Details

sample137.0ms

Algorithm

intervals

Results

31.0ms	172×	body	80	valid
21.0ms	31×	body	2560	valid
18.0ms	35×	body	1280	valid
9.0ms	20×	body	640	valid
9.0ms	82×	body	80	nan
4.0ms	5×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify445.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	77
2	43
1	25
0	14

prune43.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize124.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite343.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

209.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
22.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
29.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series621.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
96.0ms	(- (* b b) (* 4.0 (* a c)))
150.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
148.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify3.5s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1410
1	444
0	169

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize170.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite544.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
11×	`add-cube-cbrt`
10×	`fma-def` `prod-exp` `add-log-exp`
7×	`pow1` `associate-r`
5×	`distribute-rgt-neg-in` `associate-l`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sum-log` `flip3--` `sqrt-div` `1-exp` `associate-*l/` `flip--`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `associate-+l-` `div-inv` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

393.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
45.0ms	(- (* b b) (* 4.0 (* a c)))
63.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
34.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series590.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
99.0ms	(- (* b b) (* 4.0 (* a c)))
152.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
122.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.3s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	1905
1	523
0	196

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize152.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* a c) 4.0))) b) (* 2.0 a))
0.4b	(- (* b b) (* (* a c) 4.0))
0.9b	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
22.2b	(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite538.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 110

Calls

4 calls:

277.0ms	(/ (- (sqrt (- (* b b) (* (* a c) 4.0))) b) (* 2.0 a))
33.0ms	(- (* b b) (* (* a c) 4.0))
165.0ms	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
50.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(/ (- (sqrt (- (* b b) (* (* a c) 4.0))) b) (* 2.0 a))
71.0ms	(- (* b b) (* (* a c) 4.0))
135.0ms	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
137.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

simplify3.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5002
2	1614
1	519
0	197

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.0b

localize175.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* a c) 4.0))
22.2b	(sqrt (- (* b b) (* (* a c) 4.0)))
22.2b	(sqrt (- (* b b) (* (* a c) 4.0)))
24.2b	(fma (sqrt (sqrt (- (* b b) (* (* a c) 4.0)))) (sqrt (sqrt (- (* b b) (* (* a c) 4.0)))) (- b))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 64

Calls

4 calls:

41.0ms	(- (* b b) (* (* a c) 4.0))
43.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))
42.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))
3.0ms	(fma (sqrt (sqrt (- (* b b) (* (* a c) 4.0)))) (sqrt (sqrt (- (* b b) (* (* a c) 4.0)))) (- b))

series596.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* b b) (* (* a c) 4.0))
123.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))
159.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))
235.0ms	(fma (sqrt (sqrt (- (* b b) (* (* a c) 4.0)))) (sqrt (sqrt (- (* b b) (* (* a c) 4.0)))) (- b))

simplify5.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
3	2444
2	604
1	200
0	89

prune1.0s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.9b

regimes935.0ms

Accuracy

85.8% (4.1b remaining)

Error of 9.6b against oracle of 5.5b and baseline of 34.5b

bsearch183.0ms

Steps

Iters	Range		Point
6	1.6664801848567985e-94	1.3864776888564433e-93	1.1804820682342164e-93
9	-2.0274263258127503e+155	-2.0044150779320932e+149	-5.8071664004115455e+149

simplify47.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	5744×	body	80	valid
819.0ms	1056×	body	2560	valid
620.0ms	978×	body	1280	valid
391.0ms	2913×	body	80	nan
178.0ms	454×	body	640	valid
104.0ms	138×	body	5120	valid
73.0ms	257×	body	320	valid
22.0ms	119×	body	160	valid