Details

analyze1.1s

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample31.0ms

Algorithm

intervals

Results

12.0ms	256×	body	128	valid
3.0ms	61×	body	128	nan
1.0ms	29×	body	128	invalid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	806	21
1	806	21

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: 27.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
4.0b	(.f64 (.f64 x y) z)
9.3b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
9×	`sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
4×	`sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/r/_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

4.0ms	(-.f64 (.f64 z z) (.f64 t a))
5.0ms	(.f64 (.f64 x y) z)
12.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(-.f64 (.f64 z z) (.f64 t a))
50.0ms	(.f64 (.f64 x y) z)
248.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
109.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5352	1466

prune81.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	11	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 3.7b

Counts

88 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.6b	(-.f64 (.f64 z z) (.f64 t a))
2.9b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
24×	`associate-r_binary64` `sqrt-prod_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
3×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
2×	`div-inv_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))
15.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
57.0ms	(-.f64 (.f64 z z) (.f64 t a))
245.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
102.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5266	2515

prune74.0ms

Filtered

81 candidates to 123 candidates (-51.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	122	12	134

Merged error: 3.7b

Counts

134 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 z z) (.f64 t a))
1.1b	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
2.2b	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
25×	`associate-r_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`sqrt-prod_binary64`
12×	`pow1_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`pow-prod-down_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `flip--_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`

Counts

4 → 91

Calls

4 calls:

4.0ms	(-.f64 (.f64 z z) (.f64 t a))
14.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
12.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(-.f64 (.f64 z z) (.f64 t a))
145.0ms	(.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
252.0ms	(.f64 x (.f64 y (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
100.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify62.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5007	1891

prune67.0ms

Filtered

67 candidates to 103 candidates (-53.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	104	11	115

Merged error: 3.7b

Counts

115 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
5.0b	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
24.6b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

10.0ms	(/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
32.0ms	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
5.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

series741.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (*.f64 t a)))))
266.0ms	(.f64 (/.f64 (.f64 x y) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 z (sqrt.f64 (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))))
104.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
106.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

simplify89.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4971	4161
1	4971	4161

prune92.0ms

Filtered

100 candidates to 153 candidates (-53.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	153	11	164

Merged error: 3.7b

Counts

164 → 11

regimes275.0ms

Accuracy

84% (3.1b remaining)

Error of 6.5b against oracle of 3.4b and baseline of 22.5b

bsearch44.0ms

Steps

Iters	Range		Point
8	2.1001055873097394e+118	4.313786339197128e+121	1.2594073492803716e+120
7	-2.128256342722516e+73	-1.4042843312684852e+71	-2.0883144834980717e+73

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	43
1	71	43

end0.0ms

sample891.0ms

Algorithm

intervals

Results

386.0ms	8000×	body	128	valid
97.0ms	2190×	body	128	nan
41.0ms	891×	body	128	invalid

Details

analyze1.1s

sample31.0ms

simplify52.0ms

prune2.0ms

localize16.0ms

rewrite32.0ms

series461.0ms

simplify54.0ms

prune81.0ms

localize13.0ms

rewrite41.0ms

series478.0ms

simplify77.0ms

prune74.0ms

localize13.0ms

rewrite45.0ms

series547.0ms

simplify62.0ms

prune67.0ms

localize13.0ms

rewrite74.0ms

series741.0ms

simplify89.0ms

prune92.0ms

regimes275.0ms

bsearch44.0ms

simplify6.0ms

end0.0ms

sample891.0ms

Profiling