Details

analyze5.0ms (0%)

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)

sample207.0ms (2.1%)

Algorithm

1×

intervals

Results

161.0ms	131×	body	2048	valid
25.0ms	66×	body	1024	valid
5.0ms	256×	pre	128	true
5.0ms	34×	body	512	valid
2.0ms	3×	body	4096	valid
1.0ms	14×	body	256	valid
0.0ms	8×	body	128	valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	12
1	72	12

prune2.0ms (0%)

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

60.0b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
0.0b	(/.f64 1 (tan.f64 x))
0.0b	(/.f64 1 (tan.f64 x))
2.2b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite28.0ms (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

4 calls:

17.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms	(/.f64 1 (tan.f64 x))
0.0ms	(/.f64 1 (tan.f64 x))
0.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series141.0ms (1.4%)

Counts

2 → 11

Calls

2 calls:

84.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
58.0ms	(/.f64 1 (tan.f64 x))

Compiler

Compiled 171 to 140 computations (18.1% saved)

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5185	1101

prune96.0ms (1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	1	86

Error

0.3b

Counts

86 → 1

Compiler

Compiled 1051 to 646 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 6 expressions with local error:

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

rewrite19.0ms (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

6 calls:

7.0ms	(*.f64 1/45 (pow.f64 x 3))
4.0ms	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
4.0ms	(*.f64 x 1/3)
0.0ms	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
0.0ms	(*.f64 1/45 (pow.f64 x 3))

series123.0ms (1.2%)

Counts

3 → 12

Calls

3 calls:

72.0ms	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
33.0ms	(*.f64 1/45 (pow.f64 x 3))
18.0ms	(*.f64 x 1/3)

Compiler

Compiled 175 to 157 computations (10.3% saved)

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4920	699
1	4920	699

prune74.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	6	73

Error

0.1b

Counts

73 → 6

Compiler

Compiled 998 to 762 computations (23.6% saved)

localize10.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 1/3 (cbrt.f64 x)))
0.4b	(*.f64 1/3 (cbrt.f64 x))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.0b	(+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 1/3 (cbrt.f64 x))) (.f64 1/45 (pow.f64 x 3)))
0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_791`
23×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
11×	`pow1_binary64_821`
9×	`pow1/3_binary64_842`
6×	`add-exp-log_binary64_798` `swap-sqr_binary64_727` `associate-r_binary64_700` `associate-l_binary64_701`
4×	`unswap-sqr_binary64_728` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
2×	`pow-sqr_binary64_733` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831`
1×	`pow2_binary64_841` `prod-exp_binary64_809` `pow-plus_binary64_823` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`

Counts

4 → 73

Calls

8 calls:

9.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 1/3 (cbrt.f64 x))) (.f64 1/45 (pow.f64 x 3)))

series312.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
76.0ms	(cbrt.f64 x)
72.0ms	(cbrt.f64 x)
71.0ms	(cbrt.f64 x)

Compiler

Compiled 442 to 358 computations (19% saved)

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune92.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	82	9	91

Error

0.1b

Counts

91 → 9

Compiler

Compiled 1700 to 993 computations (41.6% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 x 1/3)
0.3b	(.f64 (.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (.f64 x 1/3))) (cbrt.f64 (*.f64 x 1/3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (.f64 x 1/3))) (cbrt.f64 (.f64 x 1/3))) (.f64 1/45 (pow.f64 x 3)))
0.5b	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
0.7b	(cbrt.f64 (*.f64 x 1/3))
0.7b	(cbrt.f64 (*.f64 x 1/3))
0.7b	(cbrt.f64 (*.f64 x 1/3))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64_821`
10×	`add-sqr-sqrt_binary64_782`
9×	`pow1/3_binary64_842`
8×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
7×	`cbrt-prod_binary64_791`
6×	`add-exp-log_binary64_798`
4×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `swap-sqr_binary64_727` `associate-r_binary64_700` `associate-l_binary64_701`
2×	`pow-sqr_binary64_733` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831`
1×	`pow2_binary64_841` `unswap-sqr_binary64_728` `prod-exp_binary64_809` `pow-plus_binary64_823` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`

Counts

4 → 58

Calls

8 calls:

6.0ms	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
2.0ms	(cbrt.f64 (*.f64 x 1/3))
2.0ms	(cbrt.f64 (*.f64 x 1/3))
2.0ms	(cbrt.f64 (*.f64 x 1/3))
0.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (.f64 x 1/3))) (cbrt.f64 (.f64 x 1/3))) (.f64 1/45 (pow.f64 x 3)))

series385.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
93.0ms	(cbrt.f64 (*.f64 x 1/3))
92.0ms	(cbrt.f64 (*.f64 x 1/3))
83.0ms	(cbrt.f64 (*.f64 x 1/3))

Compiler

Compiled 534 to 468 computations (12.4% saved)

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5115	556

prune92.0ms (0.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	66	13	79

Error

0.1b

Counts

79 → 13

Compiler

Compiled 1497 to 1206 computations (19.4% saved)

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	435	1019
1	435	1019

regimes149.0ms (1.5%)

Compiler: Compiled 1405 to 1128 computations (19.7% saved)

bsearch0.0ms (0%)

regimes9.0ms (0.1%)

Compiler: Compiled 8 to 11 computations (-37.5% saved)

bsearch0.0ms (0%)

regimes10.0ms (0.1%)

Accuracy

Total 0.3b remaining (66.3%)

Threshold costs 0.3b (66.3%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch2.0ms (0%)

Compiler: Compiled 16 to 15 computations (6.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	22
1	15	22

end0.0ms (0%)

sample7.8s (77.5%)

Algorithm

1×

intervals

Results

5.5s	4040×	body	2048	valid
729.0ms	2011×	body	1024	valid
161.0ms	8000×	pre	128	true
137.0ms	995×	body	512	valid
120.0ms	220×	body	4096	valid
45.0ms	514×	body	256	valid
11.0ms	220×	body	128	valid

Compiler

Compiled 710 to 569 computations (19.9% saved)

Pareto

0.7960425858218985

Details

analyze5.0ms (0%)

sample207.0ms (2.1%)

simplify101.0ms (1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite28.0ms (0.3%)

series141.0ms (1.4%)

simplify84.0ms (0.8%)

prune96.0ms (1%)

localize6.0ms (0.1%)

rewrite19.0ms (0.2%)

series123.0ms (1.2%)

simplify97.0ms (1%)

prune74.0ms (0.7%)

localize10.0ms (0.1%)

rewrite18.0ms (0.2%)

series312.0ms (3.1%)

simplify76.0ms (0.8%)

prune92.0ms (0.9%)

localize11.0ms (0.1%)

rewrite19.0ms (0.2%)

series385.0ms (3.8%)

simplify62.0ms (0.6%)

prune92.0ms (0.9%)

simplify19.0ms (0.2%)

regimes149.0ms (1.5%)

bsearch0.0ms (0%)

regimes9.0ms (0.1%)

bsearch0.0ms (0%)

regimes10.0ms (0.1%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.8s (77.5%)

Profiling