Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample42.0ms

Algorithm

intervals

Results

26.0ms	97×	body	1280	valid
5.0ms	120×	body	80	valid
2.0ms	13×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	44	10
1	44	10

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 17.6b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(hypot.f64 1 x)
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.6b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`sqrt-prod_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`difference-of-squares_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 68

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.0ms	(hypot.f64 1 x)
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series28.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.0ms	(hypot.f64 1 x)
5.0ms	(/.f64 1/2 (hypot.f64 1 x))
12.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4987	797
1	4987	797

prune53.0ms

Filtered

53 candidates to 80 candidates (-50.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	2	81

Merged error: 17.1b

Counts

81 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `associate-/l_binary64`
4×	`pow1_binary64` `distribute-lft-out_binary64`
2×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-prod_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 82

Calls

4 calls:

9.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(/.f64 1/2 (hypot.f64 1 x))
5.0ms	(/.f64 1/2 (hypot.f64 1 x))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5259	899

prune83.0ms

Filtered

67 candidates to 94 candidates (-40.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	93	3	96

Merged error: 16.7b

Counts

96 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
2.1b	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`log-pow_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-/l_binary64` `exp-prod_binary64`
5×	`pow1_binary64`
4×	`log-prod_binary64` `difference-of-squares_binary64`
2×	`sub-neg_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `exp-sum_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 88

Calls

4 calls:

3.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
12.0ms	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1/2 (hypot.f64 1 x))
5.0ms	(/.f64 1/2 (hypot.f64 1 x))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
8.0ms	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5443	896

prune97.0ms

Filtered

72 candidates to 100 candidates (-38.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	99	4	103

Merged error: 16.7b

Counts

103 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (hypot.f64 1 x))
0.2b	(*.f64 (cbrt.f64 (hypot.f64 1 x)) (cbrt.f64 (hypot.f64 1 x)))
2.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
2.1b	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64` `cbrt-prod_binary64`
15×	`add-cube-cbrt_binary64`
12×	`pow1_binary64`
7×	`pow1/3_binary64` `log-pow_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64` `exp-prod_binary64`
4×	`log-prod_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `pow-prod-up_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `pow-sqr_binary64`
1×	`flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `pow-plus_binary64` `exp-diff_binary64` `exp-sum_binary64` `prod-exp_binary64` `log-div_binary64` `flip--_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

1.0ms	(cbrt.f64 (hypot.f64 1 x))
8.0ms	(*.f64 (cbrt.f64 (hypot.f64 1 x)) (cbrt.f64 (hypot.f64 1 x)))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
8.0ms	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt.f64 (hypot.f64 1 x))
24.0ms	(*.f64 (cbrt.f64 (hypot.f64 1 x)) (cbrt.f64 (hypot.f64 1 x)))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
8.0ms	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4928	800
1	4928	800

prune106.0ms

Filtered

65 candidates to 97 candidates (-49.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	97	4	101

Merged error: 16.7b

Counts

101 → 4

regimes40.0ms

Accuracy

0% (0.3b remaining)

Error of 15.3b against oracle of 15.0b and baseline of 15.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	20
1	31	20

end0.0ms

sample1.1s

Algorithm

intervals

Results

628.0ms	2903×	body	1280	valid
159.0ms	3972×	body	80	valid
114.0ms	656×	body	640	valid
37.0ms	309×	body	320	valid
12.0ms	160×	body	160	valid

Details

analyze1.0ms

sample42.0ms

simplify7.0ms

prune4.0ms

localize7.0ms

rewrite22.0ms

series28.0ms

simplify66.0ms

prune53.0ms

localize9.0ms

rewrite24.0ms

series29.0ms

simplify59.0ms

prune83.0ms

localize12.0ms

rewrite29.0ms

series26.0ms

simplify58.0ms

prune97.0ms

localize17.0ms

rewrite27.0ms

series57.0ms

simplify48.0ms

prune106.0ms

regimes40.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling