_binary64_139
4×add-cbrt-cube_binary64_114 flip3--_binary64_82 flip--_binary64_53 add-exp-log_binary64_116 sqrt-div_binary64_95 cancel-sign-sub-inv_binary64_44
2×sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 diff-log_binary64_170 difference-of-squares_binary64_47 pow1/2_binary64_158 sub-neg_binary64_71
1×distribute-lft-out--_binary64_30
Counts
4 → 59
Calls

8 calls:

8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))

series590.0ms (0.5%)

Counts
4 → 64
Calls

4 calls:

171.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
157.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
146.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
115.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 3903 to 2904 computations (25.6% saved)

simplify86.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049461938
149461938

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
0.1b
(/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
2.2b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite25.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
10×add-log-exp_binary64_117 *-un-lft-identity_binary64_78
8×add-sqr-sqrt_binary64_100
6×sqrt-prod_binary64_94 add-cube-cbrt_binary64_113 pow1_binary64_139
4×add-cbrt-cube_binary64_114 add-exp-log_binary64_116 sqrt-div_binary64_95
3×flip3--_binary64_82 flip--_binary64_53
2×sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 distribute-lft-out_binary64_29 pow1/2_binary64_158 sum-log_binary64_169
1×+-commutative_binary64_8 associate-+l-_binary64_13 flip-+_binary64_52 diff-log_binary64_170 neg-sub0_binary64_73 distribute-rgt-neg-in_binary64_36 cancel-sign-sub-inv_binary64_44 sub-neg_binary64_71 neg-log_binary64_171 flip3-+_binary64_81
Counts
4 → 57
Calls

8 calls:

9.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

series591.0ms (0.5%)

Counts
4 → 64
Calls

4 calls:

177.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
158.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
140.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
116.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 4079 to 3004 computations (26.4% saved)

simplify82.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
051511899

prune1.2s (0.9%)

Pruning

63 alts after pruning (63 fresh and 0 done)

PrunedKeptTotal
New18163244
Fresh000
Picked000
Done202
Total18363246
Error
5.3b
Counts
246 → 63
Compiler

Compiled 8677 to 5322 computations (38.7% saved)

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)
0.1b
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite31.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
26×sqrt-div_binary64_95
25×sqrt-pow1_binary64_96
23×pow1_binary64_139
12×pow1/2_binary64_158
10×sqrt-prod_binary64_94 add-sqr-sqrt_binary64_100
9×flip3--_binary64_82 flip--_binary64_53
7×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
5×pow-prod-up_binary64_148
4×add-cbrt-cube_binary64_114 add-log-exp_binary64_117 rem-sqrt-square_binary64_91 frac-times_binary64_88 add-exp-log_binary64_116
3×pow-sqr_binary64_51 pow-prod-down_binary64_149
2×associate-*l/_binary64_21 associate-*r/_binary64_20
1×pow2_binary64_159 pow-plus_binary64_141
Counts
4 → 77
Calls

8 calls:

13.0ms
(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b))

series474.0ms (0.4%)

Counts
4 → 53
Calls

4 calls:

149.0ms
(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
123.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
103.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
99.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 4223 to 2994 computations (29.1% saved)

simplify77.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
050512112

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)
0.1b
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)
0.2b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite28.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
24×*-un-lft-identity_binary64_78
15×add-sqr-sqrt_binary64_100
14×add-cube-cbrt_binary64_113
12×times-frac_binary64_84
8×add-log-exp_binary64_117
6×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
5×distribute-lft-out_binary64_29 pow1_binary64_139
4×associate-/l*_binary64_23
3×sqrt-prod_binary64_94 associate-/r*_binary64_22
2×flip-+_binary64_52 flip3--_binary64_82 flip--_binary64_53 sqrt-div_binary64_95 associate-/l/_binary64_25 flip3-+_binary64_81
1×+-commutative_binary64_8 sqrt-pow1_binary64_96 cbrt-undiv_binary64_112 div-exp_binary64_129 rem-sqrt-square_binary64_91 diff-log_binary64_170 frac-2neg_binary64_89 div-inv_binary64_75 clear-num_binary64_77 cancel-sign-sub-inv_binary64_44 pow1/2_binary64_158 sub-neg_binary64_71 sum-log_binary64_169
Counts
4 → 72
Calls

8 calls:

9.0ms
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)
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))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)

series562.0ms (0.4%)

Counts
4 → 60
Calls

4 calls:

168.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
159.0ms
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)
126.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
109.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2799 to 2186 computations (21.9% saved)

simplify72.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
050242444

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.1b
(/.f64 (+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) a)
0.1b
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
2.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite25.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64_100
9×*-un-lft-identity_binary64_78
8×add-log-exp_binary64_117
7×sqrt-prod_binary64_94 add-cube-cbrt_binary64_113
6×pow1_binary64_139
4×add-cbrt-cube_binary64_114 flip3--_binary64_82 flip--_binary64_53 add-exp-log_binary64_116 sqrt-div_binary64_95 cancel-sign-sub-inv_binary64_44
2×sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 diff-log_binary64_170 difference-of-squares_binary64_47 pow1/2_binary64_158 sub-neg_binary64_71
1×distribute-lft-out--_binary64_30
Counts
4 → 59
Calls

8 calls:

8.0ms
(-.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)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))

series581.0ms (0.5%)

Counts
4 → 63
Calls

4 calls:

176.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
158.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
143.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
104.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 3939 to 2956 computations (25% saved)

simplify84.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049331907
149331907

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)))
0.1b
(pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)
0.1b
(/.f64 (-.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))) (*.f64 2 a))
0.1b
(/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
2.2b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
34.3b
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite33.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
18×cbrt-prod_binary64_109
15×*-un-lft-identity_binary64_78
13×add-sqr-sqrt_binary64_100
12×sqrt-prod_binary64_94
11×add-cube-cbrt_binary64_113
8×add-log-exp_binary64_117
6×unpow-prod-down_binary64_157 sqrt-div_binary64_95 cube-prod_binary64_106 pow1_binary64_139
4×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
3×flip3--_binary64_82 flip--_binary64_53
2×cbrt-div_binary64_110 sqrt-pow1_binary64_96 cube-div_binary64_107 rem-sqrt-square_binary64_91 distribute-lft-out_binary64_29 pow1/2_binary64_158 sum-log_binary64_169
1×cube-mult_binary64_108 +-commutative_binary64_8 associate-+l-_binary64_13 rem-cbrt-cube_binary64_102 flip-+_binary64_52 pow1/3_binary64_160 sqr-pow_binary64_50 neg-sub0_binary64_73 distribute-rgt-neg-in_binary64_36 unpow3_binary64_144 neg-log_binary64_171 flip3-+_binary64_81
Counts
4 → 74
Calls

8 calls:

13.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
7.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(/.f64 (*.f64 2 c) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

series507.0ms (0.4%)

Counts
4 → 55
Calls

4 calls:

167.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
147.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
116.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))
77.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 3971 to 2967 computations (25.3% saved)

simplify65.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
050372236

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)
0.1b
(/.f64 (*.f64 c 2) (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)) (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))))
0.0b
(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))
0.0b
(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))
2.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite26.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64_100
10×sqrt-prod_binary64_94 *-un-lft-identity_binary64_78
8×add-cube-cbrt_binary64_113
7×pow1_binary64_139
6×add-log-exp_binary64_117 sqrt-div_binary64_95
4×add-cbrt-cube_binary64_114 flip3--_binary64_82 flip--_binary64_53 add-exp-log_binary64_116
3×sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 cancel-sign-sub-inv_binary64_44 pow1/2_binary64_158
2×difference-of-squares_binary64_47
1×distribute-lft-out--_binary64_30 diff-log_binary64_170 sub-neg_binary64_71
Counts
4 → 62
Calls

8 calls:

9.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))

series497.0ms (0.4%)

Counts
4 → 51
Calls

4 calls:

169.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
125.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
101.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
101.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 4690 to 3289 computations (29.9% saved)

simplify63.0ms (0%)

Algorithm
1×egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
051441795

prune7.9s (6.2%)

Pruning

174 alts after pruning (170 fresh and 4 done)

PrunedKeptTotal
New490136626
Fresh243458
Picked000
Done145
Total515174689
Error
5.2b
Counts
689 → 174
Compiler

Compiled 24770 to 15369 computations (38% saved)

