Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample202.0ms (2.1%)

Algorithm

1×

intervals

Results

159.0ms	117×	body	2048	valid
21.0ms	74×	body	1024	valid
5.0ms	38×	body	512	valid
5.0ms	256×	pre	128	true
3.0ms	6×	body	4096	valid
2.0ms	17×	body	256	valid
0.0ms	4×	body	128	valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	12
1	72	12

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

60.4b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (tan.f64 x))
2.4b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_782`
36×	`times-frac_binary64_766`
35×	`*-un-lft-identity_binary64_760`
19×	`add-cube-cbrt_binary64_795`
14×	`cancel-sign-sub-inv_binary64_726`
9×	`difference-of-squares_binary64_729`
7×	`distribute-lft-out--_binary64_712`
6×	`add-exp-log_binary64_798` `div-inv_binary64_757`
4×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`associate-/r_binary64_704` `associate-/l_binary64_705` `pow1_binary64_821`
2×	`associate-/r/_binary64_706` `tan-quot_binary64_919` `div-exp_binary64_811`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `inv-pow_binary64_845` `frac-sub_binary64_769` `rec-exp_binary64_810` `clear-num_binary64_759` `sub-neg_binary64_753` `1-exp_binary64_804` `flip--_binary64_735` `pow-flip_binary64_834` `flip3--_binary64_764`

Counts

2 → 74

Calls

2 calls:

17.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms	(/.f64 1 (tan.f64 x))

series154.0ms (1.6%)

Counts

2 → 10

Calls

2 calls:

91.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
63.0ms	(/.f64 1 (tan.f64 x))

Compiler

Compiled 188 to 161 computations (14.4% saved)

simplify86.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4928	1118
1	4928	1118

prune72.0ms (0.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	1	85

Error

0.3b

Counts

85 → 1

Compiler

Compiled 1058 to 676 computations (36.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(*.f64 x 1/3)

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_782`
15×	`associate-r_binary64_700`
10×	`add-exp-log_binary64_798`
9×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
7×	`add-cbrt-cube_binary64_796`
6×	`associate-l_binary64_701`
5×	`unswap-sqr_binary64_728` `add-log-exp_binary64_799` `pow1_binary64_821`
4×	`prod-exp_binary64_809` `cube-prod_binary64_788` `unpow-prod-down_binary64_839`
2×	`sqr-pow_binary64_732` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`
1×	`cube-mult_binary64_790` `flip3-+_binary64_763` `unpow3_binary64_826` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `+-commutative_binary64_690` `sum-log_binary64_851` `pow-prod-down_binary64_831`

Counts

3 → 60

Calls

3 calls:

7.0ms	(*.f64 1/45 (pow.f64 x 3))
6.0ms	(*.f64 x 1/3)
4.0ms	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))

series127.0ms (1.3%)

Counts

3 → 12

Calls

3 calls:

75.0ms	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
34.0ms	(*.f64 1/45 (pow.f64 x 3))
18.0ms	(*.f64 x 1/3)

Compiler

Compiled 175 to 157 computations (10.3% saved)

simplify98.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4920	699
1	4920	699

prune68.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	7	73

Error

0.1b

Counts

73 → 7

Compiler

Compiled 1011 to 774 computations (23.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(*.f64 x (sqrt.f64 1/3))
0.4b	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`associate-r_binary64_700` `add-sqr-sqrt_binary64_782`
16×	`add-exp-log_binary64_798`
13×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796`
11×	`pow1_binary64_821`
7×	`prod-exp_binary64_809` `sqrt-prod_binary64_776` `associate-l_binary64_701`
6×	`unswap-sqr_binary64_728` `add-log-exp_binary64_799`
5×	`cbrt-unprod_binary64_793`
4×	`cube-prod_binary64_788` `pow-prod-down_binary64_831` `unpow-prod-down_binary64_839`
3×	`*-commutative_binary64_691`
2×	`sqr-pow_binary64_732`
1×	`cube-mult_binary64_790` `flip3-+_binary64_763` `unpow3_binary64_826` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `+-commutative_binary64_690` `sum-log_binary64_851`

