Details

Time bar (total: 8.4s)

analyze573.0ms (6.9%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
25%74.9%0.2%7
25%74.9%0.2%8
34.3%65.5%0.2%9
39%60.8%0.2%10
48.3%51.5%0.2%11
53.7%46.1%0.2%12
63.1%36.7%0.2%13
64%35.6%0.4%14
Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (13.1%)

Symmetry

(sort z t)

Results
879.0ms8256×body128valid
58.0ms349×body128invalid
Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify14.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
100×fma-def_binary64
56×fma-neg_binary64
28×cancel-sign-sub-inv_binary64
18×sub-neg_binary64
13×distribute-rgt-neg-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11410
22410
34110
45510
58510
611910
714810
818410
920210
1021910
1122510
1220210

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
3.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶3.2b
(/.f64 x (-.f64 y (*.f64 z t)))
Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 y (*.f64 z t))
✓3.2b
(/.f64 x (-.f64 y (*.f64 z t)))

series46.0ms (0.5%)

Counts
2 → 84
Calls

2 calls:

41.0ms
(/.f64 x (-.f64 y (*.f64 z t)))
5.0ms
(-.f64 y (*.f64 z t))

rewrite72.0ms (0.9%)

Algorithm
2×batch-egg-rewrite
Rules
176×egg-rr
Counts
2 → 176
Calls

2 calls:

68.0ms
((/.f64 x (-.f64 y (*.f64 z t))) (-.f64 y (*.f64 z t)))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
117717
2239317
3546517
000
100

simplify70.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
866×fma-neg_binary64
715×times-frac_binary64
452×associate-/l*_binary64
299×associate-/r*_binary64
236×associate-*l*_binary64
Counts
260 → 196
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0571604
11761544
26761492
341871492
450191492

prune151.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1897196
Fresh000
Picked011
Done000
Total1898197
Error
3.1b
Counts
197 → 8
Alt Table
StatusErrorProgram
18.8b
(/.f64 x (fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 t)) (sqrt.f64 t) y))
3.5b
(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
✓3.2b
(/.f64 x (-.f64 y (*.f64 z t)))
25.0b
(*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (pow.f64 (cbrt.f64 (-.f64 y (*.f64 z t))) 2)) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
▶3.3b
(*.f64 x (/.f64 1 (-.f64 y (*.f64 z t))))
30.9b
(/.f64 x y)
21.5b
(/.f64 x (+.f64 (fma.f64 y 1 (neg.f64 (*.f64 (*.f64 (cbrt.f64 z) t) (cbrt.f64 (*.f64 z z))))) (fma.f64 (neg.f64 (*.f64 (cbrt.f64 z) t)) (cbrt.f64 (*.f64 z z)) (*.f64 (*.f64 (cbrt.f64 z) t) (cbrt.f64 (*.f64 z z))))))
4.1b
(pow.f64 (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))) 3)
Compiler

Compiled 4175 to 1120 computations (73.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 y (*.f64 z t))
✓0.3b
(/.f64 1 (-.f64 y (*.f64 z t)))
✓2.9b
(*.f64 x (/.f64 1 (-.f64 y (*.f64 z t))))

series58.0ms (0.7%)

Counts
2 → 84
Calls

2 calls:

39.0ms
(*.f64 x (/.f64 1 (-.f64 y (*.f64 z t))))
19.0ms
(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite146.0ms (1.7%)

Algorithm
2×batch-egg-rewrite
Rules
51×egg-rr
Counts
2 → 51
Calls

2 calls:

145.0ms
((*.f64 x (/.f64 1 (-.f64 y (*.f64 z t)))) (/.f64 1 (-.f64 y (*.f64 z t))))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01020
121320
2261120
3478620
4477920
5499120
6494520
000
100

simplify76.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
922×times-frac_binary64
598×associate-/l*_binary64
403×associate-/r*_binary64
327×fma-def_binary64
145×associate-*l/_binary64
Counts
135 → 81
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0802470
12422380
29332258
349632258
450202258

prune170.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2221223
Fresh156
Picked011
Done011
Total2238231
Error
3.1b
Counts
231 → 8
Alt Table
StatusErrorProgram
18.8b
(/.f64 x (fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 t)) (sqrt.f64 t) y))
▶3.5b
(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
✓3.2b
(/.f64 x (-.f64 y (*.f64 z t)))
25.0b
(*.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (pow.f64 (cbrt.f64 (-.f64 y (*.f64 z t))) 2)) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓3.3b
(*.f64 x (/.f64 1 (-.f64 y (*.f64 z t))))
31.0b
(*.f64 x (/.f64 1 y))
21.5b
(/.f64 x (+.f64 (fma.f64 y 1 (neg.f64 (*.f64 (*.f64 (cbrt.f64 z) t) (cbrt.f64 (*.f64 z z))))) (fma.f64 (neg.f64 (*.f64 (cbrt.f64 z) t)) (cbrt.f64 (*.f64 z z)) (*.f64 (*.f64 (cbrt.f64 z) t) (cbrt.f64 (*.f64 z z))))))
4.1b
(pow.f64 (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))) 3)
Compiler

