Details

Time bar (total: 1.8min)

analyze271.0ms (0.2%)

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)

sample47.0ms (0%)

Algorithm
1×intervals
Results
14.0ms116×body256valid
9.0ms290×pre128true
7.0ms49×body512valid
5.0ms91×body128valid
2.0ms34×body128nan
Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify421.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (325.0ms)

IterNodesCost
0183424
1183424

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
51.4b
Counts
2 → 2
Compiler

Compiled 16 to 13 computations (18.8% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

26.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(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))
26.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite38.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64_782
14×*-un-lft-identity_binary64_760
9×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
8×add-cube-cbrt_binary64_795 add-log-exp_binary64_799
6×sqrt-prod_binary64_776 difference-of-squares_binary64_729 associate-/l*_binary64_705 times-frac_binary64_766
5×pow1_binary64_821
4×cancel-sign-sub-inv_binary64_726 flip--_binary64_735 flip3--_binary64_764
3×distribute-lft-out--_binary64_712
2×diff-log_binary64_852 cbrt-undiv_binary64_794 associate-/l/_binary64_707 sqrt-div_binary64_777 div-exp_binary64_811 sub-neg_binary64_753
1×rem-sqrt-square_binary64_773 frac-2neg_binary64_771 prod-exp_binary64_809 sqrt-pow1_binary64_778 associate-/r*_binary64_704 div-inv_binary64_757 div-sub_binary64_765 cbrt-unprod_binary64_793 pow1/2_binary64_840 clear-num_binary64_759
Counts
4 → 74
Calls

8 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
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series676.0ms (0.6%)

Counts
4 → 72
Calls

4 calls:

229.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
166.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
164.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
116.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1950 to 1660 computations (14.9% saved)

simplify80.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
052073272

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

26.2b
(+.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 b b) (*.f64 (*.f64 4 a) c))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(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 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
26.2b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

rewrite42.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
19×*-un-lft-identity_binary64_760
10×add-log-exp_binary64_799
9×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
8×add-sqr-sqrt_binary64_782
7×add-cube-cbrt_binary64_795
6×distribute-lft-out_binary64_711
5×associate-/l*_binary64_705 pow1_binary64_821 times-frac_binary64_766
3×sqrt-prod_binary64_776 distribute-rgt-neg-in_binary64_718
2×cbrt-undiv_binary64_794 flip3-+_binary64_763 associate-/l/_binary64_707 neg-sub0_binary64_755 sqrt-div_binary64_777 flip-+_binary64_734 sum-log_binary64_851 associate-+l-_binary64_695 div-exp_binary64_811 flip--_binary64_735 flip3--_binary64_764
1×diff-log_binary64_852 rem-sqrt-square_binary64_773 frac-2neg_binary64_771 prod-exp_binary64_809 cancel-sign-sub-inv_binary64_726 sqrt-pow1_binary64_778 associate-/r*_binary64_704 div-inv_binary64_757 neg-log_binary64_853 +-commutative_binary64_690 div-sub_binary64_765 cbrt-unprod_binary64_793 pow1/2_binary64_840 clear-num_binary64_759 sub-neg_binary64_753
Counts
4 → 70
Calls

8 calls:

14.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
13.0ms
(+.f64 (neg.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
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series675.0ms (0.6%)

Counts
4 → 72
Calls

4 calls:

230.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
166.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
165.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
113.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2001 to 1711 computations (14.5% saved)

simplify59.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
051673105

prune1.5s (1.4%)

Pruning

88 alts after pruning (86 fresh and 2 done)

PrunedKeptTotal
New20286288
Fresh000
Picked000
Done022
Total20288290
Error
0.0b
Counts
290 → 88
Compiler

Compiled 5638 to 3611 computations (36% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
0.3b
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

rewrite68.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
45×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
34×times-frac_binary64_766
32×*-un-lft-identity_binary64_760 add-sqr-sqrt_binary64_782
17×cbrt-undiv_binary64_794 div-exp_binary64_811
14×associate-/l*_binary64_705
13×prod-exp_binary64_809 cbrt-unprod_binary64_793
12×add-cube-cbrt_binary64_795
10×add-log-exp_binary64_799 difference-of-squares_binary64_729 distribute-lft-out--_binary64_712
8×sqrt-prod_binary64_776 associate-/r*_binary64_704
7×cancel-sign-sub-inv_binary64_726
6×associate-/r/_binary64_706
5×distribute-rgt-neg-in_binary64_718 flip--_binary64_735 flip3--_binary64_764
4×div-inv_binary64_757 pow1_binary64_821
3×diff-log_binary64_852
2×frac-2neg_binary64_771 clear-num_binary64_759 sub-neg_binary64_753
1×associate--l-_binary64_698 associate-/l/_binary64_707 neg-sub0_binary64_755 neg-log_binary64_853
Counts
4 → 122
Calls

8 calls:

19.0ms
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
15.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
11.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series830.0ms (0.8%)

Counts
4 → 72
Calls

4 calls:

279.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
239.0ms
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
166.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
146.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
Compiler

Compiled 2487 to 2008 computations (19.3% saved)

simplify129.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
049475531
149475531

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify10.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (*.f64 a a) (*.f64 c c))
0.3b
(/.f64 (*.f64 a c) b)
0.1b
(+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))
0.1b
(/.f64 (-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b) (*.f64 a 2))
0.3b
(/.f64 (*.f64 a c) b)
0.3b
(*.f64 (*.f64 a a) (*.f64 c c))
0.4b
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
26.2b
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)

rewrite57.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
70×add-exp-log_binary64_798
39×add-cbrt-cube_binary64_796
33×prod-exp_binary64_809
32×pow1_binary64_821
17×cbrt-unprod_binary64_793 div-exp_binary64_811
15×*-un-lft-identity_binary64_760 associate-/r*_binary64_704 times-frac_binary64_766 add-sqr-sqrt_binary64_782
14×pow-prod-down_binary64_831
13×add-cube-cbrt_binary64_795
9×add-log-exp_binary64_799
7×cbrt-undiv_binary64_794
6×cube-prod_binary64_788 unpow-prod-down_binary64_839
5×pow-exp_binary64_828 pow-to-exp_binary64_829
4×pow-plus_binary64_823 pow-prod-up_binary64_830
3×cancel-sign-sub-inv_binary64_726
2×cube-mult_binary64_790 pow2_binary64_841 diff-log_binary64_852 frac-2neg_binary64_771 unpow3_binary64_826 pow-sqr_binary64_733 div-inv_binary64_757 associate-/l*_binary64_705 sqr-pow_binary64_732 clear-num_binary64_759
1×unswap-sqr_binary64_728 difference-of-squares_binary64_729 distribute-lft-out--_binary64_712 associate-*r*_binary64_700 sum-log_binary64_851 associate-*l*_binary64_701 associate--l+_binary64_697 sub-neg_binary64_753 *-commutative_binary64_691 flip--_binary64_735 flip3--_binary64_764
Counts
4 → 123
Calls

8 calls:

20.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
10.0ms
(*.f64 (*.f64 a a) (*.f64 c c))
8.0ms
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)
5.0ms
(/.f64 (*.f64 a c) b)
0.0ms
(/.f64 (-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b) (*.f64 a 2))

series885.0ms (0.8%)

Counts
4 → 42
Calls

4 calls:

482.0ms
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)
223.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
107.0ms
(/.f64 (*.f64 a c) b)
72.0ms
(*.f64 (*.f64 a a) (*.f64 c c))
Compiler

Compiled 1893 to 1488 computations (21.4% saved)

simplify65.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
054462567

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(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 b b) (*.f64 (*.f64 4 a) c))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
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))
0.2b
(pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)
0.5b
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))
26.2b
(+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)))

