Details

sample137.0ms

Algorithm

intervals

Results

42.0ms	31×	body	1280	valid
14.0ms	205×	body	80	valid
13.0ms	31×	body	2560	valid
5.0ms	89×	body	80	nan
3.0ms	12×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	44
4	44
3	41
2	32
1	18
0	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* b_2 b_2) (* a c))
150.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
105.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
126.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify820.0ms

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1836
1	447
0	186

prune649.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`associate-r` `add-exp-log`
12×	`associate-l`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `prod-exp` `distribute-neg-frac`
3×	`flip3-+` `sqrt-prod` `flip-+` `distribute-lft-out` `unswap-sqr`
2×	`frac-times` `flip3--` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod` `flip--`
1×	`distribute-lft-neg-out` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `neg-mul-1` `sum-log` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

12.0ms	(- (* b_2 b_2) (* a c))
179.0ms	(* (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
14.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b_2 b_2) (* a c))
159.0ms	(* (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
119.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	5004
2	2839
1	516
0	178

prune676.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
83.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b_2 b_2) (* a c))
129.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
104.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify836.0ms

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1836
1	447
0	186

prune733.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))) (/ 1 a))
0.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
3.4b	(exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
18×	`associate-l`
13×	`associate-r` `add-exp-log`
12×	`log-prod` `exp-sum`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
6×	`log-div` `exp-diff` `add-log-exp`
4×	`exp-prod` `flip3-+` `prod-exp` `flip-+` `distribute-neg-frac` `distribute-lft-out`
3×	`sqrt-prod` `unswap-sqr`
2×	`frac-times` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`distribute-lft-neg-out` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `neg-mul-1` `sum-log` `sqrt-pow1` `flip3--` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `log-pow` `un-div-inv` `-commutative` `div-inv` `flip--` `rem-exp-log`

Counts

4 → 101

Calls

4 calls:

158.0ms	(* (- (exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))) (/ 1 a))
12.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (- (exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))) (/ 1 a))
93.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
98.0ms	(exp (log (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	2475
1	548
0	204

prune590.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.5b

regimes425.0ms

Accuracy

87.2% (3.7b remaining)

Error of 8.9b against oracle of 5.2b and baseline of 34.1b

bsearch335.0ms

Steps

Iters	Range		Point
8	2.072994944964499e+129	8.571507078369983e+131	2.8233354537966034e+131
8	-8.904680992578465e-52	-2.849527055171251e-56	-5.546621280225112e-56
5	-1.0933554809811831e-44	-3.3311956001427126e-45	-3.4083546428522886e-45
7	-5.856362438573669e+138	-1.280729871585891e+137	-2.1229423973235387e+137

simplify21.0ms

Iterations

Iter	Nodes
done	78
3	78
2	74
1	56
0	40

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1029×	body	2560	valid
450.0ms	5835×	body	80	valid
364.0ms	922×	body	1280	valid
261.0ms	455×	body	640	valid
231.0ms	2877×	body	80	nan
100.0ms	122×	body	5120	valid
89.0ms	242×	body	320	valid
16.0ms	123×	body	160	valid