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

sample23.0ms

Algorithm

intervals

Results

8.0ms	57×	body	1280	valid
4.0ms	38×	body	640	valid
4.0ms	136×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	12×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

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: 28.2b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
3.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 113

Calls

3 calls:

8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))
37.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series14.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.0ms	(/.f64 x (+.f64 x 1))
8.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify72.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4911	1531
1	4911	1531

prune142.0ms

Filtered

77 candidates to 122 candidates (-58.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
0.1b	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
5.5b	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
69×	`*-un-lft-identity_binary64`
56×	`times-frac_binary64`
37×	`add-cube-cbrt_binary64`
27×	`associate-r_binary64`
19×	`add-exp-log_binary64`
14×	`difference-of-squares_binary64`
13×	`add-cbrt-cube_binary64`
11×	`associate-/r*_binary64`
7×	`pow1_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64` `associate-/l*_binary64` `frac-sub_binary64`
5×	`flip3-+_binary64` `distribute-lft-out_binary64` `div-exp_binary64` `flip-+_binary64`
4×	`associate-l_binary64` `prod-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `un-div-inv_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 154

Calls

4 calls:

6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))
17.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
11.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))

series18.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/.f64 1 (-.f64 x 1))
3.0ms	(/.f64 x (+.f64 x 1))
4.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1)))
9.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (*.f64 (+.f64 x 1) (/.f64 1 (-.f64 x 1))))

simplify56.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5179	1695

prune131.0ms

Filtered

103 candidates to 166 candidates (-61.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	166	4	170

Merged error: 0.0b

Counts

170 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.1b	(.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1))
5.5b	(-.f64 (.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
16.2b	(/.f64 x (+.f64 (*.f64 x x) -1))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

10.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
14.0ms	(.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1))
20.0ms	(-.f64 (.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 x (+.f64 (*.f64 x x) -1))

series26.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1))
12.0ms	(-.f64 (.f64 (/.f64 x (+.f64 (.f64 x x) -1)) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 x (+.f64 (*.f64 x x) -1))

simplify39.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5139	2025

prune158.0ms

Filtered

123 candidates to 165 candidates (-34.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	165	4	169

Merged error: 0.0b

Counts

169 → 4

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (*.f64 x (+.f64 x 3)))
0.0b	(*.f64 x (+.f64 x 3))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-l_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip-+_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 36

Calls

2 calls:

5.0ms	(+.f64 1 (*.f64 x (+.f64 x 3)))
6.0ms	(*.f64 x (+.f64 x 3))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(+.f64 1 (*.f64 x (+.f64 x 3)))
6.0ms	(*.f64 x (+.f64 x 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4937	308
1	4937	308

prune28.0ms

Filtered

28 candidates to 42 candidates (-50.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	42	4	46

Merged error: 0.0b

Counts

46 → 4

regimes38.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.4b

bsearch24.0ms

Steps

Iters	Range		Point
8	783.9248997700159	333434.52581577527	14598.338637180132
10	-1150091520452.1025	-0.024287732823846688	-13030.927938080447

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	82	39
1	82	39

end0.0ms

sample672.0ms

Algorithm

intervals

Results

244.0ms	1665×	body	1280	valid
137.0ms	1201×	body	640	valid
128.0ms	4231×	body	80	valid
53.0ms	595×	body	320	valid
18.0ms	308×	body	160	valid

Details

analyze4.0ms

sample23.0ms

simplify69.0ms

prune2.0ms

localize6.0ms

rewrite55.0ms

series14.0ms

simplify72.0ms

prune142.0ms

localize8.0ms

rewrite45.0ms

series18.0ms

simplify56.0ms

prune131.0ms

localize9.0ms

rewrite56.0ms

series26.0ms

simplify39.0ms

prune158.0ms

localize4.0ms

rewrite12.0ms

series9.0ms

simplify67.0ms

prune28.0ms

regimes38.0ms

bsearch24.0ms

simplify2.0ms

end0.0ms

sample672.0ms

Profiling