Details

analyze1.3s

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

sample202.0ms

Algorithm

intervals

Results

136.0ms	74×	body	2048	valid
34.0ms	82×	body	1024	valid
9.0ms	49×	body	512	valid
8.0ms	6×	body	4096	valid
3.0ms	23×	body	256	valid
2.0ms	22×	body	128	valid

simplify243.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14

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: 32.0b

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)))
2.0b	(-.f64 x (tan.f64 x))
2.0b	(-.f64 x (sin.f64 x))

rewrite29.0ms

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:

10.0ms	(/.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))

series282.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
101.0ms	(-.f64 x (tan.f64 x))
54.0ms	(-.f64 x (sin.f64 x))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4906	1795
1	4906	1795

prune62.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Merged error: 0.0b

Counts

88 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.1b	(.f64 (.f64 x x) 9/40)
15.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite28.0ms

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:

7.0ms	(*.f64 27/2800 (pow.f64 x 4))
7.0ms	(.f64 (.f64 x x) 9/40)
10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

series145.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(*.f64 27/2800 (pow.f64 x 4))
35.0ms	(.f64 (.f64 x x) 9/40)
60.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

simplify36.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5030	850

prune49.0ms

Filtered

40 candidates to 66 candidates (-65.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	65	4	69

Merged error: 0.0b

Counts

69 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4)))))
15.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
15.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
15.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
6×	`diff-log_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`sub-neg_binary64` `associate--r+_binary64` `cbrt-prod_binary64` `sum-log_binary64`
2×	`cbrt-div_binary64`
1×	`pow1/3_binary64`

Counts

4 → 52

Calls

4 calls:

9.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4)))))
10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt.f64 (-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4)))))
42.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
44.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
49.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

simplify86.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5060	1737

prune133.0ms

Filtered

47 candidates to 64 candidates (-36.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	63	5	68

Merged error: 0.0b

Counts

68 → 5

localize34.0ms

Local error

Found 4 expressions with local error:

15.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
15.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
24.0b	(/.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 -1/2 (.f64 (pow.f64 x 4) -27/2800)) 3))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) 81/1600) (.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4))) (+.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4))))))))
26.6b	(+.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 -1/2 (.f64 (pow.f64 x 4) -27/2800)) 3))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

42×	`cbrt-prod_binary64`
36×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`add-log-exp_binary64`
6×	`associate-/r_binary64` `add-exp-log_binary64` `associate-/l_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `diff-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `flip-+_binary64` `sum-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64`

Counts

4 → 101

Calls

4 calls:

10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
20.0ms	(/.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 -1/2 (.f64 (pow.f64 x 4) -27/2800)) 3))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) 81/1600) (.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4))) (+.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4))))))))
11.0ms	(+.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 -1/2 (.f64 (pow.f64 x 4) -27/2800)) 3))

series439.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
47.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
239.0ms	(/.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 -1/2 (.f64 (pow.f64 x 4) -27/2800)) 3))) (cbrt.f64 (+.f64 (.f64 (pow.f64 x 4) 81/1600) (.f64 (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4))) (+.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4))))))))
102.0ms	(+.f64 (.f64 (pow.f64 x 6) 729/64000) (pow.f64 (+.f64 -1/2 (.f64 (pow.f64 x 4) -27/2800)) 3))

simplify91.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5446	8576

prune744.0ms

Filtered

99 candidates to 113 candidates (-14.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	1	1
Picked	1	0	1
Done	1	2	3
Total	114	4	118

Merged error: 0.0b

Counts

118 → 4

regimes56.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.5b

bsearch50.0ms

Steps

Iters	Range		Point
10	0.010760024704334263	364354502.8340638	0.027512049940656768
10	-723657.9594945199	-5.153875795477029e-05	-0.028423004362203453

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	88	47
1	88	47

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.8s	1961×	body	2048	valid
1.2s	3010×	body	1024	valid
291.0ms	1497×	body	512	valid
145.0ms	117×	body	4096	valid
100.0ms	741×	body	256	valid
52.0ms	674×	body	128	valid

Details

analyze1.3s

sample202.0ms

simplify243.0ms

prune3.0ms

localize10.0ms

rewrite29.0ms

series282.0ms

simplify51.0ms

prune62.0ms

localize9.0ms

rewrite28.0ms

series145.0ms

simplify36.0ms

prune49.0ms

localize13.0ms

rewrite48.0ms

series276.0ms

simplify86.0ms

prune133.0ms

localize34.0ms

rewrite76.0ms

series439.0ms

simplify91.0ms

prune744.0ms

regimes56.0ms

bsearch50.0ms

simplify3.0ms

end0.0ms

sample5.8s

Profiling