Details

Time bar (total: 6.9s)

analyze891.0ms (13%)

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
0%99.8%0.2%7
15.6%84.2%0.2%8
15.6%84.2%0.2%9
20.3%79.5%0.2%10
25.3%74.5%0.2%11
34.2%65.6%0.2%12
37.4%62%0.6%13
41.7%57.7%0.6%14
Compiler

Compiled 20 to 14 computations (30% saved)

sample30.0ms (0.4%)

Algorithm
1×intervals
Results
11.0ms256×body128valid
5.0ms105×body128invalid
Compiler

Compiled 43 to 31 computations (27.9% saved)

simplify595.0ms (8.7%)

Algorithm
1×egg-herbie
Rules
1775×cancel-sign-sub-inv_binary64
1670×distribute-rgt-in_binary64
1374×div-sub_binary64
1020×distribute-lft-in_binary64
922×associate-/r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01222
12522
25822
310722
421522
540816
677316
7179716
8201916
9215016
10274116
11292516
12302616
13476816
14348416
15353816
16365916
17365516
18366216
19371016
20372916
21373016
22373016
23282016
24336416
25398816
26370216
27480016

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.1b
Counts
2 → 2
Alt Table
StatusErrorProgram
4.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
▶4.8b
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
Compiler

Compiled 83 to 56 computations (32.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
0.4b
(/.f64 -1/3 z)
4.5b
(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))

rewrite211.0ms (3.1%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
57×add-sqr-sqrt_binary64
56×times-frac_binary64
52×cancel-sign-sub-inv_binary64
49×*-un-lft-identity_binary64
47×add-cube-cbrt_binary64
Counts
3 → 133
Calls

3 calls:

14.0ms
(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))
7.0ms
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
3.0ms
(/.f64 -1/3 z)
Compiler

Compiled 2749 to 1238 computations (55% saved)

series148.0ms (2.2%)

Error
0.1b
Counts
3 → 45
Calls

3 calls:

80.0ms
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
48.0ms
(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))
6.0ms
(/.f64 -1/3 z)
Compiler

Compiled 1250 to 833 computations (33.4% saved)

simplify127.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
555×distribute-rgt-in_binary64
254×distribute-lft-neg-out_binary64
245×distribute-rgt-neg-out_binary64
200×associate-*l*_binary64
194×associate-*r*_binary64
Counts
178 → 134
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02332845
16832692
223422518
347112518
449622518

prune110.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1268134
Fresh011
Picked011
Done000
Total12610136
Error
0.0b
Counts
136 → 10
Alt Table
StatusErrorProgram
5.0b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (*.f64 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) y)) (/.f64 -1/3 z)))
37.3b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 y (/.f64 t y)) (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) (/.f64 1/9 z)))) (+.f64 (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 1/3) x))
▶4.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
✓4.8b
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
33.1b
(+.f64 x (*.f64 (/.f64 1 (sqrt.f64 z)) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (sqrt.f64 z)))))
5.2b
(+.f64 x (*.f64 (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (cbrt.f64 z)))))
35.8b
(+.f64 x (+.f64 (*.f64 -1/3 (/.f64 y z)) (*.f64 (/.f64 t (sqrt.f64 y)) (/.f64 (/.f64 1/3 z) (sqrt.f64 y)))))
32.1b
(+.f64 x (cbrt.f64 (*.f64 -1/27 (pow.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 3))))
35.9b
(+.f64 x (/.f64 (*.f64 -1/3 (-.f64 (pow.f64 y 3) (pow.f64 (/.f64 t y) 3))) (*.f64 z (+.f64 (*.f64 y y) (*.f64 (/.f64 t y) (+.f64 y (/.f64 t y)))))))
25.7b
(+.f64 x (*.f64 1/3 (/.f64 t (*.f64 y z))))
Compiler

Compiled 1951 to 939 computations (51.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 x (/.f64 y (*.f64 z 3)))
0.2b
(*.f64 (*.f64 z 3) y)
0.2b
(/.f64 y (*.f64 z 3))
8.5b
(/.f64 t (*.f64 (*.f64 z 3) y))

rewrite138.0ms (2%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
13×*-un-lft-identity_binary64
13×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
Counts
4 → 82
Calls

