Details

analyze2.0ms

Algorithm

Search

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

sample104.0ms

Algorithm

intervals

Results

50.0ms	112×	body	1280	valid
23.0ms	24×	body	2560	valid
15.0ms	57×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	31×	body	80	valid
1.0ms	9×	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

prune3.0ms

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: 37.3b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

1.0b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.3b	(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))

series20.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

simplify53.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5348	268

prune38.0ms

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: 0.4b

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)))
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite23.0ms

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

series23.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+.f64 x (+.f64 x eps))
12.0ms	(*.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))

simplify68.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5169	541

prune80.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	43	11	54

Merged error: 0.3b

Counts

54 → 11

localize17.0ms

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))))
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite40.0ms

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(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)))))
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))

simplify55.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5064	940

prune96.0ms

Filtered

52 candidates to 73 candidates (-40.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	74	10	84

Merged error: 0.3b

Counts

84 → 10

localize15.0ms

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)))
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
0.6b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
3.3b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite25.0ms

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:

8.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (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))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
10.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series41.0ms

Counts

4 → 12

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)))
6.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
16.0ms	(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 (32.0ms)

Iter	Nodes	Cost
0	4924	1255
1	4924	1255

prune82.0ms

Filtered

57 candidates to 97 candidates (-70.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Merged error: 0.3b

Counts

107 → 10

regimes159.0ms

Accuracy

97.5% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 15.0b

bsearch64.0ms

Steps

Iters	Range		Point
9	3.157025505158146e-29	4.740471739071633e-22	4.641753169220233e-22
6	-7.919883562745137e-05	-1.057639949449253e-05	-1.0749927920685414e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	38
1	45	38

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3290×	body	1280	valid
609.0ms	646×	body	2560	valid
510.0ms	1853×	body	640	valid
153.0ms	767×	body	320	valid
62.0ms	1067×	body	80	valid
49.0ms	377×	body	160	valid

Details

analyze2.0ms

sample104.0ms

simplify7.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series20.0ms

simplify53.0ms

prune38.0ms

localize12.0ms

rewrite23.0ms

series23.0ms

simplify68.0ms

prune80.0ms

localize17.0ms

rewrite40.0ms

series36.0ms

simplify55.0ms

prune96.0ms

localize15.0ms

rewrite25.0ms

series41.0ms

simplify43.0ms

prune82.0ms

regimes159.0ms

bsearch64.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling