Details

sample101.0ms

Algorithm

intervals

Results

18.0ms	205×	body	80	valid
18.0ms	31×	body	2560	valid
14.0ms	31×	body	1280	valid
7.0ms	89×	body	80	nan
4.0ms	12×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify140.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	156
6	156
5	152
4	142
3	115
2	64
1	28
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

23.0ms	(* 4.0 (* a c))
65.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
23.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series342.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 4.0 (* a c))
118.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
96.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
101.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1734
1	452
0	172

prune611.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(* (* 4.0 a) c)
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

74.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.0ms	(* (* 4.0 a) c)
20.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
33.0ms	(* (* 4.0 a) c)
107.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	2291
1	468
0	175

prune555.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* a c))
0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
17×	`*-un-lft-identity`
13×	`prod-exp`
12×	`pow1`
10×	`associate-l`
9×	`add-cube-cbrt`
8×	`associate-r` `add-log-exp`
7×	`cbrt-unprod`
5×	`sqrt-prod`
4×	`flip3--` `div-exp` `pow-prod-down` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac`
2×	`frac-times` `cbrt-undiv` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `diff-log` `1-exp` `associate-l/` `-commutative`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-*r/` `un-div-inv` `div-inv` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

25.0ms	(* 4.0 (* a c))
136.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* 4.0 (* a c))
143.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
116.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
108.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2481
1	524
0	198

prune528.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.5b

localize47.0ms

Local error

Found 4 expressions with local error:

12.2b	(cbrt (* (* 4.0 a) c))
12.2b	(cbrt (* (* 4.0 a) c))
12.2b	(cbrt (* (* 4.0 a) c))
19.5b	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 42

Calls

4 calls:

19.0ms	(cbrt (* (* 4.0 a) c))
20.0ms	(cbrt (* (* 4.0 a) c))
21.0ms	(cbrt (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (* (* 4.0 a) c))
157.0ms	(cbrt (* (* 4.0 a) c))
140.0ms	(cbrt (* (* 4.0 a) c))
163.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 4.0 a) c)) (cbrt (* (* 4.0 a) c))) (cbrt (* (* 4.0 a) c)))))

simplify2.1s

Counts

54 → 54

Iterations

Iter	Nodes
done	5002
3	3204
2	628
1	213
0	88

prune498.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.5b

regimes351.0ms

Accuracy

87.1% (3.7b remaining)

Error of 9.0b against oracle of 5.3b and baseline of 34.1b

bsearch430.0ms

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

simplify11.0ms

Iterations

Iter	Nodes
done	58
2	58
1	57
0	45

end0.0ms

sample3.0s

Algorithm

intervals

Results

701.0ms	921×	body	1280	valid
605.0ms	1025×	body	2560	valid
592.0ms	5841×	body	80	valid
210.0ms	2877×	body	80	nan
146.0ms	457×	body	640	valid
88.0ms	122×	body	5120	valid
48.0ms	245×	body	320	valid
15.0ms	116×	body	160	valid