Details

analyze25.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

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: 37.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
35.2b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64`

Counts

2 → 54

Calls

2 calls:

10.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
7.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

series48.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
31.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4937	1096
1	4937	1096

prune60.0ms

Filtered

48 candidates to 60 candidates (-25.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	55	5	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	6	61

Merged error: 17.1b

Counts

61 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b

(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3))

0.4b

(*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3)))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3))))

35.2b

(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt_binary64`
75×	`times-frac_binary64` `sqrt-prod_binary64`
52×	`*-un-lft-identity_binary64`
48×	`add-cube-cbrt_binary64`
35×	`cbrt-prod_binary64`
25×	`associate-r_binary64`
16×	`unswap-sqr_binary64`
10×	`associate-l_binary64`
8×	`pow1_binary64`
7×	`add-exp-log_binary64`
6×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
5×	`sqrt-div_binary64`
4×	`div-inv_binary64`
3×	`pow-prod-down_binary64` `add-log-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64`
1×	`flip3-+_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

3 → 144

Calls

3 calls:

10.0ms

(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3))

27.0ms

(*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3)))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3))))

8.0ms

(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3)))

series135.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms

(/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3))

63.0ms

(*.f64 (sqrt.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3)))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3))))

48.0ms

(sqrt.f64 (/.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 z z)) (cbrt.f64 3)))

simplify64.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5166	3857

prune184.0ms

Filtered

120 candidates to 153 candidates (-27.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	150	9	159

Merged error: 17.0b

Counts

159 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (cbrt.f64 3))
0.4b	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (.f64 (cbrt.f64 3) (cbrt.f64 3)))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (cbrt.f64 3))))
35.1b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
35.1b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

150×	`sqrt-prod_binary64`
130×	`add-sqr-sqrt_binary64`
106×	`times-frac_binary64`
64×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
47×	`cbrt-prod_binary64`
43×	`associate-r_binary64`
24×	`unswap-sqr_binary64`
13×	`associate-l_binary64`
10×	`pow1_binary64` `sqrt-div_binary64`
8×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-exp_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 189

Calls

4 calls:

17.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (cbrt.f64 3))
35.0ms	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (.f64 (cbrt.f64 3) (cbrt.f64 3)))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (cbrt.f64 3))))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series137.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (cbrt.f64 3))
56.0ms	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (.f64 (cbrt.f64 3) (cbrt.f64 3)))) (sqrt.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (cbrt.f64 3))))
22.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
22.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify73.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5115	6176

prune141.0ms

Filtered

134 candidates to 201 candidates (-50.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	201	9	210

Merged error: 17.0b

Counts

210 → 9

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b	(*.f64 x (sqrt.f64 1/3))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

1 → 22

Calls

1 calls:

5.0ms

(*.f64 x (sqrt.f64 1/3))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(*.f64 x (sqrt.f64 1/3))

simplify52.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4902	133
1	4902	133

prune14.0ms

Filtered

14 candidates to 25 candidates (-78.6%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	21	13	34

Merged error: 17.0b

Counts

34 → 13

regimes789.0ms

Accuracy

62.7% (7.4b remaining)

Error of 26.0b against oracle of 18.6b and baseline of 38.4b

bsearch23.0ms

Steps

Iters	Range		Point
7	4.410730584051704e+113	7.4385695630633155e+115	6.405881481904802e+115
5	-1.2033494203004617e+79	-5.682358091236781e+78	-1.1907252457196504e+79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	31
1	47	31

end0.0ms

sample534.0ms

Algorithm

intervals

Results

363.0ms

8000×

body

valid

Details

analyze25.0ms

sample20.0ms

simplify5.0ms

prune2.0ms

localize8.0ms

rewrite18.0ms

series48.0ms

simplify56.0ms

prune60.0ms

localize13.0ms

rewrite51.0ms

series135.0ms

simplify64.0ms

prune184.0ms

localize15.0ms

rewrite75.0ms

series137.0ms

simplify73.0ms

prune141.0ms

localize3.0ms

rewrite6.0ms

series5.0ms

simplify52.0ms

prune14.0ms

regimes789.0ms

bsearch23.0ms

simplify2.0ms

end0.0ms

sample534.0ms

Profiling