Details

analyze244.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample74.0ms

Algorithm

intervals

Results

38.0ms	72×	body	1280	valid
13.0ms	53×	body	640	valid
9.0ms	27×	body	2560	valid
4.0ms	23×	body	320	valid
3.0ms	72×	body	80	valid
1.0ms	9×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

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: 52.9b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

1.1b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
1.8b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
15.9b	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 42

Calls

3 calls:

6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

series21.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
10.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5075	600

prune75.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))
0.1b	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

50×	`associate-r_binary64`
49×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`unpow-prod-down_binary64` `cube-prod_binary64`
20×	`sqrt-prod_binary64`
10×	`add-exp-log_binary64`
8×	`unswap-sqr_binary64`
6×	`add-log-exp_binary64`
4×	`add-cbrt-cube_binary64` `prod-exp_binary64`
3×	`associate-r/_binary64` `associate-l*_binary64` `cube-div_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64` `div-inv_binary64` `frac-sub_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 90

Calls

2 calls:

15.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))
16.0ms	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))

series38.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))
24.0ms	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))

simplify28.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	4998	1131
1	4998	1131

prune81.0ms

Filtered

47 candidates to 96 candidates (-104.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Merged error: 0b

Counts

100 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3))))
0.2b	(/.f64 0.125 (pow.f64 x 3))
10.9b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
18×	`add-log-exp_binary64`
13×	`unpow-prod-down_binary64` `cube-prod_binary64`
12×	`associate-/r*_binary64`
10×	`add-exp-log_binary64`
9×	`distribute-lft-out_binary64`
6×	`log-prod_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `sum-log_binary64`
4×	`diff-log_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `log-div_binary64` `associate-+r+_binary64` `frac-sub_binary64` `associate--l+_binary64`
1×	`pow-to-exp_binary64` `associate-+r-_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 123

Calls

4 calls:

24.0ms	(-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))
22.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3))))
6.0ms	(/.f64 0.125 (pow.f64 x 3))
22.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))))

series28.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))
6.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3))))
5.0ms	(/.f64 0.125 (pow.f64 x 3))
11.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4984	1775
1	4984	1775

prune108.0ms

Filtered

80 candidates to 135 candidates (-68.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	135	4	139

Merged error: 0b

Counts

139 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 0.0625 (pow.f64 x 5))
0.2b	(/.f64 0.125 (pow.f64 x 3))
12.6b	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
20.1b	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `log-div_binary64`
4×	`distribute-lft-out_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/.f64 0.0625 (pow.f64 x 5))
5.0ms	(/.f64 0.125 (pow.f64 x 3))
37.0ms	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
35.0ms	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/.f64 0.0625 (pow.f64 x 5))
5.0ms	(/.f64 0.125 (pow.f64 x 3))
12.0ms	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
7.0ms	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))

simplify57.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5361	2493

prune168.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	171	4	175

Merged error: 0b

Counts

175 → 4

regimes39.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.4b

bsearch29.0ms

Steps

Iters	Range		Point
10	1.4332844389409512e-13	15.167647912522936	0.887192876086426
10	-270.7734377663163	-7.923252455646139e-14	-1.010460937713024

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	55
1	117	55

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2411×	body	1280	valid
428.0ms	1555×	body	640	valid
273.0ms	832×	body	2560	valid
127.0ms	763×	body	320	valid
85.0ms	2076×	body	80	valid
37.0ms	363×	body	160	valid

Details

analyze244.0ms

sample74.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite18.0ms

series21.0ms

simplify42.0ms

prune75.0ms

localize8.0ms

rewrite35.0ms

series38.0ms

simplify28.0ms

prune81.0ms

localize9.0ms

rewrite78.0ms

series28.0ms

simplify55.0ms

prune108.0ms

localize13.0ms

rewrite88.0ms

series30.0ms

simplify57.0ms

prune168.0ms

regimes39.0ms

bsearch29.0ms

simplify3.0ms

end0.0ms

sample2.2s

Profiling