Details

Time bar (total: 9.2s)

analyze550.0ms (6%)

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%68.6%18.9%6
18.7%62.4%18.9%7
18.7%59.3%22%8
28.1%39%32.9%9
32.8%34.3%32.9%10
32.8%32%35.3%11
38.2%20.7%41.1%12
41%17.9%41.1%13
41%16.6%42.5%14
Compiler

Compiled 41 to 24 computations (41.5% saved)

sample60.0ms (0.7%)

Algorithm
1×intervals
Results
42.0ms247×body256valid
3.0ms38×body128nan
3.0ms9×body128valid
Compiler

Compiled 84 to 50 computations (40.5% saved)

simplify230.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
637×associate-/l*_binary64
634×div-sub_binary64
582×unsub-neg_binary64
519×sub-neg_binary64
502×times-frac_binary64
Counts
1 → 1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02052
15350
213950
338148
473548
5118948
6140948
7189348
8185348
9223548
10288948
11345748
12363948
13374948
14379748
15382148
16387148
17485848
18479948
19498048
20483448

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
39.1b
Counts
2 → 2
Alt Table
StatusErrorProgram
▶39.1b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
39.1b
(+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))))
Compiler

Compiled 182 to 100 computations (45.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.6b
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
9.8b
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
32.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
32.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite161.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Error
34.4b
Rules
14×add-sqr-sqrt_binary64
11×cbrt-prod_binary64
10×*-un-lft-identity_binary64
9×sqrt-prod_binary64
8×add-cube-cbrt_binary64
Counts
4 → 61
Calls

4 calls:

8.0ms
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
8.0ms
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 2348 to 702 computations (70.1% saved)

series280.0ms (3%)

Error
33.9b
Counts
4 → 35
Calls

4 calls:

90.0ms
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
87.0ms
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
24.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
22.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 3702 to 2573 computations (30.5% saved)

simplify113.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
885×times-frac_binary64
254×exp-sum_binary64
191×sub-neg_binary64
175×associate-*r*_binary64
167×associate-*l*_binary64
Counts
96 → 56
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02112141
14372059
29112015
326021933
448841933
549181933

prune120.0ms (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New421456
Fresh011
Picked101
Done000
Total431558
Error
34.3b
Counts
58 → 15
Alt Table
StatusErrorProgram
51.5b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 (*.f64 -1 (*.f64 (*.f64 h h) (/.f64 -1/2 (*.f64 g a)))))))
39.1b
(+.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
49.4b
(+.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 (/.f64 2 a) (/.f64 -1 g)))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
50.4b
(+.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (*.f64 (*.f64 h h) (/.f64 -1/2 (*.f64 g a))))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
51.3b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (neg.f64 g)) a) -1/2)))
50.8b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (*.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h)))) a) -1/2)))
54.2b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
45.1b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (sqrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a)))) (sqrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
45.4b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (exp.f64 (log.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
39.1b
(+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))))
43.5b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) a) -1/2)))
36.9b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (/.f64 (cbrt.f64 (*.f64 -1/2 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 a)))
▶36.5b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
39.1b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))
39.2b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a)))) (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))) (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
Compiler

Compiled 2756 to 1262 computations (54.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b
(-.f64 (*.f64 g g) (*.f64 h h))
8.6b
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
32.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
32.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite216.0ms (2.3%)

Algorithm
1×rewrite-expression-head
Error
34.0b
Rules
8×add-sqr-sqrt_binary64 sqrt-prod_binary64
6×pow1_binary64 add-log-exp_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
4×add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64
3×flip3--_binary64 flip--_binary64 difference-of-squares_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
Counts
4 → 55
Calls

4 calls:

8.0ms
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(-.f64 (*.f64 g g) (*.f64 h h))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 2167 to 675 computations (68.9% saved)

series246.0ms (2.7%)

Error
32.7b
Counts
4 → 37
Calls

4 calls:

