Details

sample327.0ms

Algorithm

intervals

Results

6.0ms	173×	body	80	valid
5.0ms	29×	body	2560	valid
4.0ms	27×	body	1280	valid
4.0ms	83×	body	80	nan
2.0ms	21×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	12×	body	320	valid
1.0ms	11×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7
done	34	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.8b	(- (* b_2 b_2) (* a c))
2.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

66.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753
done	5001	753

prune301.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* b_2 b_2) (* a c))
3.6b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.4b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 210

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
55.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* b_2 b_2) (* a c))
145.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
179.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Counts

222 → 222

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	761	3434
1	3490	3258
2	5002	3250
done	5002	3250

prune535.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize13.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* b_2 b_2) (* a c))
1.8b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
3.6b	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

3489×	`times-frac`
1827×	`add-sqr-sqrt`
1826×	`*-un-lft-identity`
1346×	`add-cube-cbrt`
267×	`associate-/l*`
240×	`distribute-lft-out--` `difference-of-squares`
123×	`sqrt-prod`
120×	`distribute-rgt-neg-in`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
6×	`associate-/r*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 1152

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
131.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
120.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify251.0ms

Counts

1164 → 1164

Iterations

Useful iterations: 1 (68.0ms)

Iter	Nodes	Cost
0	4276	24795
1	5001	24124
done	5001	24124

prune2.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.9b

localize20.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (/ 1 (/ (/ (- (- b_2) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))))) a) c)) a)
5.8b	(- (- b_2) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))))
25.5b	(cbrt (- (* b_2 b_2) (* a c)))
25.5b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

1710×	`times-frac`
743×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
134×	`associate-/l*`
53×	`div-inv`
36×	`add-exp-log`
25×	`div-exp`
18×	`add-cbrt-cube`
10×	`cbrt-undiv` `fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`pow1` `expm1-log1p-u` `cbrt-div` `associate-/r/` `log1p-expm1-u`
3×	`rec-exp` `flip3--` `1-exp` `associate-/r*` `flip--`
2×	`neg-mul-1` `pow1/3` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 632

Calls

4 calls:

67.0ms	(/ (/ 1 (/ (/ (- (- b_2) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))))) a) c)) a)
14.0ms	(- (- b_2) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))))
6.0ms	(cbrt (- (* b_2 b_2) (* a c)))
6.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(/ (/ 1 (/ (/ (- (- b_2) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c)))))) a) c)) a)
88.0ms	(- (- b_2) (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (sqrt (cbrt (- (* b_2 b_2) (* a c))))))
90.0ms	(cbrt (- (* b_2 b_2) (* a c)))
98.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify198.0ms

Counts

644 → 644

Iterations

Useful iterations: 1 (59.0ms)

Iter	Nodes	Cost
0	3740	20517
1	5001	20050
done	5001	20050

prune2.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.9b

regimes253.0ms

Accuracy

72.8% (7.3b remaining)

Error of 12.8b against oracle of 5.5b and baseline of 32.3b

bsearch132.0ms

Steps

Iters	Range		Point
4	9.113314976006761e+77	1.3987841324983815e+78	1.1632570147504631e+78
11	-1.7080554663773614e-124	-7.974260657123443e-153	-1.642868784686772e-124
6	-1.8076892665891905e-94	-1.4815128553801987e-95	-2.6632081568524963e-95
6	-28599.531274954297	-2140.8108186447075	-2200.0149638847433

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	32
1	41	32
done	41	32

end0.0ms

sample1.0s

Algorithm

intervals

Results

202.0ms	1149×	body	2560	valid
179.0ms	5797×	body	80	valid
127.0ms	887×	body	1280	valid
84.0ms	2850×	body	80	nan
54.0ms	474×	body	640	valid
23.0ms	255×	body	320	valid
20.0ms	92×	body	5120	valid
6.0ms	110×	body	160	valid