Details

analyze1.0ms (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)

sample94.0ms (1.7%)

Algorithm

1×

intervals

Results

52.0ms	147×	body	1280	valid
16.0ms	14×	body	2560	valid
14.0ms	64×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	4×	body	80	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	73	11
1	73	11

prune4.0ms (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: 39.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.8b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0b	(cos.f64 (+.f64 x eps))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cos-sum_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `associate--l-_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-cos_binary64`

Counts

2 → 23

Calls

2 calls:

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

series18.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

10.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
8.0ms	(cos.f64 (+.f64 x eps))

simplify45.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5001	429

prune39.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	20	9	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	9	30

Merged error: 0.6b

Counts

30 → 9

Compiler

Compiled 511 to 196 computations (61.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`distribute-lft-out_binary64` `sum-log_binary64`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

4 → 60

Calls

4 calls:

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

series37.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
12.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.0ms	(+.f64 x (+.f64 x eps))

simplify95.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4909	1369
1	4909	1369

prune89.0ms (1.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	61	11	72
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	66	15	81

Merged error: 0.5b

Counts

81 → 15

Compiler

Compiled 1752 to 1162 computations (33.7% saved)

localize16.0ms (0.3%)

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)))
4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`

Counts

4 → 40

Calls

4 calls:

8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 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)))

series54.0ms (1%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
15.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
15.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
6.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5503	710

prune93.0ms (1.7%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	50	17	67

Merged error: 0.5b

Counts

67 → 17

Compiler

Compiled 2089 to 1548 computations (25.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.2b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
6.2b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
6.2b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`cbrt-div_binary64` `pow1/3_binary64` `sin-mult_binary64` `cbrt-prod_binary64`

Counts

4 → 37

Calls

4 calls:

9.0ms	(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))))
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))

series100.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
30.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
30.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
6.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify86.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5059	1133

prune72.0ms (1.3%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	1	13	14
Picked	0	1	1
Done	0	2	2
Total	49	17	66

Merged error: 0.5b

Counts

66 → 17

Compiler

Compiled 2536 to 1598 computations (37% saved)

regimes164.0ms (3.1%)

Compiler: Compiled 870 to 662 computations (23.9% saved)

bsearch62.0ms (1.2%)

Steps

Iters	Range		Point
8	0.022234189668408653	24.73758204524559	0.027486047656807233
8	-2.893503646462405e-07	-2.237533505506086e-10	-2.8455796645710814e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	83	81
1	83	81

end0.0ms (0%)

sample4.1s (76.2%)

Algorithm

1×

intervals

Results

1.8s	4569×	body	1280	valid
577.0ms	623×	body	2560	valid
394.0ms	1765×	body	640	valid
106.0ms	685×	body	320	valid
31.0ms	293×	body	160	valid
4.0ms	65×	body	80	valid

Compiler

Compiled 492 to 365 computations (25.8% saved)

Details

analyze1.0ms (0%)

sample94.0ms (1.7%)

simplify15.0ms (0.3%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

rewrite12.0ms (0.2%)

series18.0ms (0.3%)

simplify45.0ms (0.8%)

prune39.0ms (0.7%)

localize12.0ms (0.2%)

rewrite39.0ms (0.7%)

series37.0ms (0.7%)

simplify95.0ms (1.8%)

prune89.0ms (1.7%)

localize16.0ms (0.3%)

rewrite15.0ms (0.3%)

series54.0ms (1%)

simplify54.0ms (1%)

prune93.0ms (1.7%)

localize17.0ms (0.3%)

rewrite35.0ms (0.6%)

series100.0ms (1.8%)

simplify86.0ms (1.6%)

prune72.0ms (1.3%)

regimes164.0ms (3.1%)

bsearch62.0ms (1.2%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample4.1s (76.2%)

Profiling