Details

sample76.0ms

Algorithm

intervals

Results

16.0ms	38×	body	2560	valid
12.0ms	178×	body	80	valid
9.0ms	104×	body	80	nan
8.0ms	24×	body	1280	valid
4.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify155.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	75
2	40
1	22
0	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(- (* b b) (* (* 3.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite106.0ms

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` `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 → 90

Calls

4 calls:

66.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
85.0ms	(- (* b b) (* (* 3.0 a) c))
119.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
113.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1376
1	435
0	167

prune693.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.4b	(- (* b b) (* 3.0 (* a c)))
1.5b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
21.4b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 94

Calls

4 calls:

12.0ms	(* 3.0 (* a c))
8.0ms	(- (* b b) (* 3.0 (* a c)))
53.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
17.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* 3.0 (* a c))
66.0ms	(- (* b b) (* 3.0 (* a c)))
99.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
90.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify1.6s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1243
1	393
0	158

prune551.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(- (* b b) (* (* 3.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite94.0ms

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` `associate-/r*` `times-frac`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-/r/` `flip-+` `flip--`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `prod-exp` `associate-+l-` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

37.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
12.0ms	(- (* b b) (* (* 3.0 a) c))
33.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
51.0ms	(- (* b b) (* (* 3.0 a) c))
88.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
88.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	1395
1	425
0	159

prune620.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) a))
0.4b	(- (* b b) (* 3.0 (* a c)))
1.5b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
21.4b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
36×	`add-cube-cbrt`
34×	`times-frac`
26×	`add-exp-log`
22×	`associate-r`
19×	`prod-diff` `sqrt-prod`
16×	`add-cbrt-cube`
13×	`associate-l`
8×	`div-exp` `prod-exp` `add-log-exp` `difference-of-squares`
7×	`pow1` `fma-neg`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 141

Calls

4 calls:

80.0ms	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) a))
7.0ms	(- (* b b) (* 3.0 (* a c)))
45.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
9.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) a))
76.0ms	(- (* b b) (* 3.0 (* a c)))
100.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
85.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify1.6s

Counts

153 → 153

Iterations

Iter	Nodes
done	5010
2	2156
1	719
0	260

prune713.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

regimes880.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 34.0b

bsearch204.0ms

Steps

Iters	Range		Point
10	2.044647849876085e-45	1.359053137570048e-33	6.407662420749315e-35
10	-8.897020078895062e+156	-1.101416214509623e+146	-8.035809894237901e+152

simplify28.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.0s	5811×	body	80	valid
502.0ms	1026×	body	2560	valid
390.0ms	885×	body	1280	valid
270.0ms	2885×	body	80	nan
172.0ms	506×	body	640	valid
78.0ms	216×	body	320	valid
62.0ms	118×	body	5120	valid
17.0ms	121×	body	160	valid