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(+.f64 b (fabs.f64 (fabs.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
0.1b
(/.f64 (+.f64 b (fabs.f64 (fabs.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))) a)
0.1b
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
2.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite26.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64_100
9×*-un-lft-identity_binary64_78
8×add-log-exp_binary64_117
7×sqrt-prod_binary64_94 add-cube-cbrt_binary64_113
6×pow1_binary64_139
4×add-cbrt-cube_binary64_114 flip3--_binary64_82 flip--_binary64_53 add-exp-log_binary64_116 sqrt-div_binary64_95 cancel-sign-sub-inv_binary64_44
2×sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 diff-log_binary64_170 difference-of-squares_binary64_47 pow1/2_binary64_158 sub-neg_binary64_71
1×distribute-lft-out--_binary64_30
Counts
4 → 59
Calls

8 calls:

9.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))

series587.0ms (0.5%)

Counts
4 → 63
Calls

4 calls:

179.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
158.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
148.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
101.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 4038 to 3055 computations (24.3% saved)

simplify84.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049331907
149331907

localize17.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
0.0b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite24.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
40×associate-*r*_binary64_18
37×times-frac_binary64_84
36×*-un-lft-identity_binary64_78
35×add-sqr-sqrt_binary64_100
30×add-cube-cbrt_binary64_113
9×distribute-rgt-out_binary64_31 distribute-lft-out_binary64_29
6×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
3×associate-*l*_binary64_19 distribute-lft1-in_binary64_33 count-2_binary64_26 distribute-rgt1-in_binary64_34 pow1_binary64_139
2×cbrt-unprod_binary64_111 prod-exp_binary64_127 unswap-sqr_binary64_46
1×*-commutative_binary64_9 add-log-exp_binary64_117 cbrt-undiv_binary64_112 div-exp_binary64_129 div-inv_binary64_75 pow-prod-down_binary64_149 associate-*r/_binary64_20
Counts
1 → 59
Calls

2 calls:

20.0ms
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
0.0ms
(*.f64 -1/2 (/.f64 (+.f64 b b) a))

series58.0ms (0%)

Counts
1 → 6
Calls

1 calls:

58.0ms
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
Compiler

Compiled 204 to 168 computations (17.6% saved)

simplify55.0ms (0%)

Algorithm
1×egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04937647
14937647

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)
0.0b
(exp.f64 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a))
0.2b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
3.8b
(log.f64 (exp.f64 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite30.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
22×*-un-lft-identity_binary64_78
17×log-pow_binary64_167
16×exp-prod_binary64_130
15×add-sqr-sqrt_binary64_100
14×add-cube-cbrt_binary64_113
12×times-frac_binary64_84
8×add-log-exp_binary64_117
6×pow1_binary64_139
4×add-cbrt-cube_binary64_114 add-exp-log_binary64_116 distribute-lft-out_binary64_29
3×sqrt-prod_binary64_94 log-prod_binary64_164
2×flip3--_binary64_82 flip--_binary64_53 sqrt-div_binary64_95
1×+-commutative_binary64_8 sqrt-pow1_binary64_96 flip-+_binary64_52 rem-sqrt-square_binary64_91 diff-log_binary64_170 div-inv_binary64_75 rem-log-exp_binary64_119 cancel-sign-sub-inv_binary64_44 pow1/2_binary64_158 sub-neg_binary64_71 sum-log_binary64_169 flip3-+_binary64_81
Counts
4 → 67
Calls

8 calls:

11.0ms
(log.f64 (exp.f64 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)))
7.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(exp.f64 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a))

series600.0ms (0.5%)

Counts
4 → 49
Calls

4 calls:

270.0ms
(log.f64 (exp.f64 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) a)))
165.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
93.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
71.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2516 to 2000 computations (20.5% saved)

simplify99.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
049191950
149191950

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) a)
0.1b
(/.f64 (*.f64 c 2) (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b))
0.0b
(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.0b
(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
9.8b
(-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite38.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64_100
9×sqrt-prod_binary64_94
8×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
7×pow1_binary64_139
6×add-log-exp_binary64_117 sqrt-div_binary64_95
4×add-cbrt-cube_binary64_114 flip3--_binary64_82 flip--_binary64_53 add-exp-log_binary64_116
3×sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 cancel-sign-sub-inv_binary64_44 pow1/2_binary64_158
1×diff-log_binary64_170 difference-of-squares_binary64_47 sub-neg_binary64_71
Counts
4 → 60
Calls

8 calls:

18.0ms
(-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
8.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

series490.0ms (0.4%)

Counts
4 → 50
Calls

4 calls:

