Details

analyze647.0ms

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	128	valid
2.0ms	68×	body	128	invalid

simplify256.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (249.0ms)

Iter	Nodes	Cost
0	1484	16
1	1484	16

prune1.0ms

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: 3.3b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 t (-.f64 1 z))
0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
3.2b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

rewrite65.0ms

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:

6.0ms	(/.f64 t (-.f64 1 z))
23.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
28.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series284.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/.f64 t (-.f64 1 z))
72.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
147.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

simplify66.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5345	1711

prune89.0ms

Filtered

72 candidates to 99 candidates (-37.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	7	100

Merged error: 0.0b

Counts

100 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 t (-.f64 z 1))
0.0b	(+.f64 (.f64 x (/.f64 y z)) (.f64 x (/.f64 t (-.f64 z 1))))
1.9b	(*.f64 x (/.f64 t (-.f64 z 1)))
4.7b	(*.f64 x (/.f64 y z))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt_binary64`
57×	`*-un-lft-identity_binary64`
53×	`times-frac_binary64`
40×	`associate-r_binary64`
36×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
8×	`pow1_binary64`
7×	`associate-/r*_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`cbrt-unprod_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 136

Calls

4 calls:

6.0ms	(/.f64 t (-.f64 z 1))
6.0ms	(+.f64 (.f64 x (/.f64 y z)) (.f64 x (/.f64 t (-.f64 z 1))))
13.0ms	(*.f64 x (/.f64 t (-.f64 z 1)))
7.0ms	(*.f64 x (/.f64 y z))

series340.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/.f64 t (-.f64 z 1))
149.0ms	(+.f64 (.f64 x (/.f64 y z)) (.f64 x (/.f64 t (-.f64 z 1))))
101.0ms	(*.f64 x (/.f64 t (-.f64 z 1)))
37.0ms	(*.f64 x (/.f64 y z))

simplify78.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4973	2089
1	4973	2089

prune109.0ms

Filtered

103 candidates to 148 candidates (-43.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	147	8	155

Merged error: 0b

Counts

155 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)
1.9b	(*.f64 x (/.f64 t (-.f64 z 1)))
2.3b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
49×	`associate-r_binary64`
42×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
30×	`add-exp-log_binary64`
23×	`add-cbrt-cube_binary64`
17×	`cbrt-prod_binary64`
10×	`cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
8×	`pow1_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64`
6×	`difference-of-squares_binary64`
4×	`add-log-exp_binary64`
3×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `associate-r/_binary64` `pow1/3_binary64` `associate-/r/_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `flip--_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 127

Calls

4 calls:

1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)
13.0ms	(*.f64 x (/.f64 t (-.f64 z 1)))
16.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt.f64 z)
151.0ms	(cbrt.f64 z)
101.0ms	(*.f64 x (/.f64 t (-.f64 z 1)))
106.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)))

simplify78.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4932	1805
1	4932	1805

prune113.0ms

Filtered

105 candidates to 139 candidates (-32.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	139	8	147

Merged error: 0b

Counts

147 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 t (-.f64 z 1))
0.0b	(+.f64 (.f64 (/.f64 x z) y) (.f64 x (/.f64 t (-.f64 z 1))))
1.9b	(*.f64 x (/.f64 t (-.f64 z 1)))
5.0b	(*.f64 (/.f64 x z) y)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt_binary64`
57×	`*-un-lft-identity_binary64`
53×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
14×	`difference-of-squares_binary64`
8×	`pow1_binary64`
7×	`associate-/r*_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
6×	`add-log-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `flip--_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 135

Calls

4 calls:

6.0ms	(/.f64 t (-.f64 z 1))
6.0ms	(+.f64 (.f64 (/.f64 x z) y) (.f64 x (/.f64 t (-.f64 z 1))))
13.0ms	(*.f64 x (/.f64 t (-.f64 z 1)))
7.0ms	(*.f64 (/.f64 x z) y)

series324.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/.f64 t (-.f64 z 1))
142.0ms	(+.f64 (.f64 (/.f64 x z) y) (.f64 x (/.f64 t (-.f64 z 1))))
94.0ms	(*.f64 x (/.f64 t (-.f64 z 1)))
41.0ms	(*.f64 (/.f64 x z) y)

simplify78.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4962	2109
1	4962	2109

prune89.0ms

Filtered

103 candidates to 147 candidates (-42.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	147	8	155

Merged error: 0b

Counts

155 → 8

regimes98.0ms

Accuracy

8.3% (3.7b remaining)

Error of 3.8b against oracle of 0.0b and baseline of 4.1b

bsearch34.0ms

Steps

Iters	Range		Point
8	8.707042056634513e-140	9.855410667993755e-137	1.2146613525368215e-138
6	-7.227842246791538e-196	-1.1198691233160065e-196	-2.175766960824216e-196

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	64
1	46	64

end0.0ms

sample631.0ms

Algorithm

intervals

Results

301.0ms	8000×	body	128	valid
65.0ms	1727×	body	128	invalid

Details

analyze647.0ms

sample22.0ms

simplify256.0ms

prune1.0ms

localize12.0ms

rewrite65.0ms

series284.0ms

simplify66.0ms

prune89.0ms

localize10.0ms

rewrite45.0ms

series340.0ms

simplify78.0ms

prune109.0ms

localize14.0ms

rewrite50.0ms

series505.0ms

simplify78.0ms

prune113.0ms

localize9.0ms

rewrite48.0ms

series324.0ms

simplify78.0ms

prune89.0ms

regimes98.0ms

bsearch34.0ms

simplify3.0ms

end0.0ms

sample631.0ms

Profiling