rewrite63.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
28×*-un-lft-identity_binary64_760
18×cbrt-prod_binary64_791
16×add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
12×sqrt-prod_binary64_776 cube-prod_binary64_788 unpow-prod-down_binary64_839
10×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
8×add-log-exp_binary64_799
6×distribute-lft-out_binary64_711 pow1_binary64_821
5×associate-/l*_binary64_705 times-frac_binary64_766
4×sqrt-div_binary64_777 cube-div_binary64_789
3×distribute-rgt-neg-in_binary64_718 pow-unpow_binary64_837 pow-pow_binary64_832
2×cube-mult_binary64_790 cbrt-undiv_binary64_794 flip3-+_binary64_763 associate-/l/_binary64_707 unpow3_binary64_826 neg-sub0_binary64_755 flip-+_binary64_734 sum-log_binary64_851 cbrt-div_binary64_792 associate-+l-_binary64_695 sqr-pow_binary64_732 div-exp_binary64_811 flip--_binary64_735 flip3--_binary64_764
1×pow1/3_binary64_842 rem-cbrt-cube_binary64_784 frac-2neg_binary64_771 prod-exp_binary64_809 sqrt-pow1_binary64_778 associate-/r*_binary64_704 pow-exp_binary64_828 div-inv_binary64_757 rem-cube-cbrt_binary64_783 pow-to-exp_binary64_829 neg-log_binary64_853 +-commutative_binary64_690 div-sub_binary64_765 cbrt-unprod_binary64_793 pow1/2_binary64_840 clear-num_binary64_759 sqrt-pow2_binary64_779
Counts
4 → 106
Calls

8 calls:

21.0ms
(/.f64 (+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))) (*.f64 2 a))
17.0ms
(+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)))
7.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))
6.0ms
(pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series693.0ms (0.6%)

Counts
4 → 72
Calls

4 calls:

225.0ms
(/.f64 (+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))) (*.f64 2 a))
185.0ms
(pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)
170.0ms
(+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)))
113.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))
Compiler

Compiled 2216 to 1876 computations (15.3% saved)

simplify102.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
051244250

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0b
(sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.6b
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.6b
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.6b
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
36.1b
(-.f64 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)

rewrite50.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
10×*-un-lft-identity_binary64_760 add-sqr-sqrt_binary64_782
9×cbrt-prod_binary64_791
8×add-cube-cbrt_binary64_795
6×add-log-exp_binary64_799 cbrt-div_binary64_792
4×add-exp-log_binary64_798 add-cbrt-cube_binary64_796 pow1_binary64_821 flip--_binary64_735 flip3--_binary64_764
3×pow1/3_binary64_842 cancel-sign-sub-inv_binary64_726
1×diff-log_binary64_852 difference-of-squares_binary64_729 distribute-lft-out--_binary64_712 sub-neg_binary64_753
Counts
4 → 55
Calls

8 calls:

28.0ms
(-.f64 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
4.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
4.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

series1.1s (1%)

Counts
4 → 81
Calls

4 calls:

307.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
302.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
295.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
193.0ms
(-.f64 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
Compiler

Compiled 4915 to 3806 computations (22.6% saved)

simplify102.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049333873
149333873

prune8.3s (7.7%)

Pruning

219 alts after pruning (213 fresh and 6 done)

PrunedKeptTotal
New525148673
Fresh166581
Picked000
Done167
Total542219761
Error
0b
Counts
761 → 219
Compiler

Compiled 17923 to 11042 computations (38.4% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.2b
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
0.3b
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))

rewrite76.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
57×*-un-lft-identity_binary64_760 add-sqr-sqrt_binary64_782
45×times-frac_binary64_766
36×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
29×add-cube-cbrt_binary64_795
27×associate-*r*_binary64_700
14×difference-of-squares_binary64_729 distribute-lft-out--_binary64_712
12×prod-exp_binary64_809 cbrt-unprod_binary64_793
10×cbrt-undiv_binary64_794 associate-/r*_binary64_704 div-exp_binary64_811
9×pow1_binary64_821
7×sqrt-prod_binary64_776 distribute-rgt-neg-in_binary64_718
6×add-log-exp_binary64_799
4×associate-/r/_binary64_706 associate-/l*_binary64_705
3×div-inv_binary64_757 pow-prod-down_binary64_831 flip--_binary64_735 flip3--_binary64_764
2×frac-2neg_binary64_771 associate-*r/_binary64_702 clear-num_binary64_759
1×diff-log_binary64_852 associate-/l/_binary64_707 cancel-sign-sub-inv_binary64_726 associate-*l*_binary64_701 sub-neg_binary64_753 *-commutative_binary64_691
Counts
4 → 132
Calls

8 calls:

23.0ms
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
19.0ms
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
13.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

series919.0ms (0.8%)

Counts
4 → 72
Calls

4 calls:

280.0ms
(*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
236.0ms
(/.f64 (*.f64 (*.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
234.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
167.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
Compiler

Compiled 2384 to 1868 computations (21.6% saved)

simplify111.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049295545
149295545

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

26.2b
(+.f64 (neg.f64 b) (*.f64 (cbrt.f64 1) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.1b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 1) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(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 (neg.f64 b) (*.f64 (cbrt.f64 1) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
26.2b
(+.f64 (neg.f64 b) (*.f64 (cbrt.f64 1) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

rewrite30.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
10×add-log-exp_binary64_799
9×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
8×add-sqr-sqrt_binary64_782
7×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795
5×pow1_binary64_821
3×sqrt-prod_binary64_776 associate-/l*_binary64_705 times-frac_binary64_766
2×cbrt-undiv_binary64_794 flip3-+_binary64_763 associate-/l/_binary64_707 neg-sub0_binary64_755 sqrt-div_binary64_777 flip-+_binary64_734 sum-log_binary64_851 associate-+l-_binary64_695 div-exp_binary64_811 flip--_binary64_735 flip3--_binary64_764
1×diff-log_binary64_852 rem-sqrt-square_binary64_773 frac-2neg_binary64_771 prod-exp_binary64_809 cancel-sign-sub-inv_binary64_726 sqrt-pow1_binary64_778 associate-/r*_binary64_704 div-inv_binary64_757 neg-log_binary64_853 +-commutative_binary64_690 div-sub_binary64_765 cbrt-unprod_binary64_793 pow1/2_binary64_840 clear-num_binary64_759 sub-neg_binary64_753
Counts
4 → 64
Calls

8 calls:

8.0ms
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 1) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
5.0ms
(+.f64 (neg.f64 b) (*.f64 (cbrt.f64 1) (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
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series698.0ms (0.6%)

Counts
4 → 72
Calls

4 calls:

233.0ms
(/.f64 (+.f64 (neg.f64 b) (*.f64 (cbrt.f64 1) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
178.0ms
(+.f64 (neg.f64 b) (*.f64 (cbrt.f64 1) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
171.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
115.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2154 to 1864 computations (13.5% saved)

simplify89.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
054703215

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))
0.1b
(/.f64 (-.f64 (+.f64 b (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))) b) (*.f64 a 2))
0.0b
(+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))
0.0b
(*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4)
0.4b
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
0.4b
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
0.7b
(pow.f64 (*.f64 a c) 3)
26.2b
(-.f64 (+.f64 b (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))) b)

rewrite87.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
76×add-exp-log_binary64_798
68×times-frac_binary64_766
43×*-un-lft-identity_binary64_760
42×unpow-prod-down_binary64_839
40×add-sqr-sqrt_binary64_782
38×add-cube-cbrt_binary64_795
28×prod-exp_binary64_809
27×add-cbrt-cube_binary64_796 div-exp_binary64_811
20×sqr-pow_binary64_732
19×associate-/r*_binary64_704
17×pow-exp_binary64_828
15×cube-prod_binary64_788
13×add-log-exp_binary64_799 pow-to-exp_binary64_829
11×cube-mult_binary64_790 unpow3_binary64_826
9×associate-/l*_binary64_705 cbrt-unprod_binary64_793
7×pow1_binary64_821
6×cbrt-undiv_binary64_794
3×diff-log_binary64_852 cancel-sign-sub-inv_binary64_726 sum-log_binary64_851 pow-unpow_binary64_837
2×frac-2neg_binary64_771 div-inv_binary64_757 rem-cube-cbrt_binary64_783 distribute-lft-out--_binary64_712 clear-num_binary64_759 pow-pow_binary64_832
1×distribute-lft-out_binary64_711 difference-of-squares_binary64_729 associate--l+_binary64_697 sub-neg_binary64_753 pow-prod-down_binary64_831 flip--_binary64_735 flip3--_binary64_764
Counts
4 → 191
Calls

8 calls:

26.0ms
(-.f64 (+.f64 b (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))) b)
15.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
8.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
4.0ms
(pow.f64 (*.f64 a c) 3)
0.0ms
(*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4)

series1.2s (1.1%)

Counts
4 → 41
Calls

4 calls:

526.0ms
(-.f64 (+.f64 b (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))) b)
326.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
219.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
86.0ms
(pow.f64 (*.f64 a c) 3)
Compiler

