Details

sample178.0ms

Algorithm

intervals

Results

55.0ms	183×	body	80	valid
42.0ms	41×	body	2560	valid
26.0ms	31×	body	1280	valid
15.0ms	84×	body	80	nan
9.0ms	12×	body	640	valid
5.0ms	4×	body	5120	valid
2.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify182.0ms

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: 30.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.8b	(- (* b b) (* 4 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
20.7b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite98.0ms

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:

56.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
9.0ms	(- (* b b) (* 4 (* a c)))
15.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
63.0ms	(- (* b b) (* 4 (* a c)))
133.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
128.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.7s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1254
1	400
0	154

prune543.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
0.8b	(+ (* b b) (* c (* a -4)))
0.9b	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
20.7b	(sqrt (+ (* b b) (* c (* a -4))))

rewrite122.0ms

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:

85.0ms	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
14.0ms	(+ (* b b) (* c (* a -4)))
15.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
6.0ms	(sqrt (+ (* b b) (* c (* a -4))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (- (- b) (sqrt (+ (* b b) (* c (* a -4))))) (* 2 a))
56.0ms	(+ (* b b) (* c (* a -4)))
118.0ms	(- (- b) (sqrt (+ (* b b) (* c (* a -4)))))
101.0ms	(sqrt (+ (* b b) (* c (* a -4))))

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1334
1	412
0	156

prune449.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
0.8b	(- (* b b) (* 4 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
20.7b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

32.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
14.0ms	(- (* b b) (* 4 (* a c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
12.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
75.0ms	(- (* b b) (* 4 (* a c)))
128.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
98.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.5s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	1799
1	571
0	229

prune683.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1/2 a) (- (+ b (sqrt (- (* b b) (* (* 4 a) c))))))
0.8b	(- (* b b) (* (* 4 a) c))
0.9b	(+ b (sqrt (- (* b b) (* (* 4 a) c))))
20.7b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite541.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

505.0ms	(* (/ 1/2 a) (- (+ b (sqrt (- (* b b) (* (* 4 a) c))))))
7.0ms	(- (* b b) (* (* 4 a) c))
13.0ms	(+ b (sqrt (- (* b b) (* (* 4 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (/ 1/2 a) (- (+ b (sqrt (- (* b b) (* (* 4 a) c))))))
80.0ms	(- (* b b) (* (* 4 a) c))
122.0ms	(+ b (sqrt (- (* b b) (* (* 4 a) c))))
103.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts

103 → 103

Iterations

Iter	Nodes
done	5004
2	2135
1	533
0	182

prune521.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

regimes311.0ms

Accuracy

83% (4.6b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 32.9b

bsearch170.0ms

Steps

Iters	Range		Point
7	5.455680955858941e+61	9.381769121995126e+63	7.052614559736995e+62
8	-9.498395151376604e-61	-6.25213087380725e-65	-1.6239127264630285e-63

simplify10.0ms

Iterations

Iter	Nodes
done	53
3	53
2	48
1	37
0	26

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.1s	1101×	body	2560	valid
788.0ms	5893×	body	80	valid
743.0ms	856×	body	1280	valid
451.0ms	3007×	body	80	nan
438.0ms	98×	body	5120	valid
260.0ms	463×	body	640	valid
110.0ms	216×	body	320	valid
30.0ms	119×	body	160	valid