Details

sample59.0ms

Algorithm

intervals

Results

25.0ms	791×	body	80	nan
10.0ms	289×	body	80	valid

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	10
1	72	10
2	192	10
3	437	10
4	816	10
5	1578	10
6	2764	10
7	5002	10

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.2b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
26×	`*-un-lft-identity` `times-frac`
24×	`add-cube-cbrt` `associate-l`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`associate-*r/` `sqrt-prod`
6×	`flip3--` `sqrt-div` `associate-r` `flip--`
4×	`frac-times` `associate-/r*` `associate-/r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `*-commutative` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `distribute-lft-out--`

Counts

4 → 114

Calls

4 calls:

10.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
14.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series536.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
186.0ms	(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
150.0ms	(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	823	1338
1	3607	1238
2	5002	1238

prune507.0ms

Filtered

126 candidates to 105 candidates (83.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	119	7	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	7	127

Merged error: 0.0b

Counts

127 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
0.1b	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-cube-cbrt`
6×	`associate-r/` `associate-l*` `add-log-exp`
5×	`flip3--` `times-frac` `flip--`
4×	`frac-times` `flip3-+` `sqrt-div` `associate-r` `associate-/r*` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `sqrt-pow1` `div-exp` `pow-prod-down` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `sum-log` `-commutative` `div-inv` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

6.0ms	(+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
14.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))
124.0ms	(* (- a (/ 1.0 3.0)) (+ 1.0 (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
78.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
200.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify76.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	693	1082
1	3160	991
2	5002	991

prune222.0ms

Filtered

94 candidates to 77 candidates (81.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	95	6	101

Merged error: 0.0b

Counts

101 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
0.1b	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
6.5b	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt` `associate-*l/`
14×	`flip3--` `flip--`
11×	`*-un-lft-identity`
10×	`associate-r` `frac-add`
9×	`pow1` `add-cube-cbrt` `times-frac` `associate-*r/`
6×	`frac-times` `sqrt-div` `associate-l` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `associate-/r*` `sqrt-prod` `associate-/r/`
2×	`sqrt-pow1` `pow-prod-down` `div-inv` `difference-of-squares`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow1/2` `clear-num` `sum-log` `-commutative` `flip-+` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

11.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
7.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
11.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
19.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))))
75.0ms	(sqrt (* 9.0 (- a (/ 1.0 3.0))))
201.0ms	(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
200.0ms	(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify124.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	887	1538
1	4258	1371
2	5003	1371

prune289.0ms

Filtered

109 candidates to 91 candidates (83.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	110	5	115

Merged error: 0.0b

Counts

115 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt 9.0))) (/ rand (sqrt (- a (/ 1.0 3.0))))))
0.2b	(/ rand (sqrt (- a (/ 1.0 3.0))))
0.3b	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt 9.0)))
6.5b	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt 9.0))) (/ rand (sqrt (- a (/ 1.0 3.0)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
82×	`times-frac`
68×	`*-un-lft-identity`
55×	`associate-r`
52×	`add-cube-cbrt` `sqrt-prod`
51×	`associate-*l/`
32×	`add-exp-log` `add-cbrt-cube`
29×	`frac-times`
27×	`flip3--` `flip--`
22×	`frac-add`
16×	`difference-of-squares`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
10×	`associate-*r/`
9×	`associate-/r*`
8×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`add-log-exp`
4×	`sqrt-div` `pow-prod-down` `associate-/r/`
3×	`div-inv` `associate-/l*` `unswap-sqr`
2×	`*-commutative`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+`

Counts

4 → 202

Calls

4 calls:

11.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt 9.0))) (/ rand (sqrt (- a (/ 1.0 3.0))))))
9.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
16.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt 9.0)))
23.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt 9.0))) (/ rand (sqrt (- a (/ 1.0 3.0)))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(+ (* (- a (/ 1.0 3.0)) 1.0) (* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt 9.0))) (/ rand (sqrt (- a (/ 1.0 3.0))))))
84.0ms	(/ rand (sqrt (- a (/ 1.0 3.0))))
115.0ms	(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt 9.0)))
193.0ms	(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt 9.0))) (/ rand (sqrt (- a (/ 1.0 3.0)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1297	3005
1	5001	2768

prune596.0ms

Filtered

214 candidates to 163 candidates (76.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	212	2	214
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	214	5	219

Merged error: 0b

Counts

219 → 5

regimes70.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	14
1	17	14

end0.0ms

sample1.8s

Algorithm

intervals

Results

903.0ms	27512×	body	80	nan
319.0ms	9111×	body	80	valid