Details

Time bar (total: 7.0s)

analyze898.0ms (12.7%)

Algorithm
1×search
2×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04877216
14877216
033
133
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)

sample39.0ms (0.5%)

Algorithm
1×intervals
Results
23.0ms256×body128valid
2.0ms25×body128nan
1.0ms7×body128invalid
Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify353.0ms (5%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (346.0ms)

IterNodesCost
0297754
1297754

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
21.9b
Counts
2 → 1
Compiler

Compiled 72 to 50 computations (30.6% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.4b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
1.8b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))) b)
24.4b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
24.4b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite26.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64
9×*-un-lft-identity_binary64
8×add-log-exp_binary64
7×add-cube-cbrt_binary64 sqrt-prod_binary64
6×pow1_binary64
4×flip3--_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 cancel-sign-sub-inv_binary64 flip--_binary64 sqrt-div_binary64
2×sub-neg_binary64 pow1/2_binary64 diff-log_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 difference-of-squares_binary64
1×distribute-lft-out--_binary64
Counts
4 → 59
Calls

4 calls:

8.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))) b)
6.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

series219.0ms (3.1%)

Counts
4 → 12
Calls

4 calls:

69.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
62.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))) b)
55.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
33.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))

simplify68.0ms (1%)

Algorithm
1×egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049471395
149471395

prune152.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New64771
Fresh000
Picked101
Done000
Total65772
Error
8.2b
Counts
72 → 7
Compiler

Compiled 3305 to 1996 computations (39.6% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.4b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
2.4b
(/.f64 (-.f64 (-.f64 (*.f64 2 (/.f64 (*.f64 c a) b)) b) b) (*.f64 2 a))
6.5b
(/.f64 (*.f64 c a) b)
24.4b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite31.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
14×add-exp-log_binary64 add-cbrt-cube_binary64 add-sqr-sqrt_binary64
13×*-un-lft-identity_binary64
9×add-cube-cbrt_binary64
8×times-frac_binary64
6×add-log-exp_binary64 associate-/l*_binary64
5×pow1_binary64
4×associate-/r*_binary64 cbrt-undiv_binary64 div-exp_binary64
3×flip3--_binary64 flip--_binary64 sqrt-prod_binary64
2×associate-/l/_binary64 cbrt-unprod_binary64 clear-num_binary64 prod-exp_binary64 frac-2neg_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 div-inv_binary64 sqrt-div_binary64
1×sub-neg_binary64 pow1/2_binary64 diff-log_binary64 cancel-sign-sub-inv_binary64 sqrt-pow1_binary64 div-sub_binary64 rem-sqrt-square_binary64
Counts
4 → 76
Calls

4 calls:

13.0ms
(/.f64 (-.f64 (-.f64 (*.f64 2 (/.f64 (*.f64 c a) b)) b) b) (*.f64 2 a))
6.0ms
(/.f64 (*.f64 c a) b)
4.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

series173.0ms (2.5%)

Counts
4 → 12
Calls

4 calls:

68.0ms
(/.f64 (-.f64 (-.f64 (*.f64 2 (/.f64 (*.f64 c a) b)) b) b) (*.f64 2 a))
56.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
31.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
17.0ms
(/.f64 (*.f64 c a) b)

simplify58.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049471535
149471535

prune158.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New83588
Fresh156
Picked101
Done000
Total851095
Error
6.9b
Counts
95 → 10
Compiler

Compiled 3939 to 2187 computations (44.5% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
1.1b
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
1.4b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
24.4b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite24.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
24×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
14×add-cube-cbrt_binary64
12×times-frac_binary64
8×add-log-exp_binary64
6×add-exp-log_binary64 add-cbrt-cube_binary64
5×pow1_binary64 distribute-lft-out_binary64
4×associate-/r*_binary64
3×associate-/l*_binary64 sqrt-prod_binary64
2×flip3-+_binary64 flip3--_binary64 associate-/r/_binary64 flip--_binary64 flip-+_binary64 sqrt-div_binary64
1×sub-neg_binary64 pow1/2_binary64 diff-log_binary64 cbrt-undiv_binary64 cancel-sign-sub-inv_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 +-commutative_binary64 sum-log_binary64
Counts
4 → 72
Calls

4 calls:

8.0ms
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
6.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

series313.0ms (4.4%)

Counts
4 → 12
Calls

4 calls:

163.0ms
(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
61.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
58.0ms
(+.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
32.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))

simplify80.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
048971972
148971972

prune147.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New76884
Fresh459
Picked101
Done000
Total811394
Error
6.6b
Counts
94 → 13
Compiler

Compiled 3417 to 1750 computations (48.8% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.4b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
2.4b
(/.f64 (-.f64 (-.f64 (*.f64 2 (*.f64 (/.f64 c (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 a (cbrt.f64 b)))) b) b) (*.f64 2 a))
3.6b
(*.f64 (/.f64 c (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 a (cbrt.f64 b)))
24.4b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite50.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
43×add-sqr-sqrt_binary64
33×times-frac_binary64
30×add-exp-log_binary64
26×*-un-lft-identity_binary64
23×add-cbrt-cube_binary64
22×associate-*r*_binary64 add-cube-cbrt_binary64
11×cbrt-prod_binary64
9×cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64
7×pow1_binary64 associate-*l*_binary64
6×add-log-exp_binary64 unswap-sqr_binary64
5×associate-/l*_binary64
3×flip3--_binary64 div-inv_binary64 flip--_binary64 sqrt-prod_binary64
2×associate-/l/_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 sqrt-div_binary64
1×pow-prod-down_binary64 associate-/r*_binary64 sub-neg_binary64 pow1/2_binary64 diff-log_binary64 associate-*r/_binary64 cancel-sign-sub-inv_binary64 sqrt-pow1_binary64 div-sub_binary64 rem-sqrt-square_binary64 clear-num_binary64 frac-2neg_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 114
Calls

4 calls:

21.0ms
(/.f64 (-.f64 (-.f64 (*.f64 2 (*.f64 (/.f64 c (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 a (cbrt.f64 b)))) b) b) (*.f64 2 a))
16.0ms
(*.f64 (/.f64 c (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 a (cbrt.f64 b)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
4.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))

series270.0ms (3.8%)

Counts
4 → 12
Calls

4 calls:

106.0ms
(/.f64 (-.f64 (-.f64 (*.f64 2 (*.f64 (/.f64 c (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 a (cbrt.f64 b)))) b) b) (*.f64 2 a))
69.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
61.0ms
(*.f64 (/.f64 c (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 a (cbrt.f64 b)))
34.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))

simplify95.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
049392429
149392429

prune230.0ms (3.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New1197126
Fresh11112
Picked101
Done000
Total12118139
Error
5.6b
Counts
139 → 18
Compiler

Compiled 5730 to 2766 computations (51.7% saved)

regimes891.0ms (12.6%)

Accuracy

Total 1.5b remaining (20.2%)

Threshold costs 0b (0%)

Compiler

Compiled 9270 to 6258 computations (32.5% saved)

bsearch7.0ms (0.1%)

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0196396
1196396

end0.0ms (0%)

sample2.6s (37.5%)

Algorithm
1×intervals
Results
709.0ms8000×body128valid
52.0ms619×body128nan
34.0ms376×body128invalid
Compiler

Compiled 2597 to 1737 computations (33.1% saved)

Profiling

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