Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample24.0ms

Algorithm

intervals

Results

8.0ms	52×	body	1280	valid
5.0ms	38×	body	640	valid
4.0ms	139×	body	80	valid
2.0ms	20×	body	320	valid
0.0ms	7×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	680	13
1	680	13

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: 27.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.2b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
47×	`add-sqr-sqrt_binary64`
18×	`distribute-lft-out--_binary64`
16×	`distribute-lft-out_binary64`
15×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64`
5×	`difference-of-sqr-1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64`

Counts

2 → 80

Calls

2 calls:

9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
39.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series10.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
7.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify55.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5769	1221

prune77.0ms

Filtered

51 candidates to 86 candidates (-68.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Merged error: 0.1b

Counts

87 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (-.f64 x 1))
0.0b	(*.f64 (+.f64 x 1) (+.f64 x 1))
0.0b	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 (*.f64 x x) -1))
16.0b	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/_binary64`
36×	`*-un-lft-identity_binary64`
32×	`frac-sub_binary64`
31×	`flip3-+_binary64` `flip-+_binary64`
27×	`add-sqr-sqrt_binary64`
20×	`frac-times_binary64`
19×	`flip3--_binary64` `add-cube-cbrt_binary64` `flip--_binary64`
18×	`associate-/l/_binary64`
13×	`pow1_binary64`
12×	`times-frac_binary64`
11×	`associate-r_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-*l/_binary64`
7×	`associate-l_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `distribute-lft-out_binary64`
5×	`sub-neg_binary64`
4×	`associate-/r*_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-sqr--1_binary64`
3×	`associate-/l*_binary64`
2×	`pow-prod-down_binary64` `associate--r+_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `associate--l+_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `pow-prod-up_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `pow-plus_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 149

Calls

4 calls:

8.0ms	(*.f64 x (-.f64 x 1))
10.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))
15.0ms	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 (*.f64 x x) -1))
10.0ms	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))

series18.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 x (-.f64 x 1))
2.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))
8.0ms	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 (*.f64 x x) -1))
4.0ms	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))

simplify82.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5095	2614

prune146.0ms

Filtered

114 candidates to 161 candidates (-41.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	162	3	165

Merged error: 0.0b

Counts

165 → 3

localize6.0ms

Local error

Found 1 expressions with local error:

13.1b

(/.f64 (-.f64 -1 (*.f64 x 3)) (+.f64 (*.f64 x x) -1))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`associate-/r*_binary64` `difference-of-sqr--1_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

1 → 36

Calls

1 calls:

8.0ms

(/.f64 (-.f64 -1 (*.f64 x 3)) (+.f64 (*.f64 x x) -1))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(/.f64 (-.f64 -1 (*.f64 x 3)) (+.f64 (*.f64 x x) -1))

simplify68.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4919	627
1	4919	627

prune38.0ms

Filtered

33 candidates to 39 candidates (-18.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0b

Counts

42 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/.f64 1 (/.f64 (+.f64 -1 (.f64 x x)) (-.f64 -1 (.f64 x 3))))
13.1b	(/.f64 (+.f64 -1 (.f64 x x)) (-.f64 -1 (.f64 x 3)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
11×	`associate-/r/_binary64`
9×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`cbrt-undiv_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`flip3-+_binary64` `inv-pow_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

2 → 115

Calls

2 calls:

9.0ms	(/.f64 1 (/.f64 (+.f64 -1 (.f64 x x)) (-.f64 -1 (.f64 x 3))))
7.0ms	(/.f64 (+.f64 -1 (.f64 x x)) (-.f64 -1 (.f64 x 3)))

series8.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (+.f64 -1 (.f64 x x)) (-.f64 -1 (.f64 x 3))))
4.0ms	(/.f64 (+.f64 -1 (.f64 x x)) (-.f64 -1 (.f64 x 3)))

simplify57.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5151	2270

prune72.0ms

Filtered

79 candidates to 121 candidates (-53.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	121	4	125

Merged error: 0b

Counts

125 → 4

regimes31.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.4b

bsearch28.0ms

Steps

Iters	Range		Point
7	175085410498400.8	34742031841824348.0	179310016481811.53
7	-4.362060889630777e+55	-2.484560983628535e+54	-1.7941879771824913e+55

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	37
1	63	37

end0.0ms

sample745.0ms

Algorithm

intervals

Results

277.0ms	1779×	body	1280	valid
148.0ms	1197×	body	640	valid
136.0ms	4068×	body	80	valid
62.0ms	658×	body	320	valid
19.0ms	298×	body	160	valid

Details

analyze4.0ms

sample24.0ms

simplify60.0ms

prune2.0ms

localize6.0ms

rewrite52.0ms

series10.0ms

simplify55.0ms

prune77.0ms

localize9.0ms

rewrite50.0ms

series18.0ms

simplify82.0ms

prune146.0ms

localize6.0ms

rewrite9.0ms

series4.0ms

simplify68.0ms

prune38.0ms

localize7.0ms

rewrite22.0ms

series8.0ms

simplify57.0ms

prune72.0ms

regimes31.0ms

bsearch28.0ms

simplify2.0ms

end0.0ms

sample745.0ms

Profiling