Compiled 4884 to 1677 computations (65.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 y (*.f64 z t))
✓0.4b
(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
✓3.2b
(/.f64 (-.f64 y (*.f64 z t)) x)

series60.0ms (0.7%)

Counts
2 → 96
Calls

2 calls:

40.0ms
(pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1)
20.0ms
(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite118.0ms (1.4%)

Algorithm
2×batch-egg-rewrite
Rules
296×egg-rr
Counts
2 → 296
Calls

2 calls:

104.0ms
((/.f64 (-.f64 y (*.f64 z t)) x) (pow.f64 (/.f64 (-.f64 y (*.f64 z t)) x) -1))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01023
122220
2293620
3502620
000
100

simplify78.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
887×fma-neg_binary64
715×times-frac_binary64
464×associate-/l*_binary64
299×associate-/r*_binary64
236×associate-*l*_binary64
Counts
392 → 320
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0661840
12001780
27211728
343021728
451521728

prune481.0ms (5.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New4593462
Fresh415
Picked101
Done022
Total4646470
Error
0.1b
Counts
470 → 6
Alt Table
StatusErrorProgram
13.5b
(pow.f64 (+.f64 (fma.f64 y (/.f64 1 x) (neg.f64 (*.f64 (/.f64 t x) (/.f64 z 1)))) (fma.f64 (neg.f64 (/.f64 t x)) (/.f64 z 1) (*.f64 (/.f64 t x) (/.f64 z 1)))) -1)
✓3.3b
(*.f64 x (/.f64 1 (-.f64 y (*.f64 z t))))
12.4b
(pow.f64 (+.f64 (fma.f64 y (/.f64 1 x) (neg.f64 (*.f64 (/.f64 z x) (/.f64 t 1)))) (fma.f64 (neg.f64 (/.f64 z x)) (/.f64 t 1) (*.f64 (/.f64 z x) (/.f64 t 1)))) -1)
▶4.2b
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)) 2)) (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)))
18.8b
(/.f64 x (fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 t)) (sqrt.f64 t) y))
✓3.2b
(/.f64 x (-.f64 y (*.f64 z t)))
Compiler

Compiled 15786 to 4062 computations (74.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(pow.f64 (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)) 2)
✓0.8b
(/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)) 2))
3.2b
(/.f64 (-.f64 y (*.f64 z t)) x)
✓15.2b
(cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x))

series1.5s (18.5%)

Counts
3 → 144
Calls

3 calls:

704.0ms
(/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)) 2))
450.0ms
(pow.f64 (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)) 2)
389.0ms
(cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x))

rewrite70.0ms (0.8%)

Algorithm
2×batch-egg-rewrite
Rules
84×egg-rr
Counts
3 → 84
Calls

2 calls:

65.0ms
((cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)) (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)) 2)) (pow.f64 (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)) 2))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01342
128338
2344338
3512038
000
100

simplify148.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
602×times-frac_binary64
465×associate-/l*_binary64
339×fma-def_binary64
241×*-commutative_binary64
124×sqr-pow_binary64
Counts
228 → 283
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
06188745
120878555
249838555

prune777.0ms (9.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New8930893
Fresh033
Picked011
Done022
Total8936899
Error
0.1b
Counts
899 → 6
Alt Table
StatusErrorProgram
13.5b
(pow.f64 (+.f64 (fma.f64 y (/.f64 1 x) (neg.f64 (*.f64 (/.f64 t x) (/.f64 z 1)))) (fma.f64 (neg.f64 (/.f64 t x)) (/.f64 z 1) (*.f64 (/.f64 t x) (/.f64 z 1)))) -1)
✓3.3b
(*.f64 x (/.f64 1 (-.f64 y (*.f64 z t))))
12.4b
(pow.f64 (+.f64 (fma.f64 y (/.f64 1 x) (neg.f64 (*.f64 (/.f64 z x) (/.f64 t 1)))) (fma.f64 (neg.f64 (/.f64 z x)) (/.f64 t 1) (*.f64 (/.f64 z x) (/.f64 t 1)))) -1)
✓4.2b
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)) 2)) (cbrt.f64 (/.f64 (-.f64 y (*.f64 z t)) x)))
18.8b
(/.f64 x (fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 t)) (sqrt.f64 t) y))
✓3.2b
(/.f64 x (-.f64 y (*.f64 z t)))
Compiler

Compiled 47189 to 16735 computations (64.5% saved)

regimes2.3s (27.6%)

Accuracy

Total 2.6b remaining (95.5%)

Threshold costs 0b (0%)

Counts
232 → 2
Compiler

Compiled 42222 to 25419 computations (39.8% saved)

bsearch30.0ms (0.4%)

Steps
ItersRangePoint
9
6.884196690981824e+177
8.213508345277784e+185
1.105352214638888e+179
Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
5×+-commutative_binary64
5×*-commutative_binary64
4×sub-neg_binary64
4×neg-sub0_binary64
4×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02453
13853
24953
35453
45553
55453

end244.0ms (2.9%)

Compiler

Compiled 294 to 166 computations (43.5% saved)

Profiling

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