4 calls:

6.0ms
(-.f64 x (/.f64 y (*.f64 z 3)))
6.0ms
(/.f64 t (*.f64 (*.f64 z 3) y))
5.0ms
(*.f64 (*.f64 z 3) y)
4.0ms
(/.f64 y (*.f64 z 3))
Compiler

Compiled 1664 to 1014 computations (39.1% saved)

series108.0ms (1.6%)

Error
0.0b
Counts
4 → 39
Calls

4 calls:

36.0ms
(-.f64 x (/.f64 y (*.f64 z 3)))
33.0ms
(/.f64 t (*.f64 (*.f64 z 3) y))
16.0ms
(/.f64 y (*.f64 z 3))
14.0ms
(*.f64 (*.f64 z 3) y)
Compiler

Compiled 1344 to 915 computations (31.9% saved)

simplify109.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
410×associate-*l/_binary64
363×associate-/l/_binary64
334×associate-*r/_binary64
329×*-commutative_binary64
312×div-sub_binary64
Counts
121 → 83
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01461365
13831211
214071210
335621209
446481209
553361209

prune82.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New80383
Fresh268
Picked101
Done011
Total831093
Error
0.0b
Counts
93 → 10
Alt Table
StatusErrorProgram
5.0b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (*.f64 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) y)) (/.f64 -1/3 z)))
37.3b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 y (/.f64 t y)) (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) (/.f64 1/9 z)))) (+.f64 (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 1/3) x))
▶4.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 z (*.f64 y 3))))
✓4.8b
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
33.1b
(+.f64 x (*.f64 (/.f64 1 (sqrt.f64 z)) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (sqrt.f64 z)))))
6.2b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (*.f64 t (/.f64 1/3 (*.f64 z y))))
5.2b
(+.f64 x (*.f64 (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (cbrt.f64 z)))))
32.1b
(+.f64 x (cbrt.f64 (*.f64 -1/27 (pow.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 3))))
4.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 1 (/.f64 3 (/.f64 t (*.f64 z y)))))
35.9b
(+.f64 x (/.f64 (*.f64 -1/3 (-.f64 (pow.f64 y 3) (pow.f64 (/.f64 t y) 3))) (*.f64 z (+.f64 (*.f64 y y) (*.f64 (/.f64 t y) (+.f64 y (/.f64 t y)))))))
Compiler

Compiled 1298 to 765 computations (41.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 x (/.f64 y (*.f64 z 3)))
0.2b
(*.f64 z (*.f64 y 3))
0.2b
(/.f64 y (*.f64 z 3))
8.5b
(/.f64 t (*.f64 z (*.f64 y 3)))

rewrite134.0ms (2%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
13×*-un-lft-identity_binary64
13×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
Counts
4 → 82
Calls

4 calls:

6.0ms
(/.f64 t (*.f64 z (*.f64 y 3)))
5.0ms
(-.f64 x (/.f64 y (*.f64 z 3)))
5.0ms
(*.f64 z (*.f64 y 3))
4.0ms
(/.f64 y (*.f64 z 3))
Compiler

Compiled 1647 to 1006 computations (38.9% saved)

series105.0ms (1.5%)

Error
0.0b
Counts
4 → 39
Calls

4 calls:

36.0ms
(-.f64 x (/.f64 y (*.f64 z 3)))
32.0ms
(/.f64 t (*.f64 z (*.f64 y 3)))
15.0ms
(/.f64 y (*.f64 z 3))
14.0ms
(*.f64 z (*.f64 y 3))
Compiler

Compiled 1344 to 915 computations (31.9% saved)

simplify121.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
768×associate-/r*_binary64
719×associate-/l*_binary64
367×associate-*l/_binary64
342×associate-/l/_binary64
115×exp-prod_binary64
Counts
121 → 83
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01521362
13941209
213291208
344561207
447761207
549981207
649411207

