Details

Time bar (total: 5.6s)

analyze1.1s (20.2%)

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)

sample71.0ms (1.3%)

Algorithm
1×intervals
Results
50.0ms256×body128valid
6.0ms108×body128invalid
Compiler

Compiled 43 to 31 computations (27.9% saved)

simplify340.0ms (6.1%)

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

prune3.0ms (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
▶3.7b
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
3.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
Compiler

Compiled 83 to 56 computations (32.5% saved)

localize9.0ms (0.2%)

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)
3.6b
(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))

rewrite163.0ms (2.9%)

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:

11.0ms
(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))
5.0ms
(+.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)

series110.0ms (2%)

Error
0.0b
Counts
3 → 45
Calls

3 calls:

55.0ms
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
37.0ms
(*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))
4.0ms
(/.f64 -1/3 z)
Compiler

Compiled 1250 to 833 computations (33.4% saved)

simplify121.0ms (2.2%)

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 → 127
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02332845
16812692
223392518
347042518
449542518

prune79.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1189127
Fresh011
Picked011
Done000
Total11811129
Error
0.0b
Counts
129 → 11
Alt Table
StatusErrorProgram
30.3b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 t y))) (sqrt.f64 (/.f64 t y))) (/.f64 -1/3 z)))
▶3.7b
(+.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)) x)
32.3b
(+.f64 x (+.f64 (*.f64 -1/3 (/.f64 y z)) (*.f64 (/.f64 t (sqrt.f64 y)) (/.f64 (/.f64 1/3 z) (sqrt.f64 y)))))
4.0b
(+.f64 x (+.f64 (*.f64 -1/3 (/.f64 y z)) (*.f64 1/3 (/.f64 t (*.f64 y z)))))
✓3.7b
(+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y))))
35.1b
(+.f64 x (*.f64 (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))) (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)))))
3.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
4.3b
(+.f64 x (*.f64 (*.f64 (*.f64 (/.f64 (cbrt.f64 -1/3) (cbrt.f64 z)) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 z))) (/.f64 (cbrt.f64 -1/3) (cbrt.f64 z))) (-.f64 y (/.f64 t y))))
20.5b
(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 -1/3 z) 3)) (-.f64 y (/.f64 t y))))
4.2b
(+.f64 x (*.f64 (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (cbrt.f64 z)))))
34.9b
(+.f64 x (*.f64 (/.f64 (*.f64 (cbrt.f64 -1/3) (cbrt.f64 -1/3)) (sqrt.f64 z)) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 (cbrt.f64 -1/3) (sqrt.f64 z)))))
Compiler

Compiled 1944 to 961 computations (50.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)) x)
0.4b
(*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))
3.4b
(/.f64 (-.f64 y (/.f64 t y)) z)

rewrite123.0ms (2.2%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
65×add-sqr-sqrt_binary64
44×times-frac_binary64
39×*-un-lft-identity_binary64
25×add-cube-cbrt_binary64
22×associate-*r*_binary64
Counts
3 → 94
Calls

3 calls:

12.0ms
(*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))
11.0ms
(+.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)) x)
8.0ms
(/.f64 (-.f64 y (/.f64 t y)) z)
Compiler

Compiled 1842 to 554 computations (69.9% saved)

series128.0ms (2.3%)

Error
0.0b
Counts
3 → 57
Calls

3 calls:

54.0ms
(+.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)) x)
32.0ms
(*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))
27.0ms
(/.f64 (-.f64 y (/.f64 t y)) z)
Compiler

Compiled 1553 to 1035 computations (33.4% saved)

simplify128.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
335×associate-*l/_binary64
335×div-sub_binary64
320×associate-*r/_binary64
288×associate-*l*_binary64
280×distribute-rgt-in_binary64
Counts
151 → 97
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01712506
14332357
211162348
335032348
447952347
549852347

prune47.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New95297
Fresh279
Picked011
Done101
Total9810108
Error
0.0b
Counts
108 → 10
Alt Table
StatusErrorProgram
4.0b
(+.f64 x (+.f64 (*.f64 -1/3 (/.f64 y z)) (*.f64 1/3 (/.f64 t (*.f64 y z)))))
▶3.7b
(+.f64 (/.f64 (*.f64 (-.f64 y (/.f64 t y)) -1/3) z) x)
30.3b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 t y))) (sqrt.f64 (/.f64 t y))) (/.f64 -1/3 z)))
✓3.7b
(+.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)) x)
32.3b
(+.f64 x (+.f64 (*.f64 -1/3 (/.f64 y z)) (*.f64 (/.f64 t (sqrt.f64 y)) (/.f64 (/.f64 1/3 z) (sqrt.f64 y)))))
35.1b
(+.f64 x (*.f64 (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))) (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)))))
3.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
20.5b
(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 -1/3 z) 3)) (-.f64 y (/.f64 t y))))
4.2b
(+.f64 x (*.f64 (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (cbrt.f64 z)))))
4.2b
(+.f64 (*.f64 (/.f64 -1/3 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (-.f64 y (/.f64 t y)) (cbrt.f64 z))) x)
Compiler

Compiled 1187 to 543 computations (54.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (/.f64 (*.f64 (-.f64 y (/.f64 t y)) -1/3) z) x)
0.3b
(*.f64 (-.f64 y (/.f64 t y)) -1/3)
3.6b
(/.f64 (*.f64 (-.f64 y (/.f64 t y)) -1/3) z)

rewrite71.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
14×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
7×add-cube-cbrt_binary64
Counts
3 → 58
Calls

3 calls:

9.0ms
(+.f64 (/.f64 (*.f64 (-.f64 y (/.f64 t y)) -1/3) z) x)
9.0ms
(/.f64 (*.f64 (-.f64 y (/.f64 t y)) -1/3) z)
7.0ms
(*.f64 (-.f64 y (/.f64 t y)) -1/3)
Compiler

Compiled 1096 to 455 computations (58.5% saved)

series110.0ms (2%)

Error
0.0b
Counts
3 → 54
Calls

3 calls:

53.0ms
(+.f64 (/.f64 (*.f64 (-.f64 y (/.f64 t y)) -1/3) z) x)
31.0ms
(/.f64 (*.f64 (-.f64 y (/.f64 t y)) -1/3) z)
16.0ms
(*.f64 (-.f64 y (/.f64 t y)) -1/3)
Compiler

Compiled 1432 to 969 computations (32.3% saved)

simplify91.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
534×associate-/l*_binary64
459×times-frac_binary64
403×associate-*l/_binary64
236×distribute-rgt-in_binary64
221×associate-/l/_binary64
Counts
112 → 82
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01341707
13601521
211241512
345611512
449621512

prune50.0ms (0.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New82082
Fresh088
Picked011
Done011
Total821092
Error
0.0b
Counts
92 → 10
Alt Table
StatusErrorProgram
4.0b
(+.f64 x (+.f64 (*.f64 -1/3 (/.f64 y z)) (*.f64 1/3 (/.f64 t (*.f64 y z)))))
✓3.7b
(+.f64 (/.f64 (*.f64 (-.f64 y (/.f64 t y)) -1/3) z) x)
30.3b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 t y))) (sqrt.f64 (/.f64 t y))) (/.f64 -1/3 z)))
✓3.7b
(+.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)) x)
32.3b
(+.f64 x (+.f64 (*.f64 -1/3 (/.f64 y z)) (*.f64 (/.f64 t (sqrt.f64 y)) (/.f64 (/.f64 1/3 z) (sqrt.f64 y)))))
35.1b
(+.f64 x (*.f64 (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))) (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)))))
▶3.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))
20.5b
(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 -1/3 z) 3)) (-.f64 y (/.f64 t y))))
4.2b
(+.f64 x (*.f64 (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (cbrt.f64 z)))))
4.2b
(+.f64 (*.f64 (/.f64 -1/3 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (-.f64 y (/.f64 t y)) (cbrt.f64 z))) x)
Compiler

Compiled 1109 to 532 computations (52% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 x (/.f64 y (*.f64 z 3)))
0.2b
(*.f64 (*.f64 z 3) y)
0.5b
(/.f64 y (*.f64 z 3))
8.2b
(/.f64 t (*.f64 (*.f64 z 3) y))

rewrite105.0ms (1.9%)

Algorithm
1×rewrite-expression-head
Error
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 y (*.f64 z 3))
4.0ms
(/.f64 t (*.f64 (*.f64 z 3) y))
4.0ms
(-.f64 x (/.f64 y (*.f64 z 3)))
4.0ms
(*.f64 (*.f64 z 3) y)
Compiler

Compiled 1664 to 1014 computations (39.1% saved)

series79.0ms (1.4%)

Error
0.0b
Counts
4 → 39
Calls

4 calls:

26.0ms
(/.f64 t (*.f64 (*.f64 z 3) y))
25.0ms
(-.f64 x (/.f64 y (*.f64 z 3)))
12.0ms
(/.f64 y (*.f64 z 3))
9.0ms
(*.f64 (*.f64 z 3) y)
Compiler

Compiled 1344 to 915 computations (31.9% saved)

simplify95.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
812×associate-/l*_binary64
397×associate-*l/_binary64
313×*-commutative_binary64
296×associate-*r/_binary64
283×associate-/l/_binary64
Counts
121 → 83
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01461365
13841211
213451211
342811210
447081209
549091209

prune51.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New80383
Fresh347
Picked101
Done022
Total84993
Error
0b
Counts
93 → 9
Alt Table
StatusErrorProgram
30.3b
(+.f64 (+.f64 (*.f64 -1/3 (/.f64 y z)) x) (*.f64 (*.f64 (neg.f64 (sqrt.f64 (/.f64 t y))) (sqrt.f64 (/.f64 t y))) (/.f64 -1/3 z)))
3.7b
(+.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)) x)
3.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 y z) 3)))
3.9b
(+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 z (*.f64 y 3))))
3.7b
(+.f64 (/.f64 (*.f64 (-.f64 y (/.f64 t y)) -1/3) z) x)
35.1b
(+.f64 x (*.f64 (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z))) (sqrt.f64 (*.f64 -1/3 (/.f64 (-.f64 y (/.f64 t y)) z)))))
32.8b
(+.f64 (-.f64 x (/.f64 (sqrt.f64 y) (/.f64 z (/.f64 (sqrt.f64 y) 3)))) (/.f64 t (*.f64 (*.f64 z 3) y)))
20.5b
(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 -1/3 z) 3)) (-.f64 y (/.f64 t y))))
4.2b
(+.f64 x (*.f64 (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (-.f64 y (/.f64 t y)) (/.f64 -1/3 (cbrt.f64 z)))))
Compiler

Compiled 1027 to 599 computations (41.7% saved)

regimes1.3s (23.9%)

Accuracy

Total 1.7b remaining (98.1%)

Threshold costs 0b (0%)

Compiler

Compiled 18518 to 12328 computations (33.4% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11622
22322
32722
43022
53122
63122

end1.0ms (0%)

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.1s (20%)

Algorithm
1×intervals
Results
440.0ms8000×body128valid
185.0ms3095×body128invalid
Compiler

Compiled 229 to 151 computations (34.1% saved)

Profiling

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