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)

sample96.0ms (1.6%)

Algorithm

1×

intervals

Results

45.0ms	71×	body	2048	valid
35.0ms	123×	body	1024	valid
7.0ms	38×	body	512	valid
2.0ms	16×	body	256	valid
1.0ms	8×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify177.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

Merged error: 42.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.4b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0b	(cos.f64 (+.f64 x eps))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64_113` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
2×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135` `cos-sum_binary64_208` `add-cube-cbrt_binary64_109`
1×	`associate--l-_binary64_17` `distribute-lft-out--_binary64_31` `sub-neg_binary64_70` `flip--_binary64_52` `difference-of-squares_binary64_46` `flip3--_binary64_81` `diff-log_binary64_166` `diff-cos_binary64_225`

Counts

2 → 23

Calls

2 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

series99.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

72.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
26.0ms	(cos.f64 (+.f64 x eps))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4863	429
1	4863	429

prune35.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	21	8	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	8	30

Merged error: 0.4b

Counts

30 → 8

Compiler

Compiled 494 to 186 computations (62.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_77`
11×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `pow1_binary64_135`
9×	`add-log-exp_binary64_113` `add-sqr-sqrt_binary64_98`
7×	`add-cube-cbrt_binary64_109`
6×	`associate-l_binary64_20`
4×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123` `associate-r_binary64_19`
3×	`distribute-lft-out_binary64_30` `sum-log_binary64_165`
2×	`sin-mult_binary64_229` `*-commutative_binary64_10`
1×	`flip-+_binary64_51` `flip3-+_binary64_80` `+-commutative_binary64_9` `associate-*r/_binary64_21` `unswap-sqr_binary64_45` `associate-+r+_binary64_11`

Counts

4 → 60

Calls

4 calls:

14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
13.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series290.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
96.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
44.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
32.0ms	(+.f64 x (+.f64 x eps))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4969	1369
1	4969	1369

prune98.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	63	9	72
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	69	11	80

Merged error: 0.4b

Counts

80 → 11

Compiler

Compiled 1680 to 1111 computations (33.9% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.3b	(.f64 (.f64 (sin.f64 (/.f64 eps 2)) -2) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_77`
8×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `pow1_binary64_135`
4×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
3×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123` `distribute-lft-out_binary64_30` `sum-log_binary64_165` `associate-r_binary64_19`
1×	`associate-l_binary64_20` `flip-+_binary64_51` `flip3-+_binary64_80` `+-commutative_binary64_9` `*-commutative_binary64_10` `associate-+r+_binary64_11`

Counts

3 → 40

Calls

3 calls:

12.0ms	(.f64 (.f64 (sin.f64 (/.f64 eps 2)) -2) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series184.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

113.0ms	(.f64 (.f64 (sin.f64 (/.f64 eps 2)) -2) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
38.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
33.0ms	(+.f64 x (+.f64 x eps))

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5054	822

prune61.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	49	11	60

Merged error: 0.4b

Counts

60 → 11

Compiler

Compiled 1177 to 776 computations (34.1% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.5b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
5.4b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
5.4b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
5.4b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113` `pow1_binary64_135` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
3×	`sin-mult_binary64_229` `cbrt-div_binary64_106` `cbrt-prod_binary64_105` `pow1/3_binary64_156`

Counts

4 → 37

Calls

4 calls:

11.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
10.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
9.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series828.0ms (14%)

Counts

4 → 12

Calls

4 calls:

267.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
266.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
260.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
33.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4855	1133
1	4855	1133

prune112.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	49	11	60

Merged error: 0.4b

Counts

60 → 11

Compiler

Compiled 2536 to 1598 computations (37% saved)

regimes119.0ms (2%)

Compiler: Compiled 502 to 396 computations (21.1% saved)

bsearch74.0ms (1.3%)

Steps

Iters	Range		Point
9	212430655738.5041	1.1029687062456818e+19	215873367925.38773
9	-4.411325659351658e-05	-2.1236664781287498e-13	-3.7601160680286725e-06

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	81
1	83	81

end0.0ms (0%)

sample3.3s (55.4%)

Algorithm

1×

intervals

Results

1.3s	2047×	body	2048	valid
1.2s	3905×	body	1024	valid
227.0ms	1283×	body	512	valid
67.0ms	509×	body	256	valid
23.0ms	254×	body	128	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 308 to 232 computations (24.7% saved)

Details

analyze2.0ms (0%)

sample96.0ms (1.6%)

simplify177.0ms (3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite13.0ms (0.2%)

series99.0ms (1.7%)

simplify98.0ms (1.7%)

prune35.0ms (0.6%)

localize13.0ms (0.2%)

rewrite45.0ms (0.8%)

series290.0ms (4.9%)

simplify57.0ms (1%)

prune98.0ms (1.7%)

localize13.0ms (0.2%)

rewrite29.0ms (0.5%)

series184.0ms (3.1%)

simplify52.0ms (0.9%)

prune61.0ms (1%)

localize18.0ms (0.3%)

rewrite43.0ms (0.7%)

series828.0ms (14%)

simplify74.0ms (1.2%)

prune112.0ms (1.9%)

regimes119.0ms (2%)

bsearch74.0ms (1.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (55.4%)

Profiling