Details

sample72.0ms

Algorithm

intervals

Results

15.0ms	157×	body	160	valid
15.0ms	534×	pre	80	true
12.0ms	278×	body	80	nan
8.0ms	99×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	88	16
1	88	16

prune8.0ms

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: 29.8b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 3.0 (* a c)))
0.3b	(* 3.0 (* a c))
0.4b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
29.7b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
13×	`*-un-lft-identity`
9×	`pow1`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-l` `pow-prod-down` `sqrt-prod` `flip--` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`frac-2neg` `div-sub` `associate-r` `clear-num` `associate-/r` `-commutative` `div-inv`

Counts

4 → 75

Calls

4 calls:

5.0ms	(- (* b b) (* 3.0 (* a c)))
5.0ms	(* 3.0 (* a c))
10.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
6.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

series50.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))
24.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
14.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)

simplify33.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5007	1209

prune133.0ms

Filtered

59 candidates to 87 candidates (-47.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	7	88

Merged error: 0.4b

Counts

88 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
0.3b	(* 3.0 (* a c))
0.4b	(/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
0.4b	(/ (/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
51×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `add-cube-cbrt`
28×	`add-exp-log` `add-cbrt-cube`
21×	`associate-/l*`
14×	`pow1`
10×	`distribute-lft-out`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`associate-l` `pow-prod-down` `associate-/r/`
5×	`associate-/r*`
4×	`div-inv` `add-log-exp`
3×	`flip3-+` `div-sub` `distribute-frac-neg` `flip-+` `associate-/l/`
2×	`frac-2neg` `sub0-neg` `associate-r` `clear-num` `*-commutative`
1×	`flip3--` `flip--`

Counts

4 → 131

Calls

4 calls:

4.0ms	(* 3.0 (* a c))
5.0ms	(* 3.0 (* a c))
8.0ms	(/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
12.0ms	(/ (/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

series101.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
3.0ms	(* 3.0 (* a c))
51.0ms	(/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
44.0ms	(/ (/ (- 0 (* 3.0 (* a c))) (+ b (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))

simplify42.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5247	2768

prune247.0ms

Filtered

97 candidates to 143 candidates (-47.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	133	10	143
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	140	10	150

Merged error: 0b

Counts

150 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
0.2b	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
0.2b	(- (* b b) (* 3.0 (* a c)))
0.3b	(* 3.0 (* a c))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
5×	`distribute-lft-out`
4×	`associate-/r*`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `associate-r` `clear-num` `sum-log` `*-commutative` `flip--` `div-inv`

Counts

4 → 75

Calls

4 calls:

6.0ms	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
5.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
3.0ms	(- (* b b) (* 3.0 (* a c)))
5.0ms	(* 3.0 (* a c))

series72.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ c (+ b (sqrt (- (* b b) (* 3.0 (* a c))))))
14.0ms	(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
8.0ms	(- (* b b) (* 3.0 (* a c)))
3.0ms	(* 3.0 (* a c))

simplify73.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4949	1193
1	4949	1193

prune146.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	88	9	97

Merged error: 0b

Counts

97 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a (* a (* c c))))
0.3b	(* a (* c c))
0.3b	(* 3.0 (* 3.0 (* a (* a (* c c)))))
0.4b	(/ (- (pow b 4) (* 3.0 (* 3.0 (* a (* a (* c c)))))) (+ (* 3.0 (* a c)) (* b b)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
43×	`pow1`
28×	`pow-prod-down` `prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac` `associate-l`
4×	`add-log-exp`
3×	`associate-r` `associate-/r` `-commutative` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

10.0ms	(* 3.0 (* a (* a (* c c))))
6.0ms	(* a (* c c))
12.0ms	(* 3.0 (* 3.0 (* a (* a (* c c)))))
11.0ms	(/ (- (pow b 4) (* 3.0 (* 3.0 (* a (* a (* c c)))))) (+ (* 3.0 (* a c)) (* b b)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* 3.0 (* a (* a (* c c))))
6.0ms	(* a (* c c))
11.0ms	(* 3.0 (* 3.0 (* a (* a (* c c)))))
21.0ms	(/ (- (pow b 4) (* 3.0 (* 3.0 (* a (* a (* c c)))))) (+ (* 3.0 (* a c)) (* b b)))

simplify57.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5055	1828

prune149.0ms

Filtered

64 candidates to 114 candidates (-78.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	114	9	123

Merged error: 0b

Counts

123 → 9

regimes213.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	31
1	40	31

end0.0ms

sample2.0s

Algorithm

intervals

Results

459.0ms	16541×	pre	80	true
414.0ms	4504×	body	160	valid
390.0ms	8541×	body	80	nan
169.0ms	3496×	body	80	valid

Details

sample72.0ms

simplify3.0ms

prune8.0ms

localize10.0ms

rewrite28.0ms

series50.0ms

simplify33.0ms

prune133.0ms

localize13.0ms

rewrite34.0ms

series101.0ms

simplify42.0ms

prune247.0ms

localize14.0ms

rewrite22.0ms

series72.0ms

simplify73.0ms

prune146.0ms

localize22.0ms

rewrite42.0ms

series45.0ms

simplify57.0ms

prune149.0ms

regimes213.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.0s

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