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)

sample91.0ms (1.7%)

Algorithm

1×

intervals

Results

36.0ms	104×	body	1024	valid
31.0ms	43×	body	2048	valid
10.0ms	46×	body	512	valid
4.0ms	26×	body	256	valid
3.0ms	37×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

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

Merged error: 37.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.0b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.8b	(sin.f64 (+.f64 x eps))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
2×	`pow1_binary64` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `diff-sin_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

2 → 26

Calls

2 calls:

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

series96.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

66.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
30.0ms	(sin.f64 (+.f64 x eps))

simplify57.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5045	441

prune67.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Merged error: 0.5b

Counts

33 → 3

Compiler

Compiled 872 to 459 computations (47.4% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.6b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-cos-mult_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

3 → 41

Calls

3 calls:

10.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(+.f64 x (+.f64 x eps))

series152.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

83.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
37.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
32.0ms	(+.f64 x (+.f64 x eps))

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4828	830
1	4828	830

prune161.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	44	9	53

Merged error: 0.4b

Counts

53 → 9

Compiler

Compiled 2618 to 1883 computations (28.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
4.6b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
15×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

13.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))

series263.0ms (5%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
85.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
35.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
32.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4860	1942
1	4860	1942

prune248.0ms (4.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	96	10	106

Merged error: 0.4b

Counts

106 → 10

Compiler

Compiled 4152 to 2979 computations (28.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 2)
0.5b	(cbrt.f64 (*.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 2) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
4.6b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.6b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`unpow2_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow3_binary64` `cbrt-prod_binary64` `pow-exp_binary64`

Counts

4 → 42

Calls

4 calls:

8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.0ms	(cbrt.f64 (*.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 2) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 2)

series175.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 2)
38.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
37.0ms	(cbrt.f64 (*.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 2) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
33.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4846	778
1	4846	778

prune239.0ms (4.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	54	10	64

Merged error: 0.4b

Counts

64 → 10

Compiler

Compiled 2035 to 1350 computations (33.7% saved)

regimes66.0ms (1.2%)

Compiler: Compiled 452 to 364 computations (19.5% saved)

bsearch85.0ms (1.6%)

Steps

Iters	Range		Point
9	3.3830031559041477e-21	5.146542428659821e-12	5.038477056110928e-12
8	-1.393243083081321e-06	-1.2851299000772763e-09	-7.005274697828146e-09

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	81
1	49	81

end0.0ms (0%)

sample3.2s (60%)

Algorithm

1×

intervals

Results

1.3s	3444×	body	1024	valid
912.0ms	1193×	body	2048	valid
308.0ms	1392×	body	512	valid
92.0ms	1351×	body	128	valid
83.0ms	618×	body	256	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 296 to 228 computations (23% saved)

Details

analyze2.0ms (0%)

sample91.0ms (1.7%)

simplify10.0ms (0.2%)

prune7.0ms (0.1%)

localize9.0ms (0.2%)

rewrite14.0ms (0.3%)

series96.0ms (1.8%)

simplify57.0ms (1.1%)

prune67.0ms (1.3%)

localize12.0ms (0.2%)

rewrite26.0ms (0.5%)

series152.0ms (2.9%)

simplify84.0ms (1.6%)

prune161.0ms (3%)

localize15.0ms (0.3%)

rewrite34.0ms (0.6%)

series263.0ms (5%)

simplify92.0ms (1.7%)

prune248.0ms (4.7%)

localize16.0ms (0.3%)

rewrite26.0ms (0.5%)

series175.0ms (3.3%)

simplify76.0ms (1.4%)

prune239.0ms (4.5%)

regimes66.0ms (1.2%)

bsearch85.0ms (1.6%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.2s (60%)

Profiling