Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample85.0ms (1%)

Algorithm

1×

intervals

Results

33.0ms	68×	body	2048	valid
32.0ms	112×	body	1024	valid
9.0ms	56×	body	512	valid
1.0ms	12×	body	256	valid
0.0ms	8×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify104.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

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

37.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.6b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.0b	(cos.f64 (+.f64 x eps))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

17.2b

Rules

5×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`add-log-exp_binary64_117`
3×	`add-cube-cbrt_binary64_113` `cancel-sign-sub-inv_binary64_44`
2×	`cos-sum_binary64_212` `pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
1×	`diff-cos_binary64_229` `diff-log_binary64_170` `flip3--_binary64_82` `sub-neg_binary64_71` `flip--_binary64_53` `difference-of-squares_binary64_47` `distribute-lft-out--_binary64_30` `associate--l-_binary64_16`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
5.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 382 to 101 computations (73.6% saved)

series144.0ms (1.7%)

Error

11.3b

Counts

2 → 24

Calls

2 calls:

73.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
42.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 702 to 440 computations (37.3% saved)

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5016	764

prune58.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	6	51

Error

0.2b

Counts

51 → 6

Compiler

Compiled 734 to 269 computations (63.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
0.0b	(+.f64 x (+.f64 eps x))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
1.7b	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

rewrite117.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

12×	`*-un-lft-identity_binary64_78`
11×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
9×	`add-log-exp_binary64_117` `add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113`
6×	`associate-l_binary64_19`
4×	`pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `associate-r_binary64_18`
3×	`sum-log_binary64_169` `distribute-lft-out_binary64_29`
2×	`sin-mult_binary64_233` `*-commutative_binary64_9`
1×	`unswap-sqr_binary64_46` `flip3-+_binary64_81` `flip-+_binary64_52` `associate-+r+_binary64_10` `+-commutative_binary64_8` `associate-*r/_binary64_20`

Counts

4 → 60

Calls

4 calls:

12.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
6.0ms	(+.f64 x (+.f64 eps x))

Compiler

Compiled 1452 to 895 computations (38.4% saved)

series436.0ms (5%)

Error

0.2b

Counts

4 → 48

Calls

4 calls:

145.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
124.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
64.0ms	(+.f64 x (+.f64 eps x))
53.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

Compiler

Compiled 2082 to 1744 computations (16.2% saved)

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4912	2057
1	4912	2057

prune129.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Error

0.1b

Counts

114 → 11

Compiler

Compiled 2303 to 1539 computations (33.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
6.6b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
6.6b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
6.6b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite134.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

4×	`pow1_binary64_139` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
3×	`pow1/3_binary64_160` `sin-mult_binary64_233` `cbrt-div_binary64_110` `cbrt-prod_binary64_109`

Counts

4 → 37

Calls

4 calls:

13.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
10.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
10.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 2079 to 1284 computations (38.2% saved)

series1.4s (16.5%)

Error

0.1b

Counts

4 → 42

Calls

4 calls:

420.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
416.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
407.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))))
76.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 6500 to 4751 computations (26.9% saved)

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5468	2188

prune207.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	79	11	90

Error

0.1b

Counts

90 → 11

Compiler

Compiled 4421 to 2846 computations (35.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
1.7b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

rewrite89.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

9×	`cbrt-prod_binary64_109`
7×	`add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`pow1_binary64_139` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
3×	`pow1/3_binary64_160`

Counts

4 → 40

Calls

4 calls:

9.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))

Compiler

Compiled 1389 to 1024 computations (26.3% saved)

series346.0ms (4%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

86.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
80.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
76.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
67.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 2075 to 1705 computations (17.8% saved)

simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5173	854

prune100.0ms (1.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	64	11	75

Error

0.1b

Counts

75 → 11

Compiler

Compiled 2060 to 1523 computations (26.1% saved)

regimes594.0ms (6.9%)

Accuracy

Total 0.3b remaining (57.8%)

Threshold costs 0.3b (57.8%)

Compiler

Compiled 5316 to 3911 computations (26.4% saved)

bsearch71.0ms (0.8%)

Steps

Iters	Range		Point
9	2.1116146862821702e-07	0.020014123197599813	0.003354314107967996
8	-1.7748282342909867	-0.0005848115290786374	-0.0033351182275355245

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	665	106
1	665	106

end0.0ms (0%)

sample4.2s (48.9%)

Algorithm

1×

intervals

Results

1.1s	2110×	body	2048	valid
939.0ms	3841×	body	1024	valid
232.0ms	1326×	body	512	valid
53.0ms	471×	body	256	valid
20.0ms	250×	body	128	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 1826 to 1335 computations (26.9% saved)

Details

analyze2.0ms (0%)

sample85.0ms (1%)

simplify104.0ms (1.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite42.0ms (0.5%)

series144.0ms (1.7%)

simplify63.0ms (0.7%)

prune58.0ms (0.7%)

localize11.0ms (0.1%)

rewrite117.0ms (1.4%)

series436.0ms (5%)

simplify78.0ms (0.9%)

prune129.0ms (1.5%)

localize16.0ms (0.2%)

rewrite134.0ms (1.5%)

series1.4s (16.5%)

simplify60.0ms (0.7%)

prune207.0ms (2.4%)

localize21.0ms (0.2%)

rewrite89.0ms (1%)

series346.0ms (4%)

simplify53.0ms (0.6%)

prune100.0ms (1.2%)

regimes594.0ms (6.9%)

bsearch71.0ms (0.8%)

simplify26.0ms (0.3%)

end0.0ms (0%)

sample4.2s (48.9%)

Profiling