Details

sample37.0ms

Algorithm

intervals

Results

7.0ms	33×	body	2560	valid
7.0ms	183×	body	80	valid
5.0ms	31×	body	1280	valid
3.0ms	85×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

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: 35.5b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
42.0ms	(- (* b b) (* (* 3.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune213.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 7.9b

Counts

83 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.7b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
13.1b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
19.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
139.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
176.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	635	2579
1	3125	2333
2	5001	2320

prune363.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	160	11	171

Merged error: 7.8b

Counts

171 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`times-frac`
26×	`add-exp-log`
21×	`add-cube-cbrt`
19×	`associate-r`
16×	`add-cbrt-cube`
13×	`associate-l`
10×	`add-log-exp`
8×	`div-exp` `prod-exp` `distribute-lft-out`
7×	`pow1`
6×	`unswap-sqr`
4×	`cbrt-undiv` `distribute-rgt-neg-in` `cbrt-unprod`
3×	`sqrt-prod`
2×	`rec-exp` `flip3--` `sqrt-div` `1-exp` `sum-log` `flip--` `div-inv`
1×	`+-commutative` `neg-sub0` `frac-times` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 104

Calls

4 calls:

18.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(- (* b b) (* (* 3.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	612	1234
1	2986	1078
2	5001	1068

prune261.0ms

Filtered

116 candidates to 79 candidates (68.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	117	10	127

Merged error: 7.8b

Counts

127 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

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

series222.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* 3.0 a) c)
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
49.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune149.0ms

Filtered

72 candidates to 52 candidates (72.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	71	11	82

Merged error: 7.8b

Counts

82 → 11

regimes423.0ms

Accuracy

83.5% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 33.8b

bsearch78.0ms

Steps

Iters	Range		Point
5	8.197812324294091e-94	2.3646460195328382e-93	1.3424876507599846e-93
7	-2.129980745276144e+116	-9.287529331322677e+113	-9.597540061084627e+115

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

223.0ms	1068×	body	2560	valid
214.0ms	5876×	body	80	valid
155.0ms	881×	body	1280	valid
94.0ms	2896×	body	80	nan
64.0ms	446×	body	640	valid
27.0ms	103×	body	5120	valid
24.0ms	222×	body	320	valid
8.0ms	114×	body	160	valid