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)

sample91.0ms (1.9%)

Algorithm

1×

intervals

Results

49.0ms	112×	body	1280	valid
16.0ms	59×	body	640	valid
13.0ms	14×	body	2560	valid
4.0ms	23×	body	320	valid
2.0ms	40×	body	80	valid
1.0ms	8×	body	160	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	73	11
1	73	11

prune9.0ms (0.2%)

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: 35.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.7b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0b	(sin.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` `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 → 23

Calls

2 calls:

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

series14.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

simplify101.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5399	426

prune27.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.5b

Counts

30 → 3

Compiler

Compiled 404 to 129 computations (68.1% saved)

localize13.0ms (0.3%)

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)))
4.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite22.0ms (0.4%)

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:

8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series21.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.0ms	(+.f64 x (+.f64 x eps))

simplify98.0ms (2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5171	830

prune55.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	8	53

Merged error: 0.4b

Counts

53 → 8

Compiler

Compiled 1156 to 756 computations (34.6% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.6b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
4.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`log-prod_binary64` `exp-prod_binary64`
8×	`pow1_binary64` `log-pow_binary64`
7×	`associate-r_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64`
3×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 61

Calls

4 calls:

14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
9.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
8.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series31.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
9.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))

simplify89.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5066	1476

prune81.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	72	9	81

Merged error: 0.4b

Counts

81 → 9

Compiler

Compiled 1865 to 1243 computations (33.4% saved)

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.2b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-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×	`cbrt-prod_binary64`
1×	`pow1/3_binary64`

Counts

4 → 32

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))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))

series36.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify141.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4881	644
1	4881	644

prune59.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	44	9	53

Merged error: 0.4b

Counts

53 → 9

Compiler

Compiled 1837 to 1110 computations (39.6% saved)

regimes125.0ms (2.6%)

Compiler: Compiled 450 to 354 computations (21.3% saved)

bsearch62.0ms (1.3%)

Steps

Iters	Range		Point
8	3.3195574703473597e-10	2.0992381794616983e-07	1.181394862584651e-08
8	-2.893503646462405e-07	-2.237533505506086e-10	-8.40520369698623e-09

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	81
1	49	81

end0.0ms (0%)

sample3.6s (74.8%)

Algorithm

1×

intervals

Results

1.5s	3394×	body	1280	valid
603.0ms	623×	body	2560	valid
459.0ms	1733×	body	640	valid
143.0ms	802×	body	320	valid
65.0ms	1093×	body	80	valid
42.0ms	355×	body	160	valid

Compiler

Compiled 295 to 223 computations (24.4% saved)

Details

analyze1.0ms (0%)

sample91.0ms (1.9%)

simplify15.0ms (0.3%)

prune9.0ms (0.2%)

localize8.0ms (0.2%)

rewrite12.0ms (0.2%)

series14.0ms (0.3%)

simplify101.0ms (2.1%)

prune27.0ms (0.6%)

localize13.0ms (0.3%)

rewrite22.0ms (0.4%)

series21.0ms (0.4%)

simplify98.0ms (2%)

prune55.0ms (1.1%)

localize18.0ms (0.4%)

rewrite40.0ms (0.8%)

series31.0ms (0.6%)

simplify89.0ms (1.8%)

prune81.0ms (1.7%)

localize24.0ms (0.5%)

rewrite26.0ms (0.5%)

series36.0ms (0.7%)

simplify141.0ms (2.9%)

prune59.0ms (1.2%)

regimes125.0ms (2.6%)

bsearch62.0ms (1.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.6s (74.8%)

Profiling