Compiled 2645 to 2034 computations (23.1% saved)

simplify94.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
051994733

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.2b
(pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)
0.5b
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))
26.2b
(+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)))
26.2b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite57.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
21×*-un-lft-identity_binary64_760
19×add-sqr-sqrt_binary64_782
18×cbrt-prod_binary64_791
15×add-cube-cbrt_binary64_795
13×sqrt-prod_binary64_776
12×cube-prod_binary64_788 unpow-prod-down_binary64_839
10×add-log-exp_binary64_799
6×pow1_binary64_821
5×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
4×sqrt-div_binary64_777 cube-div_binary64_789
3×cancel-sign-sub-inv_binary64_726 pow-unpow_binary64_837 flip--_binary64_735 pow-pow_binary64_832 flip3--_binary64_764
2×cube-mult_binary64_790 distribute-lft-out_binary64_711 unpow3_binary64_826 difference-of-squares_binary64_729 sum-log_binary64_851 cbrt-div_binary64_792 sqr-pow_binary64_732
1×pow1/3_binary64_842 rem-cbrt-cube_binary64_784 diff-log_binary64_852 flip3-+_binary64_763 sqrt-pow1_binary64_778 pow-exp_binary64_828 neg-sub0_binary64_755 rem-cube-cbrt_binary64_783 flip-+_binary64_734 pow-to-exp_binary64_829 distribute-lft-out--_binary64_712 neg-log_binary64_853 +-commutative_binary64_690 associate-+l-_binary64_695 distribute-rgt-neg-in_binary64_718 pow1/2_binary64_840 sub-neg_binary64_753 sqrt-pow2_binary64_779
Counts
4 → 95
Calls

8 calls:

17.0ms
(+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)))
11.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))
9.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
7.0ms
(pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series413.0ms (0.4%)

Counts
4 → 36
Calls

4 calls:

123.0ms
(pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)
107.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
105.0ms
(+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)))
77.0ms
(cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3))
Compiler

Compiled 2448 to 1918 computations (21.7% saved)

simplify82.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
051672464

prune15.2s (14%)

Pruning

367 alts after pruning (359 fresh and 8 done)

PrunedKeptTotal
New522181703
Fresh30178208
Picked000
Done3811
Total555367922
Error
0b
Counts
922 → 367
Compiler

Compiled 26197 to 16611 computations (36.6% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
0.3b
(/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
0.3b
(/.f64 (*.f64 a 2) (/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))

rewrite146.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
560×times-frac_binary64_766
352×*-un-lft-identity_binary64_760 add-sqr-sqrt_binary64_782
212×add-cube-cbrt_binary64_795
120×associate-/r*_binary64_704
70×difference-of-squares_binary64_729 distribute-lft-out--_binary64_712
38×sqrt-prod_binary64_776
35×distribute-rgt-neg-in_binary64_718
32×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
26×associate-/r/_binary64_706
16×cbrt-undiv_binary64_794 div-exp_binary64_811
15×div-inv_binary64_757
12×flip--_binary64_735 flip3--_binary64_764
8×add-log-exp_binary64_799
7×associate-/l*_binary64_705
6×cancel-sign-sub-inv_binary64_726
4×pow1_binary64_821
3×frac-2neg_binary64_771 prod-exp_binary64_809 cbrt-unprod_binary64_793 clear-num_binary64_759
2×diff-log_binary64_852
1×associate--l-_binary64_698 neg-sub0_binary64_755 neg-log_binary64_853 sub-neg_binary64_753
Counts
4 → 390
Calls

8 calls:

30.0ms
(/.f64 (*.f64 a 2) (/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))
18.0ms
(/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
17.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
11.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))

series864.0ms (0.8%)

Counts
4 → 72
Calls

4 calls:

249.0ms
(/.f64 (*.f64 a 2) (/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))))
232.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4))))))
228.0ms
(/.f64 a (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))))
154.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 a 4)))))
Compiler

Compiled 2404 to 1909 computations (20.6% saved)

simplify200.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
462 → 462
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
0497118371
1497118371

