Details

analyze263.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample71.0ms

Algorithm

intervals

Results

35.0ms	79×	body	1280	valid
11.0ms	41×	body	640	valid
9.0ms	28×	body	2560	valid
5.0ms	33×	body	320	valid
3.0ms	67×	body	80	valid
1.0ms	8×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

prune2.0ms

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: 52.8b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.6b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
2.0b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
15.1b	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 42

Calls

3 calls:

9.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

series21.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0)))
11.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1.0))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5075	600

prune77.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0.0b

Counts

52 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))
0.1b	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

50×	`associate-r_binary64`
49×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`unpow-prod-down_binary64` `cube-prod_binary64`
20×	`sqrt-prod_binary64`
10×	`add-exp-log_binary64`
8×	`unswap-sqr_binary64`
6×	`add-log-exp_binary64`
4×	`add-cbrt-cube_binary64` `prod-exp_binary64`
3×	`associate-r/_binary64` `associate-l*_binary64` `cube-div_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64` `div-inv_binary64` `frac-sub_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 90

Calls

2 calls:

14.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))
16.0ms	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))

series39.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(-.f64 (+.f64 (log.f64 (sqrt.f64 1.0)) (/.f64 x (sqrt.f64 1.0))) (*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3)))
21.0ms	(*.f64 1/6 (pow.f64 (/.f64 x (sqrt.f64 1.0)) 3))

simplify30.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	4998	1131
1	4998	1131

prune82.0ms

Filtered

47 candidates to 96 candidates (-104.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Merged error: 0.0b

Counts

100 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 0.125 (pow.f64 x 3))
0.2b	(/.f64 0.0625 (pow.f64 x 5))
11.9b	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
17.2b	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `log-div_binary64`
4×	`distribute-lft-out_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/.f64 0.125 (pow.f64 x 3))
8.0ms	(/.f64 0.0625 (pow.f64 x 5))
33.0ms	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
37.0ms	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 0.125 (pow.f64 x 3))
6.0ms	(/.f64 0.0625 (pow.f64 x 5))
12.0ms	(log.f64 (-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5)))))
7.0ms	(-.f64 (/.f64 0.125 (pow.f64 x 3)) (+.f64 (/.f64 0.5 x) (/.f64 0.0625 (pow.f64 x 5))))

simplify56.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5361	2493

prune178.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Merged error: 0.0b

Counts

175 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 0.5 x))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3))))
0.1b	(/.f64 0.125 (pow.f64 x 3))
10.2b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
15×	`add-log-exp_binary64`
12×	`associate-/r*_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
10×	`add-exp-log_binary64`
9×	`distribute-lft-out_binary64`
6×	`log-prod_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `sum-log_binary64`
4×	`sqr-pow_binary64` `distribute-lft-out--_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`diff-log_binary64` `log-div_binary64` `+-commutative_binary64` `associate-+r+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-+r-_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64` `associate--l+_binary64`

Counts

4 → 113

Calls

4 calls:

6.0ms	(+.f64 x (/.f64 0.5 x))
21.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3))))
5.0ms	(/.f64 0.125 (pow.f64 x 3))
21.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))))

series29.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 x (/.f64 0.5 x))
6.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3))))
5.0ms	(/.f64 0.125 (pow.f64 x 3))
12.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 0.5 x)) (/.f64 0.125 (pow.f64 x 3)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5056	1415

prune89.0ms

Filtered

73 candidates to 125 candidates (-71.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	125	4	129

Merged error: 0.0b

Counts

129 → 4

regimes76.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.5b

bsearch27.0ms

Steps

Iters	Range		Point
9	0.00015376982843717858	26598.371815489856	0.8962476229902214
9	-157274.44498914763	-0.024100400356733092	-1.0076583790961935

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	55
1	117	55

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2328×	body	1280	valid
421.0ms	1492×	body	640	valid
271.0ms	813×	body	2560	valid
137.0ms	797×	body	320	valid
90.0ms	2187×	body	80	valid
37.0ms	383×	body	160	valid

Details

analyze263.0ms

sample71.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite21.0ms

series21.0ms

simplify44.0ms

prune77.0ms

localize11.0ms

rewrite35.0ms

series39.0ms

simplify30.0ms

prune82.0ms

localize11.0ms

rewrite89.0ms

series30.0ms

simplify56.0ms

prune178.0ms

localize9.0ms

rewrite58.0ms

series29.0ms

simplify45.0ms

prune89.0ms

regimes76.0ms

bsearch27.0ms

simplify3.0ms

end0.0ms

sample2.2s

Profiling