88.0ms
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
31.0ms
(-.f64 (*.f64 g g) (*.f64 h h))
23.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
22.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 3188 to 2186 computations (31.4% saved)

simplify115.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
191×unswap-sqr_binary64
189×exp-prod_binary64
184×exp-sum_binary64
177×associate-*l*_binary64
172×associate-+r+_binary64
Counts
92 → 59
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01441492
13031375
26691363
320341319
447131318
549721318
649291318

prune192.0ms (2.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New54559
Fresh21214
Picked101
Done000
Total571774
Error
32.5b
Counts
74 → 17
Alt Table
StatusErrorProgram
51.5b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 (*.f64 -1 (*.f64 (*.f64 h h) (/.f64 -1/2 (*.f64 g a)))))))
41.0b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
48.7b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (neg.f64 g)) a) -1/2)))
44.6b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (neg.f64 g) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
39.1b
(+.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
48.2b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) 3)) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
50.4b
(+.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (*.f64 (*.f64 h h) (/.f64 -1/2 (*.f64 g a))))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
51.3b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (neg.f64 g)) a) -1/2)))
50.8b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (*.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h)))) a) -1/2)))
54.2b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
45.1b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (sqrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a)))) (sqrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
45.4b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (exp.f64 (log.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
39.1b
(+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))))
43.5b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) a) -1/2)))
▶34.6b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)) (cbrt.f64 (/.f64 1/2 a))) (/.f64 (cbrt.f64 (*.f64 -1/2 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 a)))
39.1b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))
39.2b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a)))) (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))) (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
Compiler

Compiled 2878 to 1348 computations (53.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b
(-.f64 (*.f64 g g) (*.f64 h h))
3.2b
(-.f64 (*.f64 g g) (*.f64 h h))
32.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
32.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite214.0ms (2.3%)

Algorithm
1×rewrite-expression-head
Error
32.5b
Rules
8×add-log-exp_binary64 add-sqr-sqrt_binary64 sqrt-prod_binary64
6×pow1_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
4×add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 sqrt-div_binary64 flip--_binary64 difference-of-squares_binary64
2×pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 diff-log_binary64 sub-neg_binary64 cancel-sign-sub-inv_binary64
Counts
4 → 58
Calls

4 calls:

4.0ms
(-.f64 (*.f64 g g) (*.f64 h h))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(-.f64 (*.f64 g g) (*.f64 h h))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 2325 to 728 computations (68.7% saved)

series211.0ms (2.3%)

Error
32.5b
Counts
4 → 44
Calls

4 calls:

33.0ms
(-.f64 (*.f64 g g) (*.f64 h h))
32.0ms
(-.f64 (*.f64 g g) (*.f64 h h))
30.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
28.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 3219 to 2172 computations (32.5% saved)

simplify126.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
611×associate-/l*_binary64
329×associate-/r*_binary64
266×associate-*l/_binary64
246×unswap-sqr_binary64
213×associate-*r/_binary64
Counts
102 → 66
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0751356
11631248
24371248
316561248
446861248
549801248
649961248
749421248

prune188.0ms (2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New63366
Fresh11516
Picked101
Done000
Total651883
Error
32.5b
Counts
83 → 18
Alt Table
StatusErrorProgram
51.5b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 (*.f64 -1 (*.f64 (*.f64 h h) (/.f64 -1/2 (*.f64 g a)))))))
41.0b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
48.7b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (neg.f64 g)) a) -1/2)))
44.6b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (neg.f64 g) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
39.1b
(+.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
52.3b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g)) (cbrt.f64 (/.f64 1/2 a))) (/.f64 (cbrt.f64 (*.f64 -1/2 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 a)))
47.0b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)) (cbrt.f64 (/.f64 1/2 a))) (/.f64 (cbrt.f64 (*.f64 -1/2 (+.f64 g (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) 3))))) (cbrt.f64 a)))
48.2b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) 3)) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
50.4b
(+.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (*.f64 (*.f64 h h) (/.f64 -1/2 (*.f64 g a))))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
47.6b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (-.f64 g (*.f64 1/2 (/.f64 (*.f64 h h) g))) g)) (cbrt.f64 (/.f64 1/2 a))) (/.f64 (cbrt.f64 (*.f64 -1/2 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 a)))
51.3b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (neg.f64 g)) a) -1/2)))
50.8b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (*.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h)))) a) -1/2)))
45.1b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (sqrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a)))) (sqrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
45.4b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (exp.f64 (log.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
39.1b
(+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))))
43.5b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) a) -1/2)))
▶39.1b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))
39.2b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a)))) (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))) (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
Compiler