prune81.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New82183
Fresh178
Picked011
Done011
Total831093
Error
0.0b
Counts
93 → 10
Alt Table
StatusErrorProgram
5.0b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (*.f64 (*.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) y)) (/.f64 -1/3 z)))
▶4.7b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 1 (/.f64 z (/.f64 t (*.f64 y 3)))))
37.3b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 y (/.f64 t y)) (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) (/.f64 1/9 z)))) (+.f64 (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 1/3) x))
✓4.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 z (*.f64 y 3))))
✓4.8b
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
33.1b
(+.f64 x (*.f64 (/.f64 1 (sqrt.f64 z)) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (sqrt.f64 z)))))
6.2b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (*.f64 t (/.f64 1/3 (*.f64 z y))))
5.2b
(+.f64 x (*.f64 (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (cbrt.f64 z)))))
32.1b
(+.f64 x (cbrt.f64 (*.f64 -1/27 (pow.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 3))))
4.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 1 (/.f64 3 (/.f64 t (*.f64 z y)))))
Compiler

Compiled 1268 to 752 computations (40.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 y (*.f64 z 3))
0.2b
(/.f64 t (*.f64 y 3))
0.3b
(/.f64 1 (/.f64 z (/.f64 t (*.f64 y 3))))
5.5b
(/.f64 z (/.f64 t (*.f64 y 3)))

rewrite408.0ms (6%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
237×times-frac_binary64
107×*-un-lft-identity_binary64
107×add-sqr-sqrt_binary64
107×add-cube-cbrt_binary64
57×add-exp-log_binary64
Counts
4 → 226
Calls

4 calls:

11.0ms
(/.f64 1 (/.f64 z (/.f64 t (*.f64 y 3))))
6.0ms
(/.f64 z (/.f64 t (*.f64 y 3)))
4.0ms
(/.f64 t (*.f64 y 3))
4.0ms
(/.f64 y (*.f64 z 3))
Compiler

Compiled 5880 to 3701 computations (37.1% saved)

series105.0ms (1.5%)

Error
0.0b
Counts
4 → 30
Calls

4 calls:

32.0ms
(/.f64 z (/.f64 t (*.f64 y 3)))
31.0ms
(/.f64 1 (/.f64 z (/.f64 t (*.f64 y 3))))
18.0ms
(/.f64 t (*.f64 y 3))
16.0ms
(/.f64 y (*.f64 z 3))
Compiler

Compiled 1294 to 909 computations (29.8% saved)

simplify238.0ms (3.5%)

Algorithm
1×egg-herbie
Rules
465×*-commutative_binary64
377×sqr-pow_binary64
248×distribute-rgt-in_binary64
248×unsub-neg_binary64
223×sub-neg_binary64
Counts
256 → 201
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02384601
15063999
218523890
325343890
437223890
543483890
649033890

prune179.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1983201
Fresh347
Picked101
Done022
Total2029211
Error
0.0b
Counts
211 → 9
Alt Table
StatusErrorProgram
2.1b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (*.f64 (/.f64 1 y) (/.f64 (/.f64 t 3) z)))
4.7b
(+.f64 (-.f64 x (/.f64 1 (/.f64 3 (/.f64 y z)))) (/.f64 1 (/.f64 z (/.f64 t (*.f64 y 3)))))
37.3b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 y (/.f64 t y)) (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) (/.f64 1/9 z)))) (+.f64 (*.f64 (/.f64 (-.f64 y (/.f64 t y)) z) 1/3) x))
4.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 z (*.f64 y 3))))
4.8b
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
33.1b
(+.f64 x (*.f64 (/.f64 1 (sqrt.f64 z)) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (sqrt.f64 z)))))
2.1b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (*.f64 (/.f64 t z) (/.f64 1/3 y)))
6.2b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (*.f64 t (/.f64 1/3 (*.f64 z y))))
4.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 1 (/.f64 3 (/.f64 t (*.f64 z y)))))
Compiler

Compiled 2791 to 1541 computations (44.8% saved)

regimes1.7s (25.2%)

Accuracy

Total 1.1b remaining (98.7%)

Threshold costs 0b (0%)

Compiler

Compiled 25118 to 17074 computations (32% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify7.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
040141
156141
267141
376141
482141
584141
683141

end2.0ms (0%)

Compiler

Compiled 98 to 64 computations (34.7% saved)

sample1.1s (16.6%)

Algorithm
1×intervals
Results
354.0ms8000×body128valid
147.0ms3119×body128invalid
Compiler

Compiled 317 to 209 computations (34.1% saved)

Profiling

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