Details

analyze2.0ms

Algorithm

Search

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

sample98.0ms

Algorithm

intervals

Results

48.0ms	93×	body	1280	valid
17.0ms	18×	body	2560	valid
16.0ms	59×	body	640	valid
5.0ms	26×	body	320	valid
3.0ms	45×	body	80	valid
2.0ms	15×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune2.0ms

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: 32.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.7b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.2b	(sin.f64 (+.f64 x eps))

rewrite11.0ms

Algorithm

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))
4.0ms	(sin.f64 (+.f64 x eps))

series13.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5348	268

prune40.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	25	4	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	4	30

Merged error: 0.3b

Counts

30 → 4

localize12.0ms

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)))
2.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite21.0ms

Algorithm

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:

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

series21.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+.f64 x (+.f64 x eps))
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))

simplify64.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5169	541

prune69.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	47	7	54

Merged error: 0.2b

Counts

54 → 7

localize14.0ms

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)))
0.4b	(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))
2.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite23.0ms

Algorithm

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:

9.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
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))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series36.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
13.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
6.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify43.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4924	1255
1	4924	1255

prune91.0ms

Filtered

57 candidates to 97 candidates (-70.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	97	7	104

Merged error: 0.2b

Counts

104 → 7

localize16.0ms

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)))))
0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
2.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite41.0ms

Algorithm

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:

8.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
13.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
10.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series32.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
6.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5064	940

prune74.0ms

Filtered

54 candidates to 73 candidates (-35.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	73	7	80

Merged error: 0.2b

Counts

80 → 7

regimes124.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.5b

bsearch94.0ms

Steps

Iters	Range		Point
10	3.557075959307803e-16	2.082004678179395	1.2818489336853672e-08
11	-0.013396683979028528	-6.339096501967977e-23	-1.2815089861330691e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	51
1	47	51

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.6s	3369×	body	1280	valid
719.0ms	1846×	body	640	valid
612.0ms	626×	body	2560	valid
148.0ms	739×	body	320	valid
65.0ms	1056×	body	80	valid
50.0ms	364×	body	160	valid

Details

analyze2.0ms

sample98.0ms

simplify7.0ms

prune2.0ms

localize8.0ms

rewrite11.0ms

series13.0ms

simplify51.0ms

prune40.0ms

localize12.0ms

rewrite21.0ms

series21.0ms

simplify64.0ms

prune69.0ms

localize14.0ms

rewrite23.0ms

series36.0ms

simplify43.0ms

prune91.0ms

localize16.0ms

rewrite41.0ms

series32.0ms

simplify51.0ms

prune74.0ms

regimes124.0ms

bsearch94.0ms

simplify2.0ms

end0.0ms

sample3.4s

Profiling