Details

sample46.0ms

Algorithm

intervals

Results

9.0ms	186×	body	80	valid
9.0ms	33×	body	2560	valid
7.0ms	32×	body	1280	valid
4.0ms	95×	body	80	nan
2.0ms	5×	body	5120	valid
2.0ms	9×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	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: 35.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.1b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.8b	(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	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
42.0ms	(- (* b b) (* (* 3.0 a) c))
79.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	391	774
1	1518	684
2	5001	674

prune214.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 6.4b

Counts

83 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.7b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.8b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series854.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
233.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
278.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	644	2693
1	3143	2447
2	5001	2434

prune427.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	165	11	176

Merged error: 6.3b

Counts

176 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.6b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
10.9b	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`cbrt-undiv` `div-exp`
18×	`prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*` `add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`associate-/r*` `sqrt-prod`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

10.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
14.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
221.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
275.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify120.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	697	2051
1	4478	1590
2	5002	1549

prune278.0ms

Filtered

128 candidates to 86 candidates (67.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	128	11	139

Merged error: 6.3b

Counts

139 → 11

localize33.0ms

Local error

Found 4 expressions with local error:

5.5b	(exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))
10.2b	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))))
16.1b	(- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `log-prod` `exp-sum` `add-log-exp`
7×	`pow1` `sqrt-prod`
6×	`cbrt-undiv` `exp-prod` `div-exp`
4×	`flip3--` `sqrt-div` `flip--`
3×	`log-pow` `difference-of-squares`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff` `diff-log` `associate-*r/` `associate-/r/` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `times-frac` `neg-log` `clear-num` `associate-/r` `div-inv` `rem-exp-log` `associate-/l`

Counts

4 → 83

Calls

4 calls:

5.0ms	(exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))
16.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))))
10.0ms	(- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))
303.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))))
75.0ms	(- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	518	1193
1	2897	916
2	5003	876

prune232.0ms

Filtered

95 candidates to 65 candidates (68.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	95	11	106

Merged error: 6.3b

Counts

106 → 11

regimes404.0ms

Accuracy

82.1% (4.8b remaining)

Error of 10.2b against oracle of 5.4b and baseline of 32.4b

bsearch101.0ms

Steps

Iters	Range		Point
4	2.4689314423018332e-42	4.020507772702371e-42	2.7435023374162605e-42
9	-6.551078454010515e+117	-3.119450221310465e+111	-6.589053059524542e+113

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.3s

Algorithm

intervals

Results

290.0ms	1034×	body	2560	valid
285.0ms	5865×	body	80	valid
209.0ms	906×	body	1280	valid
134.0ms	2892×	body	80	nan
79.0ms	457×	body	640	valid
41.0ms	118×	body	5120	valid
31.0ms	233×	body	320	valid
11.0ms	125×	body	160	valid

Details

sample46.0ms

simplify11.0ms

prune2.0ms

localize13.0ms

rewrite27.0ms

series337.0ms

simplify44.0ms

prune214.0ms

localize19.0ms

rewrite47.0ms

series854.0ms

simplify116.0ms

prune427.0ms

localize14.0ms

rewrite49.0ms

series642.0ms

simplify120.0ms

prune278.0ms

localize33.0ms

rewrite40.0ms

series525.0ms

simplify80.0ms

prune232.0ms

regimes404.0ms

bsearch101.0ms

simplify1.0ms

end0.0ms

sample1.3s

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