Compiled 2948 to 1435 computations (51.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.5b
(cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))
9.8b
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
32.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
32.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite312.0ms (3.4%)

Algorithm
1×rewrite-expression-head
Error
32.4b
Rules
26×cbrt-prod_binary64
24×*-un-lft-identity_binary64
22×add-sqr-sqrt_binary64
18×times-frac_binary64
16×add-cube-cbrt_binary64
Counts
4 → 76
Calls

4 calls:

8.0ms
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
7.0ms
(cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 2998 to 859 computations (71.3% saved)

series336.0ms (3.6%)

Error
32.5b
Counts
4 → 35
Calls

4 calls:

94.0ms
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
73.0ms
(cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))
25.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
22.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 3762 to 2618 computations (30.4% saved)

simplify132.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
955×times-frac_binary64
256×exp-sum_binary64
188×sub-neg_binary64
160×associate-*r*_binary64
154×associate-*l*_binary64
Counts
111 → 57
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02402739
14682657
29542610
326092508
449282508
550262508

prune189.0ms (2.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New54357
Fresh11617
Picked101
Done000
Total561975
Error
32.5b
Counts
75 → 19
Alt Table
StatusErrorProgram
51.5b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 (*.f64 -1 (*.f64 (*.f64 h h) (/.f64 -1/2 (*.f64 g a)))))))
41.0b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) (sqrt.f64 (cbrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
48.7b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (neg.f64 g)) a) -1/2)))
44.6b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (neg.f64 g) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
39.1b
(+.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
52.3b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h))) g)) (cbrt.f64 (/.f64 1/2 a))) (/.f64 (cbrt.f64 (*.f64 -1/2 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 a)))
37.6b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (cbrt.f64 -1/2) (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (/.f64 (sqrt.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))) a)))))
47.0b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g)) (cbrt.f64 (/.f64 1/2 a))) (/.f64 (cbrt.f64 (*.f64 -1/2 (+.f64 g (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) 3))))) (cbrt.f64 a)))
48.2b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) 3)) g)) (cbrt.f64 (/.f64 1/2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
50.4b
(+.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (*.f64 (*.f64 h h) (/.f64 -1/2 (*.f64 g a))))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2)))
47.6b
(+.f64 (*.f64 (cbrt.f64 (-.f64 (-.f64 g (*.f64 1/2 (/.f64 (*.f64 h h) g))) g)) (cbrt.f64 (/.f64 1/2 a))) (/.f64 (cbrt.f64 (*.f64 -1/2 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 a)))
51.3b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (neg.f64 g)) a) -1/2)))
37.1b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (cbrt.f64 -1/2) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))) (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))) (cbrt.f64 (/.f64 (cbrt.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))) a)))))
50.8b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (cbrt.f64 (*.f64 (/.f64 (+.f64 g (*.f64 (sqrt.f64 (+.f64 h g)) (sqrt.f64 (-.f64 g h)))) a) -1/2)))
50.4b
(+.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 (*.f64 (*.f64 h h) (/.f64 -1/2 (*.f64 g a))))) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))
45.1b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (sqrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a)))) (sqrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
45.4b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (exp.f64 (log.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
39.1b
(+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))))
39.2b
(+.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a))) (*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a)))) (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))) (cbrt.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a))))))
Compiler

Compiled 2300 to 1026 computations (55.4% saved)

regimes2.7s (29.6%)

Accuracy

Total 1.0b remaining (3.2%)

Threshold costs 0b (0%)

Compiler

Compiled 57435 to 31606 computations (45% saved)

bsearch84.0ms (0.9%)

Steps
ItersRangePoint
9
2.453119366447889e-170
7.856718127830462e-164
7.709860458119759e-164
Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
10×+-commutative_binary64
9×*-commutative_binary64
7×sub-neg_binary64
4×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039117
157117
267117
374117
479117
580117
680117

end2.0ms (0%)

Compiler

Compiled 77 to 40 computations (48.1% saved)

sample2.3s (25.2%)

Algorithm
1×intervals
Results
1.3s7569×body256valid
113.0ms1288×body128nan
40.0ms431×body128valid
Compiler

Compiled 880 to 492 computations (44.1% saved)

Profiling

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