175.0ms
(-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
109.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
104.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
100.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 4214 to 3041 computations (27.8% saved)

simplify85.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
050291702

localize48.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (*.f64 c 2) (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)) (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))))
0.0b
(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))
0.0b
(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))
0.0b
(*.f64 4 (*.f64 (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 a c)))
17.3b
(sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 a c)))))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
34.4b
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 a c))))))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite50.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
121×sqrt-prod_binary64_94
101×add-sqr-sqrt_binary64_100
78×times-frac_binary64_84
63×*-un-lft-identity_binary64_78
49×add-cube-cbrt_binary64_113
42×difference-of-squares_binary64_47
35×sqr-pow_binary64_50
14×unpow-prod-down_binary64_157
13×associate-/l*_binary64_23
10×sqrt-div_binary64_95
7×distribute-lft-out--_binary64_30 pow1_binary64_139
6×add-cbrt-cube_binary64_114 associate-/r*_binary64_22 add-exp-log_binary64_116
4×add-log-exp_binary64_117
3×sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 flip3--_binary64_82 flip--_binary64_53 pow1/2_binary64_158
2×flip-+_binary64_52 associate-/r/_binary64_24 associate-/l/_binary64_25 flip3-+_binary64_81
1×cbrt-undiv_binary64_112 div-exp_binary64_129 frac-2neg_binary64_89 div-inv_binary64_75 sqrt-undiv_binary64_99 clear-num_binary64_77
Counts
4 → 159
Calls

8 calls:

19.0ms
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 a c))))))
5.0ms
(sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 a c)))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(*.f64 4 (*.f64 (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 a c)))

series722.0ms (0.6%)

Counts
4 → 60
Calls

4 calls:

269.0ms
(sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 a c)))))
214.0ms
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (*.f64 a c))))))
121.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
117.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 6576 to 4661 computations (29.1% saved)

simplify152.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
219 → 219
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0496011415
1496011415

prune14.8s (11.6%)

Pruning

309 alts after pruning (304 fresh and 5 done)

PrunedKeptTotal
New475157632
Fresh18147165
Picked000
Done459
Total497309806
Error
5.2b
Counts
806 → 309
Compiler

Compiled 38159 to 24546 computations (35.7% saved)

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(+.f64 b (fabs.f64 (fabs.f64 (fabs.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
0.1b
(/.f64 (+.f64 b (fabs.f64 (fabs.f64 (fabs.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) a)
0.1b
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
2.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite26.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64_100
9×*-un-lft-identity_binary64_78
8×add-log-exp_binary64_117
7×sqrt-prod_binary64_94 add-cube-cbrt_binary64_113
6×pow1_binary64_139
4×add-cbrt-cube_binary64_114 flip3--_binary64_82 flip--_binary64_53 add-exp-log_binary64_116 sqrt-div_binary64_95 cancel-sign-sub-inv_binary64_44
2×sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 diff-log_binary64_170 difference-of-squares_binary64_47 pow1/2_binary64_158 sub-neg_binary64_71
1×distribute-lft-out--_binary64_30
Counts
4 → 59
Calls

8 calls:

9.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))

series587.0ms (0.5%)

Counts
4 → 63
Calls

4 calls:

180.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
158.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
148.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
101.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 4137 to 3154 computations (23.8% saved)

simplify82.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049331907
149331907

localize18.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b
(*.f64 (neg.f64 b) (/.f64 1 a))
0.2b
(*.f64 (neg.f64 b) (/.f64 1 a))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite14.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64_100
13×associate-*r*_binary64_18
12×*-un-lft-identity_binary64_78
11×add-cube-cbrt_binary64_113 times-frac_binary64_84
10×associate-*l*_binary64_19 add-exp-log_binary64_116
6×add-cbrt-cube_binary64_114
4×prod-exp_binary64_127
3×distribute-lft-neg-in_binary64_35 unswap-sqr_binary64_46 distribute-rgt-neg-in_binary64_36 pow1_binary64_139
2×cbrt-unprod_binary64_111 div-exp_binary64_129
1×*-commutative_binary64_9 add-log-exp_binary64_117 cbrt-undiv_binary64_112 neg-mul-1_binary64_74 un-div-inv_binary64_76 1-exp_binary64_122 div-inv_binary64_75 distribute-lft-neg-out_binary64_37 rec-exp_binary64_128 pow-prod-down_binary64_149 associate-*r/_binary64_20
Counts
1 → 44
Calls

2 calls:

11.0ms
(*.f64 (neg.f64 b) (/.f64 1 a))
0.0ms
(*.f64 (neg.f64 b) (/.f64 1 a))

series56.0ms (0%)

