Details

sample89.0ms

Algorithm

intervals

Results

17.0ms	43×	body	2560	valid
13.0ms	185×	body	80	valid
13.0ms	119×	body	80	nan
9.0ms	25×	body	1280	valid
2.0ms	10×	body	640	valid
2.0ms	5×	body	5120	valid
2.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify123.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
26.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite261.0ms

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:

143.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
17.0ms	(- (* b b) (* (* 3.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
54.0ms	(- (* b b) (* (* 3.0 a) c))
109.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
110.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify793.0ms

Counts: 82 → 82

prune363.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.2b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.9b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.0b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
26.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite337.0ms

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:

45.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
126.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
137.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
229.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
237.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
93.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.8s

Counts: 166 → 166

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.8b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
11.0b	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
26.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite191.0ms

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:

39.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
51.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
86.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series716.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
229.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
281.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
98.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.0s

Counts: 128 → 128

prune502.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.1b

localize30.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.8b	(/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
11.0b	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
26.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
58×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
29×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
10×	`associate-/r*` `sqrt-prod` `associate-/r/`
8×	`add-log-exp`
7×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `div-exp` `flip--`
6×	`div-inv`
5×	`pow1`
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` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 136

Calls

4 calls:

27.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
86.0ms	(/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
54.0ms	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series667.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
190.0ms	(/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
251.0ms	(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
86.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts: 148 → 148

prune524.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

regimes501.0ms

Accuracy

91.4% (2.3b remaining)

Error of 7.8b against oracle of 5.5b and baseline of 32.0b

bsearch244.0ms

Steps

Iters	Range		Point
8	1.890514070312107e+96	2.5656331724562416e+99	1.2233387524666403e+97
8	2.660725689425777e-220	4.704576784285924e-217	4.62812776285934e-217
9	-1.4887366307331679e+153	-1.51868681961906e+147	-1.0438412008680944e+150

simplify531.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

763.0ms	860×	body	1280	valid
503.0ms	1143×	body	2560	valid
465.0ms	5798×	body	80	valid
238.0ms	3013×	body	80	nan
164.0ms	438×	body	640	valid
53.0ms	126×	body	5120	valid
41.0ms	243×	body	320	valid
12.0ms	110×	body	160	valid