Details

sample73.0ms

Algorithm

intervals

Results

19.0ms	187×	body	80	valid
13.0ms	36×	body	2560	valid
9.0ms	30×	body	1280	valid
5.0ms	79×	body	80	nan
2.0ms	10×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify112.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	164
6	164
5	160
4	153
3	121
2	64
1	29
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (* 2.0 a))
0.4b	(fma (* (- a) c) 4.0 (* b b))
0.9b	(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
22.6b	(sqrt (fma (* (- a) c) 4.0 (* b b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `times-frac` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `sqrt-prod` `distribute-lft-out`
2×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 69

Calls

4 calls:

31.0ms	(/ (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (* 2.0 a))
0.0ms	(fma (* (- a) c) 4.0 (* b b))
6.0ms	(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
1.0ms	(sqrt (fma (* (- a) c) 4.0 (* b b)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (* 2.0 a))
84.0ms	(fma (* (- a) c) 4.0 (* b b))
150.0ms	(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
148.0ms	(sqrt (fma (* (- a) c) 4.0 (* b b)))

simplify800.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1064
1	303
0	124

prune579.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (/ 1 (* a 2.0)))
0.4b	(fma (* (- a) c) 4.0 (* b b))
0.9b	(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
22.6b	(sqrt (fma (* (- a) c) 4.0 (* b b)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
13×	`*-un-lft-identity` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`prod-exp`
9×	`add-cube-cbrt`
7×	`pow1` `associate-r`
6×	`add-log-exp`
4×	`expm1-log1p-u` `div-exp` `associate-l` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

58.0ms	(* (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (/ 1 (* a 2.0)))
0.0ms	(fma (* (- a) c) 4.0 (* b b))
10.0ms	(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
2.0ms	(sqrt (fma (* (- a) c) 4.0 (* b b)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (+ b (sqrt (fma (* (- a) c) 4.0 (* b b)))) (/ 1 (* a 2.0)))
100.0ms	(fma (* (- a) c) 4.0 (* b b))
128.0ms	(+ b (sqrt (fma (* (- a) c) 4.0 (* b b))))
120.0ms	(sqrt (fma (* (- a) c) 4.0 (* b b)))

simplify1.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1992
1	398
0	154

prune555.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b))))) a))
0.2b	(* (/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b))))) a)
0.9b	(+ b (sqrt (fma c (* (- a) 4.0) (* b b))))
22.6b	(sqrt (fma c (* (- a) 4.0) (* b b)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
25×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`add-cbrt-cube` `associate-l`
17×	`add-cube-cbrt`
16×	`times-frac`
10×	`pow1` `div-exp`
8×	`prod-exp`
6×	`add-log-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`rec-exp` `fma-def` `1-exp` `associate-r` `associate-/r/` `sqrt-prod` `associate-/l*`
2×	`flip3-+` `pow-prod-down` `associate-*l/` `flip-+` `div-inv` `pow-flip` `unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `-commutative` `inv-pow`

Counts

4 → 106

Calls

4 calls:

27.0ms	(/ 1 (* (/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b))))) a))
52.0ms	(* (/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b))))) a)
6.0ms	(+ b (sqrt (fma c (* (- a) 4.0) (* b b))))
1.0ms	(sqrt (fma c (* (- a) 4.0) (* b b)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ 1 (* (/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b))))) a))
179.0ms	(* (/ 2.0 (+ b (sqrt (fma c (* (- a) 4.0) (* b b))))) a)
104.0ms	(+ b (sqrt (fma c (* (- a) 4.0) (* b b))))
110.0ms	(sqrt (fma c (* (- a) 4.0) (* b b)))

simplify1.7s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	2084
1	488
0	190

prune778.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ b (sqrt (fma c (* (- a) 4.0) (* b b))))
0.9b	(+ b (sqrt (fma (* c (- a)) 4.0 (* b b))))
22.6b	(sqrt (fma (* c (- a)) 4.0 (* b b)))
22.6b	(sqrt (fma c (* (- a) 4.0) (* b b)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `fma-def` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`

Counts

4 → 64

Calls

4 calls:

10.0ms	(+ b (sqrt (fma c (* (- a) 4.0) (* b b))))
11.0ms	(+ b (sqrt (fma (* c (- a)) 4.0 (* b b))))
2.0ms	(sqrt (fma (* c (- a)) 4.0 (* b b)))
2.0ms	(sqrt (fma c (* (- a) 4.0) (* b b)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ b (sqrt (fma c (* (- a) 4.0) (* b b))))
96.0ms	(+ b (sqrt (fma (* c (- a)) 4.0 (* b b))))
101.0ms	(sqrt (fma (* c (- a)) 4.0 (* b b)))
108.0ms	(sqrt (fma c (* (- a) 4.0) (* b b)))

simplify2.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	4679
2	761
1	217
0	95

prune671.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.8b

regimes496.0ms

Accuracy

80.3% (5.6b remaining)

Error of 11.4b against oracle of 5.8b and baseline of 34.3b

bsearch240.0ms

Steps

Iters	Range		Point
9	3.768382185355077e+69	1.107955803311012e+78	9.027398388687083e+77
8	-1.2670716760605177e-136	-3.392970635093907e-140	-1.2471576748785859e-136

simplify11.0ms

Iterations

Iter	Nodes
done	69
3	69
2	68
1	55
0	34

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.0s	1045×	body	2560	valid
719.0ms	5898×	body	80	valid
430.0ms	875×	body	1280	valid
390.0ms	2811×	body	80	nan
186.0ms	448×	body	640	valid
92.0ms	227×	body	320	valid
73.0ms	121×	body	5120	valid
17.0ms	105×	body	160	valid