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

sample26.0ms

Algorithm

intervals

Results

8.0ms	51×	body	1280	valid
6.0ms	47×	body	640	valid
4.0ms	129×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	11×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

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: 30.1b

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))
2.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite57.0ms

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:

9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))
38.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series13.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify77.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4911	1531
1	4911	1531

prune142.0ms

Filtered

77 candidates to 122 candidates (-58.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	3	123

Merged error: 0.0b

Counts

123 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.4b	(/.f64 x (+.f64 1 (pow.f64 x 3)))
7.9b	(-.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
15.7b	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 149

Calls

4 calls:

9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
8.0ms	(/.f64 x (+.f64 1 (pow.f64 x 3)))
27.0ms	(-.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
20.0ms	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))

series29.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
7.0ms	(/.f64 x (+.f64 1 (pow.f64 x 3)))
13.0ms	(-.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))

simplify49.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4959	2597
1	4959	2597

prune203.0ms

Filtered

113 candidates to 161 candidates (-42.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	160	4	164

Merged error: 0.0b

Counts

164 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt.f64 (pow.f64 (-.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x))) (/.f64 (+.f64 x 1) (-.f64 x 1))) 3))
6.4b	(/.f64 x (+.f64 1 (pow.f64 x 3)))
7.9b	(-.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
15.7b	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64` `times-frac_binary64`
18×	`associate-l_binary64`
12×	`cbrt-prod_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`frac-sub_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
7×	`cbrt-div_binary64` `distribute-lft-out_binary64` `cube-div_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `associate-*r/_binary64` `frac-times_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64`
3×	`associate-r_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `associate-/l_binary64` `associate-l/_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `pow1/3_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 122

Calls

4 calls:

29.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x))) (/.f64 (+.f64 x 1) (-.f64 x 1))) 3))
8.0ms	(/.f64 x (+.f64 1 (pow.f64 x 3)))
25.0ms	(-.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
18.0ms	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x))) (/.f64 (+.f64 x 1) (-.f64 x 1))) 3))
7.0ms	(/.f64 x (+.f64 1 (pow.f64 x 3)))
12.0ms	(-.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x))) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4942	3024
1	4942	3024

prune183.0ms

Filtered

98 candidates to 134 candidates (-36.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	134	4	138

Merged error: 0.0b

Counts

138 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

7.9b	(-.f64 (pow.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x))) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
15.7b	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))
15.7b	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))
15.7b	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64`
54×	`associate-l_binary64`
51×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
31×	`add-cube-cbrt_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`difference-of-squares_binary64`
11×	`flip3-+_binary64` `flip-+_binary64`
10×	`pow1_binary64` `cube-div_binary64`
9×	`distribute-lft-out_binary64` `associate-r_binary64`
8×	`associate-*r/_binary64` `sqr-pow_binary64` `frac-times_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
5×	`frac-sub_binary64`
4×	`unpow-prod-down_binary64` `cube-prod_binary64` `associate-*l/_binary64`
3×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`difference-cubes_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 159

Calls

4 calls:

44.0ms	(-.f64 (pow.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x))) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
18.0ms	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))
18.0ms	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))
20.0ms	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(-.f64 (pow.f64 (.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x))) 3) (pow.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) 3))
5.0ms	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))
5.0ms	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))
6.0ms	(.f64 (/.f64 x (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 1 x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5327	3923

prune677.0ms

Filtered

128 candidates to 171 candidates (-33.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	170	5	175

Merged error: 0.0b

Counts

175 → 5

regimes49.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.1b

bsearch24.0ms

Steps

Iters	Range		Point
8	63.474764878248116	106410.96103200753	9787.463873477589
10	-15803896510245.844	-1.8993785803446641	-9786.608325632764

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	50
1	81	50

end0.0ms

sample724.0ms

Algorithm

intervals

Results

264.0ms	1709×	body	1280	valid
144.0ms	1197×	body	640	valid
136.0ms	4147×	body	80	valid
57.0ms	629×	body	320	valid
20.0ms	318×	body	160	valid

Details

analyze4.0ms

sample26.0ms

simplify59.0ms

prune2.0ms

localize6.0ms

rewrite57.0ms

series13.0ms

simplify77.0ms

prune142.0ms

localize15.0ms

rewrite69.0ms

series29.0ms

simplify49.0ms

prune203.0ms

localize16.0ms

rewrite84.0ms

series37.0ms

simplify62.0ms

prune183.0ms

localize23.0ms

rewrite106.0ms

series47.0ms

simplify53.0ms

prune677.0ms

regimes49.0ms

bsearch24.0ms

simplify2.0ms

end0.0ms

sample724.0ms

Profiling