Details

analyze521.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample39.0ms

Algorithm

intervals

Results

15.0ms	56×	body	1280	valid
7.0ms	41×	body	640	valid
6.0ms	131×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid

simplify563.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	5284	15

prune4.0ms

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: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(/.f64 (-.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`pow1_binary64`
12×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`difference-of-squares_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `associate-/r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 104

Calls

4 calls:

3.0ms	(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
7.0ms	(/.f64 (-.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series95.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
51.0ms	(/.f64 (-.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
10.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
23.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify59.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4951	1205
1	4951	1205

prune170.0ms

Filtered

82 candidates to 116 candidates (-41.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	105	11	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	11	117

Merged error: 0.0b

Counts

117 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (cos.f64 x) 2)
0.2b	(pow.f64 (cos.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `pow-unpow_binary64` `add-cube-cbrt_binary64` `unpow-prod-down_binary64` `add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow.f64 (cos.f64 x) 2)
3.0ms	(pow.f64 (cos.f64 x) 2)
3.0ms	(pow.f64 (sin.f64 x) 2)
3.0ms	(pow.f64 (sin.f64 x) 2)

series16.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (cos.f64 x) 2)
4.0ms	(pow.f64 (cos.f64 x) 2)
4.0ms	(pow.f64 (sin.f64 x) 2)
4.0ms	(pow.f64 (sin.f64 x) 2)

simplify43.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5266	424

prune95.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 0.0b

Counts

95 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1.0 (cbrt.f64 (pow.f64 (tan.f64 x) 6))) (+.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.6b	(pow.f64 (tan.f64 x) 6)
9.6b	(cbrt.f64 (pow.f64 (tan.f64 x) 6))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`
19×	`cbrt-prod_binary64`
16×	`difference-of-squares_binary64`
12×	`pow1_binary64`
10×	`unpow-prod-down_binary64`
9×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
6×	`sqr-pow_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `tan-quot_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l*_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow1/3_binary64` `pow-pow_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `pow-exp_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 112

Calls

4 calls:

10.0ms	(/.f64 (-.f64 1.0 (cbrt.f64 (pow.f64 (tan.f64 x) 6))) (+.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))))
7.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 6)
3.0ms	(cbrt.f64 (pow.f64 (tan.f64 x) 6))

series87.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/.f64 (-.f64 1.0 (cbrt.f64 (pow.f64 (tan.f64 x) 6))) (+.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))))
10.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
21.0ms	(pow.f64 (tan.f64 x) 6)
11.0ms	(cbrt.f64 (pow.f64 (tan.f64 x) 6))

simplify60.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4946	1517
1	4946	1517

prune134.0ms

Filtered

78 candidates to 124 candidates (-59.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	123	12	135

Merged error: 0.0b

Counts

135 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (sqrt.f64 1.0) (tan.f64 x))
0.2b	(/.f64 (-.f64 (sqrt.f64 1.0) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))
0.2b	(*.f64 (+.f64 (tan.f64 x) (sqrt.f64 1.0)) (/.f64 (-.f64 (sqrt.f64 1.0) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)))
0.3b	(pow.f64 (tan.f64 x) 2)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`associate-r_binary64` `add-cube-cbrt_binary64`
20×	`difference-of-squares_binary64`
14×	`distribute-lft-out_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
10×	`distribute-lft-out--_binary64` `sqrt-prod_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64`
4×	`flip3-+_binary64` `associate-/r_binary64` `associate-/r/_binary64` `associate-l*_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `unpow2_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 137

Calls

4 calls:

5.0ms	(-.f64 (sqrt.f64 1.0) (tan.f64 x))
12.0ms	(/.f64 (-.f64 (sqrt.f64 1.0) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))
22.0ms	(*.f64 (+.f64 (tan.f64 x) (sqrt.f64 1.0)) (/.f64 (-.f64 (sqrt.f64 1.0) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)))
3.0ms	(pow.f64 (tan.f64 x) 2)

series113.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 1.0) (tan.f64 x))
36.0ms	(/.f64 (-.f64 (sqrt.f64 1.0) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))
57.0ms	(*.f64 (+.f64 (tan.f64 x) (sqrt.f64 1.0)) (/.f64 (-.f64 (sqrt.f64 1.0) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)))
11.0ms	(pow.f64 (tan.f64 x) 2)

simplify69.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4963	2307
1	4963	2307

prune136.0ms

Filtered

93 candidates to 149 candidates (-60.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	149	12	161

Merged error: 0.0b

Counts

161 → 12

regimes110.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	18
1	24	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

403.0ms	1574×	body	1280	valid
203.0ms	1219×	body	640	valid
162.0ms	4244×	body	80	valid
76.0ms	641×	body	320	valid
29.0ms	322×	body	160	valid

Details

analyze521.0ms

sample39.0ms

simplify563.0ms

prune4.0ms

localize10.0ms

rewrite27.0ms

series95.0ms

simplify59.0ms

prune170.0ms

localize12.0ms

rewrite12.0ms

series16.0ms

simplify43.0ms

prune95.0ms

localize10.0ms

rewrite27.0ms

series87.0ms

simplify60.0ms

prune134.0ms

localize13.0ms

rewrite47.0ms

series113.0ms

simplify69.0ms

prune136.0ms

regimes110.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling