Details

Time bar (total: 6.7s)

analyze704.0ms (10.5%)

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
12.5%87.4%0.1%6
20.3%73.3%6.4%7
27.3%66.3%6.4%8
38.2%53%8.7%9
46%40.6%13.4%10
49.9%35.1%15%11
54.9%26.9%18.1%12
57.4%22%20.6%13
59.7%18%22.4%14
Compiler

Compiled 39 to 27 computations (30.8% saved)

sample40.0ms (0.6%)

Algorithm
1×intervals
Results
25.0ms256×body128valid
1.0ms15×body128nan
1.0ms11×body128invalid
Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify258.0ms (3.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (84.0ms)

IterNodesCost
0122454
1122454

prune18.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 20.3b

Counts
2 → 1
Compiler

Compiled 148 to 102 computations (31.1% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
1.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
24.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
24.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite36.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
16×*-un-lft-identity_binary64
14×add-sqr-sqrt_binary64
12×add-log-exp_binary64
10×sqrt-prod_binary64
8×add-cube-cbrt_binary64
6×pow1_binary64 cancel-sign-sub-inv_binary64
4×add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64
3×flip3--_binary64 flip--_binary64
2×pow1/2_binary64 diff-log_binary64 distribute-lft-out_binary64 neg-sub0_binary64 sqrt-pow1_binary64 distribute-rgt-neg-in_binary64 rem-sqrt-square_binary64 neg-log_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 sum-log_binary64
1×flip3-+_binary64 sub-neg_binary64 associate--l-_binary64 associate-+l-_binary64 +-commutative_binary64 flip-+_binary64
Counts
4 → 68
Calls

4 calls:

11.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
10.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
7.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series521.0ms (7.8%)

Counts
4 → 12
Calls

4 calls:

144.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
140.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
122.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
114.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

simplify104.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
048601694
148601694

prune374.0ms (5.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New74680
Fresh000
Picked011
Done000
Total74781

Merged error: 7.4b

Counts
81 → 7
Compiler

Compiled 8787 to 5620 computations (36% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

5.1b
(-.f64 (neg.f64 b) (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
24.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
25.3b
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
25.3b
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite23.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
8×add-log-exp_binary64 add-sqr-sqrt_binary64
7×*-un-lft-identity_binary64 add-cube-cbrt_binary64
6×cbrt-prod_binary64
5×pow1_binary64
4×cbrt-div_binary64 flip3--_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip--_binary64
3×sqrt-prod_binary64
2×diff-log_binary64 pow1/3_binary64 sqrt-div_binary64
1×sub-neg_binary64 pow1/2_binary64 associate--l-_binary64 neg-sub0_binary64 cancel-sign-sub-inv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 neg-log_binary64
Counts
4 → 55
Calls

4 calls:

7.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(-.f64 (neg.f64 b) (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
5.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series708.0ms (10.6%)

Counts
4 → 12
Calls

4 calls:

235.0ms
(-.f64 (neg.f64 b) (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
179.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
177.0ms
(cbrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
116.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

simplify76.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049451854
149451854

prune179.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New67067
Fresh055
Picked011
Done011
Total67774

Merged error: 7.4b

Counts
74 → 7
Compiler

Compiled 4436 to 2657 computations (40.1% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
4.3b
(/.f64 (*.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)) (*.f64 2 a))
5.4b
(/.f64 (*.f64 a c) b)
24.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite39.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
21×add-exp-log_binary64 add-cbrt-cube_binary64
14×add-sqr-sqrt_binary64
13×*-un-lft-identity_binary64
9×add-cube-cbrt_binary64
8×add-log-exp_binary64
7×sqrt-prod_binary64
6×cbrt-undiv_binary64 cancel-sign-sub-inv_binary64 div-exp_binary64
5×pow1_binary64 cbrt-unprod_binary64 prod-exp_binary64
4×associate-/r*_binary64 times-frac_binary64
3×flip3--_binary64 flip--_binary64
2×associate-/l/_binary64 diff-log_binary64 associate-*r/_binary64 clear-num_binary64 frac-2neg_binary64 difference-of-squares_binary64 associate-/l*_binary64 distribute-lft-out--_binary64 div-inv_binary64 sqrt-div_binary64
1×sub-neg_binary64 pow1/2_binary64 associate--l-_binary64 neg-sub0_binary64 sqrt-pow1_binary64 distribute-rgt-neg-in_binary64 rem-sqrt-square_binary64 neg-log_binary64
Counts
4 → 82
Calls

4 calls:

16.0ms
(/.f64 (*.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)) (*.f64 2 a))
11.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(/.f64 (*.f64 a c) b)
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series391.0ms (5.8%)

Counts
4 → 12
Calls

4 calls:

129.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
128.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
99.0ms
(/.f64 (*.f64 2 (-.f64 (/.f64 (*.f64 a c) b) b)) (*.f64 2 a))
34.0ms
(/.f64 (*.f64 a c) b)

simplify80.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049231615
149231615

prune386.0ms (5.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New89594
Fresh134
Picked101
Done022
Total9110101

Merged error: 7.0b

Counts
101 → 10
Compiler

Compiled 9278 to 5792 computations (37.6% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.4b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
1.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
24.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite38.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64
21×*-un-lft-identity_binary64
10×add-log-exp_binary64
9×add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-prod_binary64
7×associate-/r*_binary64 cancel-sign-sub-inv_binary64 times-frac_binary64
6×difference-of-squares_binary64 distribute-lft-out--_binary64
5×pow1_binary64
4×flip3--_binary64 flip--_binary64
3×diff-log_binary64 distribute-rgt-neg-in_binary64
2×sub-neg_binary64 cbrt-undiv_binary64 associate-/r/_binary64 div-exp_binary64 sqrt-div_binary64
1×pow1/2_binary64 associate--l-_binary64 cbrt-unprod_binary64 neg-sub0_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 neg-log_binary64 prod-exp_binary64 frac-2neg_binary64 associate-/l*_binary64 div-inv_binary64
Counts
4 → 81
Calls

4 calls:

14.0ms
(/.f64 (*.f64 2 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
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

series665.0ms (9.9%)

Counts
4 → 12
Calls

4 calls:

349.0ms
(/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
131.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
122.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
63.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify63.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
055712205

prune339.0ms (5.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89493
Fresh347
Picked101
Done112
Total949103

Merged error: 6.8b

Counts
103 → 9
Compiler

Compiled 8179 to 5001 computations (38.9% saved)

regimes211.0ms (3.1%)

Compiler

Compiled 1266 to 898 computations (29.1% saved)

bsearch3.0ms (0%)

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0129437
1129437

end0.0ms (0%)

sample1.3s (20.1%)

Algorithm
1×intervals
Results
676.0ms8000×body128valid
54.0ms645×body128nan
30.0ms375×body128invalid
Compiler

Compiled 625 to 404 computations (35.4% saved)

Profiling

Loading profile data...