Details

sample97.0ms

Algorithm

intervals

Results

24.0ms	43×	body	2560	valid
18.0ms	190×	body	80	valid
12.0ms	24×	body	1280	valid
10.0ms	12×	body	320	valid
8.0ms	85×	body	80	nan
4.0ms	12×	body	640	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	5120	valid

simplify115.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.8b	(- (* b b) (* 4 (* a c)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 81

Calls

4 calls:

101.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
9.0ms	(- (* b b) (* 4 (* a c)))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
18.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
63.0ms	(- (* b b) (* 4 (* a c)))
108.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
102.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1254
1	400
0	154

prune508.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
0.8b	(+ (* b b) (* c (* a -4)))
0.8b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
22.0b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`insert-posit16`
3×	`distribute-rgt-neg-in`
2×	`cbrt-undiv` `flip3-+` `flip3--` `sqrt-div` `diff-log` `div-exp` `flip-+` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 80

Calls

4 calls:

75.0ms	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
9.0ms	(+ (* b b) (* c (* a -4)))
32.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
9.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
47.0ms	(+ (* b b) (* c (* a -4)))
100.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
76.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify1.6s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1334
1	412
0	156

prune522.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (/ 1/2 a))
0.8b	(+ (* b b) (* c (* a -4)))
0.8b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
22.0b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
13×	`associate-r` `add-cube-cbrt`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `associate-l`
5×	`sqrt-prod`
4×	`insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-times` `distribute-rgt-neg-in` `flip3-+` `sqrt-div` `diff-log` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

103.0ms	(* (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (/ 1/2 a))
10.0ms	(+ (* b b) (* c (* a -4)))
31.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
8.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (/ 1/2 a))
49.0ms	(+ (* b b) (* c (* a -4)))
104.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
75.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify1.3s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	1697
1	466
0	179

prune504.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* b b) (* c (* a -4)))
12.8b	(- (- b) (* (sqrt (sqrt (+ (* b b) (* c (* a -4))))) (sqrt (sqrt (+ (* b b) (* c (* a -4)))))))
22.0b	(sqrt (+ (* b b) (* c (* a -4))))
22.0b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`
1×	`associate--l-` `neg-sub0` `+-commutative` `sum-log` `sub-neg` `flip3--` `neg-log` `flip--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

9.0ms	(+ (* b b) (* c (* a -4)))
11.0ms	(- (- b) (* (sqrt (sqrt (+ (* b b) (* c (* a -4))))) (sqrt (sqrt (+ (* b b) (* c (* a -4)))))))
8.0ms	(sqrt (+ (* b b) (* c (* a -4))))
15.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (* b b) (* c (* a -4)))
118.0ms	(- (- b) (* (sqrt (sqrt (+ (* b b) (* c (* a -4))))) (sqrt (sqrt (+ (* b b) (* c (* a -4)))))))
79.0ms	(sqrt (+ (* b b) (* c (* a -4))))
85.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify2.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	3414
2	764
1	255
0	102

prune433.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

regimes521.0ms

Accuracy

81.6% (5.0b remaining)

Error of 10.3b against oracle of 5.3b and baseline of 32.7b

bsearch142.0ms

Steps

Iters	Range		Point
8	4.664337482673326e-05	0.17679972651571432	0.17389787404847717
7	-2.1239343788780832e-66	-2.400891841159577e-68	-1.264659490877098e-67

simplify8.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample3.2s

Algorithm

intervals

Results

946.0ms	5823×	body	80	valid
644.0ms	1103×	body	2560	valid
462.0ms	877×	body	1280	valid
323.0ms	2975×	body	80	nan
211.0ms	440×	body	640	valid
126.0ms	125×	body	5120	valid
94.0ms	249×	body	320	valid
20.0ms	121×	body	160	valid