Details

analyze661.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
7.8%	92%	0.2%	8
16.4%	83.4%	0.2%	9
23.8%	76%	0.2%	10
25.1%	74.7%	0.2%	11
38.1%	59.4%	2.5%	12
41.8%	55.3%	2.9%	13
46.5%	50.3%	3.1%	14

sample22.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
2.0ms	53×	body	80	invalid

simplify200.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (198.0ms)

Iter	Nodes	Cost
0	1483	11
1	1483	11

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: 4.3b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
0.0b	(/.f64 t (-.f64 1 z))
4.2b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64` `difference-of-squares_binary64`
12×	`distribute-lft-out--_binary64`
10×	`associate-r_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `associate-r/_binary64` `associate-l_binary64` `associate-/l_binary64` `flip--_binary64`
2×	`associate-/r/_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

3 → 90

Calls

3 calls:

20.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
6.0ms	(/.f64 t (-.f64 1 z))
28.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series34.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
9.0ms	(/.f64 t (-.f64 1 z))
16.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

simplify49.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5441	1135

prune121.0ms

Filtered

72 candidates to 99 candidates (-37.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	9	100

Merged error: 0.0b

Counts

100 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 z))
0.0b	(-.f64 (/.f64 y z) (*.f64 t (/.f64 1 (-.f64 1 z))))
0.1b	(*.f64 t (/.f64 1 (-.f64 1 z)))
4.2b	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
38×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
27×	`associate-r_binary64`
19×	`add-exp-log_binary64`
14×	`difference-of-squares_binary64`
13×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`associate-*r/_binary64` `distribute-lft-out--_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l*_binary64`
5×	`prod-exp_binary64`
4×	`flip3--_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64` `flip--_binary64` `frac-sub_binary64`
3×	`sub-neg_binary64` `cbrt-unprod_binary64` `associate-/l*_binary64` `un-div-inv_binary64`
2×	`pow-prod-down_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 129

Calls

4 calls:

6.0ms	(/.f64 1 (-.f64 1 z))
7.0ms	(-.f64 (/.f64 y z) (*.f64 t (/.f64 1 (-.f64 1 z))))
14.0ms	(*.f64 t (/.f64 1 (-.f64 1 z)))
9.0ms	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/.f64 1 (-.f64 1 z))
9.0ms	(-.f64 (/.f64 y z) (*.f64 t (/.f64 1 (-.f64 1 z))))
6.0ms	(*.f64 t (/.f64 1 (-.f64 1 z)))
17.0ms	(.f64 x (-.f64 (/.f64 y z) (.f64 t (/.f64 1 (-.f64 1 z)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5544	1327

prune135.0ms

Filtered

88 candidates to 141 candidates (-60.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	141	9	150

Merged error: 0.0b

Counts

150 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

4.2b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
5.0b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
5.0b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
5.0b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
12×	`associate-*r/_binary64`
10×	`associate-r_binary64`
9×	`cbrt-div_binary64`
8×	`times-frac_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-sub_binary64`
3×	`pow1/3_binary64` `associate-l_binary64` `cbrt-prod_binary64`
2×	`sub-neg_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 66

Calls

4 calls:

25.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
22.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
25.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
23.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
57.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
60.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
60.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5126	1103

prune130.0ms

Filtered

64 candidates to 78 candidates (-21.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	6	6
Picked	0	1	1
Done	1	1	2
Total	77	10	87

Merged error: 0.0b

Counts

87 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

4.2b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
5.0b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
5.0b	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
6.0b	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
12×	`cbrt-prod_binary64`
10×	`associate-r_binary64`
9×	`cbrt-div_binary64` `associate-*r/_binary64`
8×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `frac-sub_binary64`
3×	`pow1/3_binary64` `associate-l_binary64`
2×	`sub-neg_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

24.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
24.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
21.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
20.0ms	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series166.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
58.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
59.0ms	(cbrt.f64 (*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
33.0ms	(cbrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4961	1288
1	4961	1288

prune120.0ms

Filtered

74 candidates to 87 candidates (-17.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	87	10	97

Merged error: 0.0b

Counts

97 → 10

regimes665.0ms

Accuracy

95.6% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 4.4b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	155	115
1	155	115

end0.0ms

sample608.0ms

Algorithm

intervals

Results

297.0ms	8000×	body	80	valid
62.0ms	1773×	body	80	invalid

Details

analyze661.0ms

sample22.0ms

simplify200.0ms

prune4.0ms

localize8.0ms

rewrite58.0ms

series34.0ms

simplify49.0ms

prune121.0ms

localize9.0ms

rewrite42.0ms

series34.0ms

simplify57.0ms

prune135.0ms

localize13.0ms

rewrite98.0ms

series194.0ms

simplify63.0ms

prune130.0ms

localize19.0ms

rewrite91.0ms

series166.0ms

simplify51.0ms

prune120.0ms

regimes665.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample608.0ms

Profiling