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(/.f64 (*.f64 a c) b)
0.2b
(/.f64 (neg.f64 (/.f64 (*.f64 a c) b)) a)
0.2b
(/.f64 (neg.f64 (/.f64 (*.f64 a c) b)) a)
0.3b
(/.f64 (*.f64 a c) b)

rewrite21.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
81×times-frac_binary64_766
43×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
28×distribute-lft-neg-in_binary64_717 distribute-rgt-neg-in_binary64_718
19×associate-/l*_binary64_705
10×div-inv_binary64_757
9×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
6×associate-/r*_binary64_704
4×neg-mul-1_binary64_756
3×cbrt-undiv_binary64_794 div-exp_binary64_811
2×frac-2neg_binary64_771 add-log-exp_binary64_799 pow1_binary64_821 clear-num_binary64_759
1×distribute-neg-frac_binary64_724 prod-exp_binary64_809 associate-/l/_binary64_707 distribute-frac-neg_binary64_723 neg-sub0_binary64_755 div-sub_binary64_765 cbrt-unprod_binary64_793
Counts
2 → 111
Calls

4 calls:

7.0ms
(/.f64 (neg.f64 (/.f64 (*.f64 a c) b)) a)
5.0ms
(/.f64 (*.f64 a c) b)
0.0ms
(/.f64 (neg.f64 (/.f64 (*.f64 a c) b)) a)
0.0ms
(/.f64 (*.f64 a c) b)

series194.0ms (0.2%)

Counts
2 → 18
Calls

2 calls:

108.0ms
(/.f64 (*.f64 a c) b)
86.0ms
(/.f64 (neg.f64 (/.f64 (*.f64 a c) b)) a)
Compiler

Compiled 234 to 234 computations (0% saved)

simplify69.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
051262000

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b) (*.f64 a 2))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(log.f64 (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 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b) (*.f64 a 2))
2.7b
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
49.5b
(-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)

rewrite50.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64_782
16×*-un-lft-identity_binary64_760
12×exp-sum_binary64_806 log-prod_binary64_846
10×add-cube-cbrt_binary64_795
9×add-exp-log_binary64_798 difference-of-squares_binary64_729 add-cbrt-cube_binary64_796
8×add-log-exp_binary64_799
7×associate-/l*_binary64_705 times-frac_binary64_766
6×sqrt-prod_binary64_776 exp-prod_binary64_812 pow1_binary64_821
4×cancel-sign-sub-inv_binary64_726 flip--_binary64_735 flip3--_binary64_764
3×log-pow_binary64_849 distribute-lft-out--_binary64_712
2×diff-log_binary64_852 log-div_binary64_847 cbrt-undiv_binary64_794 associate-/l/_binary64_707 exp-diff_binary64_808 sqrt-div_binary64_777 div-exp_binary64_811 sub-neg_binary64_753
1×frac-2neg_binary64_771 prod-exp_binary64_809 sqrt-pow1_binary64_778 associate-/r*_binary64_704 rem-exp-log_binary64_800 div-inv_binary64_757 div-sub_binary64_765 cbrt-unprod_binary64_793 pow1/2_binary64_840 clear-num_binary64_759
Counts
4 → 84
Calls

8 calls:

16.0ms
(/.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b) (*.f64 a 2))
13.0ms
(-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
7.0ms
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

series860.0ms (0.8%)

Counts
4 → 72
Calls

4 calls:

280.0ms
(/.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b) (*.f64 a 2))
211.0ms
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
197.0ms
(-.f64 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
172.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
Compiler

Compiled 2417 to 1904 computations (21.2% saved)

simplify93.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
050473191

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
0.1b
(+.f64 (neg.f64 b) (*.f64 (neg.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.3b
(/.f64 (*.f64 (*.f64 4 a) c) (+.f64 (neg.f64 b) (*.f64 (neg.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))))
0.3b
(*.f64 (neg.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.6b
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
0.6b
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

rewrite45.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64_782
15×add-exp-log_binary64_798 add-cbrt-cube_binary64_796
14×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795
10×associate-*l*_binary64_701 cbrt-prod_binary64_791
9×associate-*r*_binary64_700
8×sqrt-prod_binary64_776
6×cbrt-div_binary64_792 pow1_binary64_821
4×prod-exp_binary64_809 add-log-exp_binary64_799 cbrt-unprod_binary64_793
3×unswap-sqr_binary64_728 cbrt-undiv_binary64_794 distribute-lft-neg-in_binary64_717 associate-/r*_binary64_704 distribute-rgt-neg-in_binary64_718 div-exp_binary64_811 times-frac_binary64_766 flip--_binary64_735 flip3--_binary64_764
2×pow1/3_binary64_842 associate-/r/_binary64_706 sqrt-div_binary64_777 associate-*r/_binary64_702
1×neg-mul-1_binary64_756 frac-2neg_binary64_771 flip3-+_binary64_763 div-inv_binary64_757 flip-+_binary64_734 distribute-lft-neg-out_binary64_719 associate-/l*_binary64_705 clear-num_binary64_759 pow-prod-down_binary64_831 *-commutative_binary64_691
Counts
4 → 87
Calls

8 calls:

12.0ms
(*.f64 (neg.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
10.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (+.f64 (neg.f64 b) (*.f64 (neg.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))))
5.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
5.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
0.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))

series2.7s (2.5%)

Counts
4 → 75
Calls

4 calls:

1.6s
(/.f64 (*.f64 (*.f64 4 a) c) (+.f64 (neg.f64 b) (*.f64 (neg.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))))
478.0ms
(*.f64 (neg.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
316.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
311.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
Compiler

Compiled 6339 to 5056 computations (20.2% saved)

simplify203.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (130.0ms)

IterNodesCost
049288216
149288216

localize36.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
0.5b
(*.f64 (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
0.5b
(cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.5b
(cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.5b
(cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

rewrite92.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
69×cbrt-prod_binary64_791
63×*-un-lft-identity_binary64_760
59×add-sqr-sqrt_binary64_782
22×distribute-lft-out--_binary64_712
18×difference-of-squares_binary64_729 swap-sqr_binary64_727 cbrt-div_binary64_792
15×add-cube-cbrt_binary64_795
11×distribute-rgt-neg-in_binary64_718 pow1_binary64_821
10×associate-*r*_binary64_700 associate-*l*_binary64_701
9×pow1/3_binary64_842 sqrt-prod_binary64_776 flip--_binary64_735 flip3--_binary64_764
6×add-exp-log_binary64_798
4×unswap-sqr_binary64_728 add-log-exp_binary64_799 add-cbrt-cube_binary64_796 frac-times_binary64_770
2×associate-*l/_binary64_703 pow-sqr_binary64_733 associate-*r/_binary64_702 pow-prod-up_binary64_830 pow-prod-down_binary64_831
1×pow2_binary64_841 prod-exp_binary64_809 pow-plus_binary64_823 cbrt-unprod_binary64_793 *-commutative_binary64_691
Counts
4 → 119
Calls

8 calls:

30.0ms
(*.f64 (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
10.0ms
(cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
10.0ms
(cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
10.0ms
(cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

series2.5s (2.3%)

Counts
4 → 72
Calls

4 calls:

955.0ms
(*.f64 (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
532.0ms
(cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
519.0ms
(cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
514.0ms
(cbrt.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
Compiler

Compiled 7442 to 5695 computations (23.5% saved)

simplify122.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049788057
149788057

prune44.3s (40.8%)

Pruning

652 alts after pruning (642 fresh and 10 done)

PrunedKeptTotal
New7473531100
Fresh65289354
Picked000
Done31013
Total8156521467
Error
0b
Counts
1467 → 652
Compiler

Compiled 27364 to 14905 computations (45.5% saved)

simplify1.0s (0.9%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0531170893

regimes16.3s (15%)

Compiler

Compiled 174601 to 121728 computations (30.3% saved)

bsearch0.0ms (0%)

regimes339.0ms (0.3%)

Compiler

Compiled 2730 to 2337 computations (14.4% saved)

bsearch0.0ms (0%)

regimes183.0ms (0.2%)

Compiler

Compiled 1209 to 1140 computations (5.7% saved)

bsearch0.0ms (0%)

regimes175.0ms (0.2%)

Compiler

Compiled 1107 to 1059 computations (4.3% saved)

bsearch0.0ms (0%)

regimes26.0ms (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch0.0ms (0%)

regimes21.0ms (0%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch5.0ms (0%)

Compiler

Compiled 57 to 53 computations (7% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
012484
112484

end0.0ms (0%)

sample2.3s (2.1%)

Algorithm
1×intervals
Results
394.0ms3816×body256valid
272.0ms8837×pre128true
216.0ms1448×body512valid
139.0ms2736×body128valid
40.0ms837×body128nan
Compiler

Compiled 43766 to 30536 computations (30.2% saved)

Profiling

Loading profile data...