Counts
1 → 6
Calls

1 calls:

56.0ms
(*.f64 (neg.f64 b) (/.f64 1 a))
Compiler

Compiled 204 to 168 computations (17.6% saved)

simplify82.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
04814434
14814434

localize32.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.2b
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)
0.1b
(/.f64 (+.f64 b (fabs.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) a)
0.1b
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) b))
2.2b
(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) b)
22.9b
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite38.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
32×cbrt-prod_binary64_109
29×add-sqr-sqrt_binary64_100
23×sqrt-prod_binary64_94
15×*-un-lft-identity_binary64_78
13×add-cube-cbrt_binary64_113
8×unpow-prod-down_binary64_157 cube-prod_binary64_106
6×add-log-exp_binary64_117 rem-sqrt-square_binary64_91 difference-of-squares_binary64_47 pow1_binary64_139
4×add-cbrt-cube_binary64_114 cbrt-div_binary64_110 cube-div_binary64_107 flip3--_binary64_82 sqr-pow_binary64_50 flip--_binary64_53 add-exp-log_binary64_116 sqrt-div_binary64_95
3×sqrt-pow1_binary64_96 cancel-sign-sub-inv_binary64_44
2×cube-mult_binary64_108 pow1/3_binary64_160 pow1/2_binary64_158 unpow3_binary64_144
1×rem-cbrt-cube_binary64_102 distribute-lft-out--_binary64_30 diff-log_binary64_170 sub-neg_binary64_71
Counts
4 → 91
Calls

8 calls:

15.0ms
(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) b)
8.0ms
(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))
6.0ms
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(/.f64 (*.f64 c 2) (-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) b))

series586.0ms (0.5%)

Counts
4 → 63
Calls

4 calls:

172.0ms
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
163.0ms
(-.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))) b)
145.0ms
(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))
106.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 4005 to 3022 computations (24.5% saved)

simplify69.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
052472800

localize38.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(+.f64 (*.f64 b b) (+.f64 (*.f64 a (*.f64 c -4)) (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
0.1b
(pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)
0.1b
(/.f64 (/.f64 (+.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3) (pow.f64 b 3)) (+.f64 (*.f64 b b) (+.f64 (*.f64 a (*.f64 c -4)) (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))) a)
0.1b
(*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
15.3b
(+.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3) (pow.f64 b 3))
20.7b
(/.f64 (+.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3) (pow.f64 b 3)) (+.f64 (*.f64 b b) (+.f64 (*.f64 a (*.f64 c -4)) (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite67.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
70×*-un-lft-identity_binary64_78
27×times-frac_binary64_84
25×distribute-lft-out_binary64_29
22×add-sqr-sqrt_binary64_100
20×unpow-prod-down_binary64_157 add-cube-cbrt_binary64_113 cube-prod_binary64_106
9×associate-/l*_binary64_23
6×add-cbrt-cube_binary64_114 sqrt-prod_binary64_94 add-log-exp_binary64_117 add-exp-log_binary64_116 pow1_binary64_139
5×sum-cubes_binary64_79
4×sqrt-div_binary64_95
3×flip-+_binary64_52 associate-/r*_binary64_22 flip3-+_binary64_81
2×sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 flip3--_binary64_82 flip--_binary64_53 associate-/r/_binary64_24 associate-/l/_binary64_25 pow1/2_binary64_158
1×+-commutative_binary64_8 cbrt-undiv_binary64_112 div-exp_binary64_129 frac-2neg_binary64_89 div-inv_binary64_75 clear-num_binary64_77 sum-log_binary64_169
Counts
4 → 102
Calls

8 calls:

30.0ms
(/.f64 (+.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3) (pow.f64 b 3)) (+.f64 (*.f64 b b) (+.f64 (*.f64 a (*.f64 c -4)) (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))))
22.0ms
(+.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3) (pow.f64 b 3))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

series825.0ms (0.6%)

Counts
4 → 49
Calls

4 calls:

350.0ms
(/.f64 (+.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3) (pow.f64 b 3)) (+.f64 (*.f64 b b) (+.f64 (*.f64 a (*.f64 c -4)) (*.f64 b (-.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))))
226.0ms
(+.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3) (pow.f64 b 3))
160.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
89.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 4646 to 3330 computations (28.3% saved)

simplify127.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
049656485
149656485

localize53.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (*.f64 c 2) (*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)) (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))))
0.0b
(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))
0.0b
(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b))
0.0b
(*.f64 4 (*.f64 (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)) (*.f64 a c)))
18.9b
(+.f64 b (exp.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)) (*.f64 a c)))))))))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
23.8b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
34.4b
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)) (*.f64 a c))))))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite88.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
118×sqrt-prod_binary64_94
99×add-sqr-sqrt_binary64_100
78×times-frac_binary64_84
64×*-un-lft-identity_binary64_78
48×add-cube-cbrt_binary64_113
42×difference-of-squares_binary64_47
35×sqr-pow_binary64_50
14×unpow-prod-down_binary64_157
13×associate-/l*_binary64_23
8×sqrt-div_binary64_95
7×distribute-lft-out--_binary64_30
6×add-cbrt-cube_binary64_114 add-log-exp_binary64_117 associate-/r*_binary64_22 add-exp-log_binary64_116 pow1_binary64_139
3×flip3--_binary64_82 flip--_binary64_53
2×sqrt-pow1_binary64_96 flip-+_binary64_52 rem-sqrt-square_binary64_91 associate-/r/_binary64_24 associate-/l/_binary64_25 pow1/2_binary64_158 flip3-+_binary64_81
1×+-commutative_binary64_8 cbrt-undiv_binary64_112 div-exp_binary64_129 frac-2neg_binary64_89 div-inv_binary64_75 sqrt-undiv_binary64_99 clear-num_binary64_77 distribute-lft-out_binary64_29 sum-log_binary64_169
Counts
4 → 156
Calls

8 calls:

47.0ms
(+.f64 b (exp.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)) (*.f64 a c)))))))))
20.0ms
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)) (*.f64 a c))))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(*.f64 4 (*.f64 (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)) (*.f64 a c)))

series615.0ms (0.5%)

Counts
4 → 45
Calls

4 calls:

188.0ms
(+.f64 b (exp.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)) (*.f64 a c)))))))))
181.0ms
(/.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))) (sqrt.f64 (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (+.f64 (*.f64 (*.f64 4 a) c) (*.f64 b b)) (*.f64 a c))))))
124.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
122.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 5318 to 3748 computations (29.5% saved)

simplify157.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
0506211274

prune24.4s (19.2%)

Pruning

442 alts after pruning (436 fresh and 6 done)

PrunedKeptTotal
New529149678
Fresh12287299
Picked000
Done4610
Total545442987
Error
5.2b
Counts
987 → 442
Compiler

Compiled 23845 to 14617 computations (38.7% saved)

simplify1.2s (1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
0500994194

regimes23.0s (18.1%)

Compiler

Compiled 148188 to 102828 computations (30.6% saved)

bsearch152.0ms (0.1%)

Steps
ItersRangePoint
8
5.710486079104589e+96
1.580006395237835e+99
8.08598480039997e+98
7
-4.956057904971686e+157
-2.830445824334434e+156
-2.858304761937573e+156
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes200.0ms (0.2%)

Compiler

Compiled 1485 to 1194 computations (19.6% saved)

bsearch36.0ms (0%)

Steps
ItersRangePoint
8
5.710486079104589e+96
1.580006395237835e+99
6.276311452461952e+97
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes403.0ms (0.3%)

Compiler

Compiled 1116 to 921 computations (17.5% saved)

bsearch26.0ms (0%)

Steps
ItersRangePoint
5
8.838291860038957e-66
2.052880049407838e-65
1.1256675104227095e-65
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes157.0ms (0.1%)

Compiler

Compiled 966 to 804 computations (16.8% saved)

bsearch34.0ms (0%)

Steps
ItersRangePoint
7
1.0682363162431274e-105
2.0175673800325314e-103
1.9845063829023164e-103
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes90.0ms (0.1%)

Compiler

Compiled 834 to 699 computations (16.2% saved)

bsearch0.0ms (0%)

regimes26.0ms (0%)

Accuracy

Total 1.3b remaining (18.7%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch10.0ms (0%)

Compiler

Compiled 256 to 179 computations (30.1% saved)

simplify6.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0141381
1141381

end0.0ms (0%)

sample40.9s (32.2%)

Algorithm
1×intervals
Results
693.0ms8000×body128valid
52.0ms646×body128nan
35.0ms370×body128invalid
Compiler

Compiled 50201 to 34837 computations (30.6% saved)

Pareto

0.449263612219248

Profiling

Loading profile data...