Counts

4 → 85

Calls

4 calls:

8.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))
7.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
7.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 x (sqrt.f64 1/3))

series215.0ms (2.2%)

Counts

4 → 15

Calls

4 calls:

97.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))
51.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
35.0ms	(*.f64 1/45 (pow.f64 x 3))
32.0ms	(*.f64 x (sqrt.f64 1/3))

Compiler

Compiled 316 to 292 computations (7.6% saved)

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4914	941
1	4914	941

prune113.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	97	10	107

Error

0.1b

Counts

107 → 10

Compiler

Compiled 1700 to 1395 computations (17.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
0.4b	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`associate-r_binary64_700`
29×	`add-sqr-sqrt_binary64_782`
24×	`add-exp-log_binary64_798`
15×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
13×	`prod-exp_binary64_809` `sqrt-prod_binary64_776` `add-cbrt-cube_binary64_796`
12×	`unpow-prod-down_binary64_839`
8×	`unswap-sqr_binary64_728`
7×	`associate-l_binary64_701`
6×	`add-log-exp_binary64_799` `pow1_binary64_821`
5×	`cbrt-unprod_binary64_793`
4×	`sqr-pow_binary64_732` `cube-prod_binary64_788`
3×	`pow-exp_binary64_828` `pow-to-exp_binary64_829` `*-commutative_binary64_691`
1×	`cube-mult_binary64_790` `flip3-+_binary64_763` `unpow3_binary64_826` `flip-+_binary64_734` `+-commutative_binary64_690` `sum-log_binary64_851` `pow-prod-down_binary64_831`

Counts

4 → 96

Calls

4 calls:

10.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
10.0ms	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))
7.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
7.0ms	(*.f64 1/45 (pow.f64 x 3))

series262.0ms (2.7%)

Counts

4 → 15

Calls

4 calls:

99.0ms	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))
82.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
50.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
31.0ms	(*.f64 1/45 (pow.f64 x 3))

Compiler

Compiled 358 to 334 computations (6.7% saved)

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4873	1199
1	4873	1199

prune131.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	7	1	8
Picked	0	1	1
Done	0	1	1
Total	116	5	121

Error

Counts

121 → 5

Compiler

Compiled 2003 to 1693 computations (15.5% saved)

regimes152.0ms (1.6%)

Accuracy

Total 0.4b remaining (85.2%)

Threshold costs 0.4b (85.2%)

Compiler

Compiled 1502 to 1283 computations (14.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms (0%)

sample7.6s (78.2%)

Algorithm

1×

intervals

Results

5.4s	4038×	body	2048	valid
700.0ms	2044×	body	1024	valid
157.0ms	8000×	pre	128	true
133.0ms	971×	body	512	valid
114.0ms	220×	body	4096	valid
42.0ms	474×	body	256	valid
12.0ms	253×	body	128	valid

Compiler

Compiled 768 to 654 computations (14.8% saved)

Details

analyze6.0ms (0.1%)

sample202.0ms (2.1%)

simplify99.0ms (1%)

prune7.0ms (0.1%)

localize5.0ms (0.1%)

rewrite27.0ms (0.3%)

series154.0ms (1.6%)

simplify86.0ms (0.9%)

prune72.0ms (0.7%)

localize6.0ms (0.1%)

rewrite21.0ms (0.2%)

series127.0ms (1.3%)

simplify98.0ms (1%)

prune68.0ms (0.7%)

localize8.0ms (0.1%)

rewrite33.0ms (0.3%)

series215.0ms (2.2%)

simplify85.0ms (0.9%)

prune113.0ms (1.2%)

localize12.0ms (0.1%)

rewrite42.0ms (0.4%)

series262.0ms (2.7%)

simplify92.0ms (0.9%)

prune131.0ms (1.3%)

regimes152.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.6s (78.2%)

Profiling