Details

Time bar (total: 3.1s)

analyze4.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0%14
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.3s (42.6%)

Results
496.0ms2049×body512valid
458.0ms4751×body128valid
188.0ms1033×body256valid
145.0ms423×body1024valid
Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify11.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
14×cancel-sign-sub-inv_binary64
13×sub-neg_binary64
10×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0816
11616
22116
32916
43716
55516
68016
79716
811416
912416
1012816
1113016
1211616

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
15.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶15.2b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
Compiler

Compiled 47 to 39 computations (17% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (-.f64 x 1))
✓0.0b
(/.f64 1 (+.f64 x 1))
✓4.5b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series8.0ms (0.3%)

Counts
3 → 36
Calls

3 calls:

3.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
3.0ms
(/.f64 1 (-.f64 x 1))
2.0ms
(/.f64 1 (+.f64 x 1))

rewrite108.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
867×prod-diff_binary64
441×fma-def_binary64
272×fma-neg_binary64
197×egg-rr
162×expm1-udef_binary64
Counts
3 → 197
Calls

3 calls:

104.0ms
(/.f64 1 (-.f64 x 1))
104.0ms
(/.f64 1 (+.f64 x 1))
104.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0830
119230
2253730
3491030
4493830

simplify61.0ms (2%)

Algorithm
1×egg-herbie
Rules
748×unswap-sqr_binary64
435×associate-*l*_binary64
355×fma-neg_binary64
344×associate-/r*_binary64
301×associate-*r*_binary64
Counts
233 → 238
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
065575
1197543
2573540
31610537
44128537
55539537

prune189.0ms (6.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New2353238
Fresh000
Picked101
Done000
Total2363239
Error
0.4b
Counts
239 → 3
Alt Table
StatusErrorProgram
14.5b
(/.f64 (/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x)) (-.f64 x 1))
33.6b
(/.f64 -2 (pow.f64 x 2))
▶14.5b
(/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (fma.f64 x x -1))
Compiler

Compiled 6055 to 4929 computations (18.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (fma.f64 x x -1))
✓3.9b
(-.f64 (-.f64 x 1) (+.f64 1 x))

series5.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

4.0ms
(/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (fma.f64 x x -1))
1.0ms
(-.f64 (-.f64 x 1) (+.f64 1 x))

rewrite74.0ms (2.4%)

Algorithm
1×batch-egg-rewrite
Rules
480×fma-def_binary64
326×fma-neg_binary64
206×egg-rr
202×log-div_binary64
179×log1p-udef_binary64
Counts
2 → 206
Calls

2 calls:

71.0ms
(/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (fma.f64 x x -1))
71.0ms
(-.f64 (-.f64 x 1) (+.f64 1 x))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0927
120921
2291121
3505021

simplify70.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
675×fma-def_binary64
414×unswap-sqr_binary64
344×distribute-neg-frac_binary64
327×div-sub_binary64
243×associate-*l*_binary64
Counts
230 → 222
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
038239
1116221
2328218
3957215
42990212
54474212
64946212

prune236.0ms (7.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New2202222
Fresh112
Picked101
Done000
Total2223225
Error
0.4b
Counts
225 → 3
Alt Table
StatusErrorProgram
14.5b
(/.f64 (/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x)) (-.f64 x 1))
47.2b
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x -1))) (/.f64 (-.f64 x (+.f64 2 x)) (sqrt.f64 (fma.f64 x x -1))))
▶0.4b
(/.f64 -2 (fma.f64 x x -1))
Compiler

Compiled 4498 to 3149 computations (30% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 -2 (fma.f64 x x -1))

series3.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

3.0ms
(/.f64 -2 (fma.f64 x x -1))

rewrite72.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
502×log1p-expm1-u_binary64
502×expm1-log1p-u_binary64
260×unpow-prod-down_binary64
229×log-prod_binary64
145×pow2_binary64
Counts
1 → 38
Calls

1 calls:

71.0ms
(/.f64 -2 (fma.f64 x x -1))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11228
213208
349418
450558

simplify61.0ms (2%)

Algorithm
1×egg-herbie
Rules
675×fma-def_binary64
414×unswap-sqr_binary64
344×distribute-neg-frac_binary64
327×div-sub_binary64
243×associate-*l*_binary64
Counts
50 → 53
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
038227
1116209
2328206
3957203
42990200
54474200
64946200

prune42.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New49453
Fresh112
Picked011
Done000
Total50656
Error
0.3b
Counts
56 → 6
Alt Table
StatusErrorProgram
9.5b
(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))
1.4b
(*.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) (pow.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) 2))
1.7b
(pow.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) 3)
▶0.5b
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -1) -2)) 2) -1) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))
14.5b
(/.f64 (/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x)) (-.f64 x 1))
✓0.4b
(/.f64 -2 (fma.f64 x x -1))
Compiler

Compiled 839 to 659 computations (21.5% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.7b
(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -1) -2)) 2)
✓1.1b
(pow.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -1) -2)) 2) -1)
✓13.7b
(cbrt.f64 (/.f64 (fma.f64 x x -1) -2))
✓13.8b
(cbrt.f64 (/.f64 -2 (fma.f64 x x -1)))

series256.0ms (8.3%)

Counts
4 → 48
Calls

4 calls:

117.0ms
(pow.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -1) -2)) 2) -1)
78.0ms
(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -1) -2)) 2)
31.0ms
(cbrt.f64 (/.f64 (fma.f64 x x -1) -2))
29.0ms
(cbrt.f64 (/.f64 -2 (fma.f64 x x -1)))

rewrite60.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
890×log1p-expm1-u_binary64
890×expm1-log1p-u_binary64
118×egg-rr
109×add-sqr-sqrt_binary64
103×add-cbrt-cube_binary64
Counts
4 → 118
Calls

4 calls:

58.0ms
(pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -1) -2)) 2)
58.0ms
(pow.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -1) -2)) 2) -1)
58.0ms
(cbrt.f64 (/.f64 (fma.f64 x x -1) -2))
58.0ms
(cbrt.f64 (/.f64 -2 (fma.f64 x x -1)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01246
124846
2241746
3543746

simplify73.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
933×fma-neg_binary64
425×times-frac_binary64
412×*-commutative_binary64
313×cancel-sign-sub-inv_binary64
216×sub-neg_binary64
Counts
166 → 180
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01591940
14871870
215321694
334951690
450681690

prune206.0ms (6.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1773180
Fresh134
Picked011
Done011
Total1788186
Error
0.3b
Counts
186 → 8
Alt Table
StatusErrorProgram
1.7b
(*.f64 (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1)))) 2) -1) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))
0.6b
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -1) -2)) 2) -1) (*.f64 (cbrt.f64 -2) (/.f64 1 (cbrt.f64 (fma.f64 x x -1)))))
9.5b
(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))
1.7b
(pow.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) 3)
✓0.5b
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -1) -2)) 2) -1) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))
33.7b
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x x -1) -2)) 2) -1) (*.f64 (cbrt.f64 -2) (cbrt.f64 (/.f64 1 (*.f64 x x)))))
14.5b
(/.f64 (/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x)) (-.f64 x 1))
✓0.4b
(/.f64 -2 (fma.f64 x x -1))
Compiler

Compiled 5188 to 4306 computations (17% saved)

regimes87.0ms (2.8%)

Accuracy

Total 0.0b remaining (12.2%)

Threshold costs 0.0b (12.2%)

Counts
44 → 1
Compiler

Compiled 1676 to 1346 computations (19.7% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
168

end118.0ms (3.8%)

Compiler

Compiled 144 to 114 computations (20.8% saved)

Profiling

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