Details

sample105.0ms

Algorithm

intervals

Results

34.0ms	30×	body	2560	valid
18.0ms	193×	body	80	valid
16.0ms	31×	body	1280	valid
9.0ms	91×	body	80	nan
6.0ms	14×	body	640	valid
3.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify132.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.3b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.4b	(- (* b b) (* 4 (* a c)))
22.7b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite140.0ms

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:

85.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
31.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
9.0ms	(- (* b b) (* 4 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
66.0ms	(- (* b b) (* 4 (* a c)))
129.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.1s

Counts

93 → 93

Iterations

Iter	Nodes
3	4241
2	1197
1	400
0	154

prune973.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
0.3b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.4b	(- (* b b) (* 4 (* a c)))
22.7b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite123.0ms

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×	`flip3--` `sqrt-prod` `flip--`
4×	`insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

72.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
15.0ms	(- (* b b) (* 4 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series341.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
89.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
64.0ms	(- (* b b) (* 4 (* a c)))
93.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.7s

Counts

101 → 101

Iterations

Iter	Nodes
3	5864
2	1453
1	450
0	177

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
0.3b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.4b	(- (* b b) (* 4 (* a c)))
22.7b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite93.0ms

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:

59.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms	(- (* b b) (* 4 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
100.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
72.0ms	(- (* b b) (* 4 (* a c)))
88.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify3.5s

Counts

141 → 141

Iterations

Iter	Nodes
3	6394
2	1609
1	554
0	229

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* a (/ -2 (- (- b) (sqrt (- (* b b) (* (* a c) 4))))))
0.3b	(- (- b) (sqrt (- (* b b) (* (* a c) 4))))
1.4b	(- (* b b) (* (* a c) 4))
22.7b	(sqrt (- (* b b) (* (* a c) 4)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

78.0ms	(* a (/ -2 (- (- b) (sqrt (- (* b b) (* (* a c) 4))))))
24.0ms	(- (- b) (sqrt (- (* b b) (* (* a c) 4))))
8.0ms	(- (* b b) (* (* a c) 4))
10.0ms	(sqrt (- (* b b) (* (* a c) 4)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(* a (/ -2 (- (- b) (sqrt (- (* b b) (* (* a c) 4))))))
99.0ms	(- (- b) (sqrt (- (* b b) (* (* a c) 4))))
51.0ms	(- (* b b) (* (* a c) 4))
99.0ms	(sqrt (- (* b b) (* (* a c) 4)))

simplify1.8s

Counts

107 → 107

Iterations

Iter	Nodes
3	3733
2	1251
1	439
0	175

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.1b

regimes434.0ms

Accuracy

82.3% (4.9b remaining)

Error of 10.4b against oracle of 5.5b and baseline of 33.3b

bsearch224.0ms

Steps

Iters	Range		Point
7	1.3534154308951418e+51	2.3844270322569095e+52	2.3648644896474148e+52
9	-5.573104320306828e-19	-3.9027827987942555e-24	-4.179137486378021e-24

simplify8.0ms

Iterations

Iter	Nodes
2	30
1	30
0	24

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.4s	5885×	body	80	valid
1.1s	909×	body	1280	valid
1.0s	1013×	body	2560	valid
400.0ms	2878×	body	80	nan
386.0ms	440×	body	640	valid
167.0ms	122×	body	5120	valid
95.0ms	242×	body	320	valid
29.0ms	112×	body	160	valid