Details

Time bar (total: 2.3s)

analyze23.0ms (1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample30.0ms (1.3%)

Algorithm
1×intervals
Results
13.0ms75×body2048valid
4.0ms123×body128valid
3.0ms27×body1024valid
2.0ms20×body512valid
1.0ms11×body256valid
Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify12.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
15×sub-neg_binary64
14×cancel-sign-sub-inv_binary64
10×distribute-rgt-in_binary64
9×neg-mul-1_binary64
8×associate--r+_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21611
32211
42811
54311
66511
77711
88911
99111
108511
117111

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
14.8b
Counts
1 → 1
Alt Table
StatusErrorProgram
▶14.8b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

1.2b
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite28.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Error
13.5b
Rules
4×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
3×add-log-exp_binary64 cancel-sign-sub-inv_binary64
2×add-cube-cbrt_binary64
1×diff-atan_binary64 diff-log_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
Counts
1 → 17
Calls

1 calls:

4.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 252 to 159 computations (36.9% saved)

series6.0ms (0.3%)

Error
14.8b
Counts
1 → 3
Calls

1 calls:

5.0ms
(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
Compiler

Compiled 56 to 42 computations (25% saved)

simplify79.0ms (3.4%)

Algorithm
1×egg-herbie
Rules
980×unsub-neg_binary64
508×neg-sub0_binary64
492×neg-mul-1_binary64
430×associate-*l*_binary64
361×distribute-rgt-neg-in_binary64
Counts
20 → 7
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
045338
198315
2182306
3550306
41678306
52671306
64022306
74958306

prune6.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New617
Fresh000
Picked101
Done000
Total718
Error
0.1b
Counts
8 → 1
Alt Table
StatusErrorProgram
▶0.1b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 87 to 62 computations (28.7% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0b
(*.f64 N (+.f64 N 1))
0.1b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite64.0ms (2.8%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
7×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
5×pow1_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64
4×associate-*r*_binary64
3×associate-*l*_binary64
2×distribute-rgt-in_binary64 distribute-lft-in_binary64 flip3-+_binary64 associate-*r/_binary64 flip-+_binary64 associate-+r+_binary64
Counts
3 → 43
Calls

3 calls:

8.0ms
(*.f64 N (+.f64 N 1))
3.0ms
(+.f64 1 (*.f64 N (+.f64 N 1)))
0.0ms
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 658 to 506 computations (23.1% saved)

series38.0ms (1.7%)

Error
0.1b
Counts
3 → 18
Calls

3 calls:

12.0ms
(+.f64 1 (*.f64 N (+.f64 N 1)))
10.0ms
(*.f64 N (+.f64 N 1))
6.0ms
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
Compiler

Compiled 291 to 235 computations (19.2% saved)

simplify130.0ms (5.7%)

Algorithm
1×egg-herbie
Rules
521×unswap-sqr_binary64
356×distribute-rgt-in_binary64
317×sub-neg_binary64
312×distribute-rgt-out_binary64
296×distribute-lft-in_binary64
Counts
61 → 49
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
072692
1184640
2527638
31539638
42834635
54833635
64971635
74999635
84918635

prune41.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New46349
Fresh000
Picked011
Done000
Total46450
Error
0.1b
Counts
50 → 4
Alt Table
StatusErrorProgram
✓0.1b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶0.6b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
1.3b
(*.f64 (*.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))) (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
8.3b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))) 3))
Compiler

Compiled 637 to 396 computations (37.8% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
0.6b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
17.5b
(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
17.5b
(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))

rewrite117.0ms (5.1%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
32×add-sqr-sqrt_binary64
24×sqrt-prod_binary64
21×pow1_binary64
14×add-cube-cbrt_binary64 *-un-lft-identity_binary64
10×pow1/2_binary64 sqrt-pow1_binary64
Counts
4 → 84
Calls

4 calls:

7.0ms
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
1.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
1.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
0.0ms
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
Compiler

Compiled 2083 to 1360 computations (34.7% saved)

series38.0ms (1.6%)

Error
0.1b
Counts
4 → 12
Calls

4 calls:

10.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
10.0ms
(sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
9.0ms
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
6.0ms
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
Compiler

Compiled 508 to 393 computations (22.6% saved)

simplify133.0ms (5.8%)

Algorithm
1×egg-herbie
Rules
449×unswap-sqr_binary64
442×log-div_binary64
427×log-prod_binary64
325×sqr-pow_binary64
265×associate-+l+_binary64
Counts
96 → 69
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
0571963
1791802
21851744
33981634
47351466
513331466
624931450
744191450
848461450

prune39.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New68169
Fresh112
Picked011
Done011
Total69473
Error
0.1b
Counts
73 → 4
Alt Table
StatusErrorProgram
✓0.1b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
▶1.3b
(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
✓0.6b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
8.3b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))) 3))
Compiler

Compiled 738 to 494 computations (33.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
0.2b
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) 2)
18.2b
(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
18.2b
(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))

rewrite73.0ms (3.2%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
9×add-cube-cbrt_binary64 cbrt-prod_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
6×unpow-prod-down_binary64
5×pow1_binary64 add-exp-log_binary64
4×add-log-exp_binary64 add-cbrt-cube_binary64
3×pow1/3_binary64 pow-unpow_binary64
Counts
4 → 51
Calls

4 calls:

2.0ms
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) 2)
1.0ms
(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
1.0ms
(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
0.0ms
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
Compiler

Compiled 1579 to 1068 computations (32.4% saved)

series97.0ms (4.2%)

Error
0.1b
Counts
4 → 12
Calls

4 calls:

31.0ms
(pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) 2)
28.0ms
(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
25.0ms
(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
8.0ms
(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
Compiler

Compiled 690 to 547 computations (20.7% saved)

simplify125.0ms (5.4%)

Algorithm
1×egg-herbie
Rules
712×distribute-rgt-in_binary64
649×distribute-lft-in_binary64
414×associate-/l/_binary64
401×log-prod_binary64
351×sqr-pow_binary64
Counts
63 → 43
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
0571184
11041130
22131118
36501118
412101110
531241096
645761096
749771096
848471096

prune25.0ms (1.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New41243
Fresh011
Picked011
Done022
Total41647
Error
0.1b
Counts
47 → 6
Alt Table
StatusErrorProgram
0.1b
(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))
1.3b
(*.f64 (pow.f64 (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) 2) (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
0.6b
(*.f64 (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))) (sqrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
1.9b
(*.f64 (exp.f64 (*.f64 2/3 (log.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))) (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
8.3b
(cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))) 3))
5.8b
(*.f64 (cbrt.f64 (pow.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))) 2)) (cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))))
Compiler

Compiled 586 to 398 computations (32.1% saved)

regimes126.0ms (5.5%)

Accuracy

Total 0.0b remaining (10.5%)

Threshold costs 0.0b (10.5%)

Compiler

Compiled 1742 to 1302 computations (25.3% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×+-commutative_binary64
1×1-exp_binary64 *-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
11213
21113

end1.0ms (0%)

Compiler

Compiled 10 to 8 computations (20% saved)

sample1.0s (44.9%)

Algorithm
1×intervals
Results
361.0ms2071×body2048valid
138.0ms4182×body128valid
118.0ms978×body1024valid
45.0ms499×body512valid
20.0ms270×body256valid
Compiler

Compiled 138 to 101 computations (26.8% saved)

Profiling

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