Details

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample206.0ms

Algorithm

intervals

Results

110.0ms	46×	body	2560	valid
62.0ms	91×	body	1280	valid
14.0ms	52×	body	640	valid
6.0ms	35×	body	320	valid
3.0ms	19×	body	160	valid
1.0ms	13×	body	80	valid

simplify465.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

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: 29.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.1b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 x (sin.f64 x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 78

Calls

3 calls:

19.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
6.0ms	(-.f64 x (sin.f64 x))

series39.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
12.0ms	(-.f64 x (tan.f64 x))
15.0ms	(-.f64 x (sin.f64 x))

simplify71.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune52.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(.f64 (.f64 x x) 9/40)
0.1b	(*.f64 27/2800 (pow.f64 x 4))
17.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 57

Calls

3 calls:

6.0ms	(.f64 (.f64 x x) 9/40)
6.0ms	(*.f64 27/2800 (pow.f64 x 4))
10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

series14.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(.f64 (.f64 x x) 9/40)
4.0ms	(*.f64 27/2800 (pow.f64 x 4))
6.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

simplify32.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4961	578
1	4961	578

prune35.0ms

Filtered

40 candidates to 66 candidates (-65.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 x) 3)
2.1b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))
33.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 x x) (.f64 (sin.f64 x) (+.f64 x (sin.f64 x)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

159×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
81×	`difference-of-squares_binary64`
75×	`times-frac_binary64`
63×	`unpow-prod-down_binary64` `cube-prod_binary64`
41×	`sqr-pow_binary64`
37×	`add-cube-cbrt_binary64`
26×	`distribute-lft-out--_binary64`
25×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`difference-cubes_binary64` `pow1_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 189

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 x) 3)
4.0ms	(-.f64 x (tan.f64 x))
12.0ms	(-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))
22.0ms	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 x x) (.f64 (sin.f64 x) (+.f64 x (sin.f64 x)))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(pow.f64 (sin.f64 x) 3)
10.0ms	(-.f64 x (tan.f64 x))
17.0ms	(-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))
24.0ms	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 x x) (.f64 (sin.f64 x) (+.f64 x (sin.f64 x)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5109	4905

prune87.0ms

Filtered

105 candidates to 201 candidates (-91.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	202	3	205

Merged error: 0.0b

Counts

205 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

2.1b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))
2.8b	(log.f64 (exp.f64 (-.f64 x (tan.f64 x))))
33.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 x x) (.f64 (sin.f64 x) (+.f64 x (sin.f64 x)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt_binary64`
90×	`*-un-lft-identity_binary64`
82×	`difference-of-squares_binary64`
75×	`times-frac_binary64`
60×	`unpow-prod-down_binary64` `cube-prod_binary64`
40×	`sqr-pow_binary64`
36×	`add-cube-cbrt_binary64`
27×	`distribute-lft-out--_binary64`
25×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
6×	`log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`difference-cubes_binary64` `pow1_binary64` `exp-prod_binary64`
4×	`log-prod_binary64`
3×	`associate-/r*_binary64` `sub-neg_binary64` `flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `div-sub_binary64` `clear-num_binary64` `exp-sum_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `log-div_binary64` `flip-+_binary64`

Counts

4 → 185

Calls

4 calls:

4.0ms	(-.f64 x (tan.f64 x))
14.0ms	(-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))
4.0ms	(log.f64 (exp.f64 (-.f64 x (tan.f64 x))))
20.0ms	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 x x) (.f64 (sin.f64 x) (+.f64 x (sin.f64 x)))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 x (tan.f64 x))
13.0ms	(-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3))
10.0ms	(log.f64 (exp.f64 (-.f64 x (tan.f64 x))))
23.0ms	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 x x) (.f64 (sin.f64 x) (+.f64 x (sin.f64 x)))))

simplify82.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4947	4987
1	4947	4987

prune98.0ms

Filtered

122 candidates to 197 candidates (-61.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	197	3	200

Merged error: 0.0b

Counts

200 → 3

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.0b

bsearch36.0ms

Steps

Iters	Range		Point
8	1.7335659165222967e-05	0.19444162343550836	0.03330002947331547
10	-1031697.7088828364	-2.160466327547021e-07	-0.02738655254074898

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	31
1	86	31

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.1s	1618×	body	2560	valid
1.6s	2682×	body	1280	valid
503.0ms	1840×	body	640	valid
180.0ms	996×	body	320	valid
64.0ms	487×	body	160	valid
30.0ms	377×	body	80	valid

Details

analyze1.2s

sample206.0ms

simplify465.0ms

prune3.0ms

localize10.0ms

rewrite33.0ms

series39.0ms

simplify71.0ms

prune52.0ms

localize9.0ms

rewrite24.0ms

series14.0ms

simplify32.0ms

prune35.0ms

localize18.0ms

rewrite51.0ms

series56.0ms

simplify52.0ms

prune87.0ms

localize19.0ms

rewrite52.0ms

series56.0ms

simplify82.0ms

prune98.0ms

regimes50.0ms

bsearch36.0ms

simplify3.0ms

end0.0ms

sample6.7s

Profiling