Details

sample60.0ms

Algorithm

intervals

Results

11.0ms	196×	body	80	valid
8.0ms	27×	body	2560	valid
8.0ms	31×	body	1280	valid
5.0ms	92×	body	80	nan
3.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
0.0ms	4×	body	160	valid
0.0ms	3×	body	320	valid

simplify106.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	119	16
5	128	16
done	128	16

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
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×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
27.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(- (* b b) (* 4.0 (* a c)))
25.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
120.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
64.0ms	(- (* b b) (* 4.0 (* a c)))
109.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	165	1697
1	452	1588
2	1989	1361
done	5000	1352

prune452.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
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×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

86.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
56.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
117.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
53.0ms	(- (* b b) (* 4.0 (* a c)))
102.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	165	1697
1	452	1588
2	1989	1361
done	5000	1352

prune509.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

97.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
105.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series522.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
101.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
70.0ms	(- (* b b) (* 4.0 (* a c)))
112.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.7s

Counts

164 → 164

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	259	4025
1	672	3498
2	3592	3142
done	5000	3072

prune530.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

10.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* b b) (* 4.0 (* a c)))
61.0ms	(- (* b b) (* 4.0 (* a c)))
88.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
81.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify4.2s

Counts

78 → 78

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	69	1146
1	184	1058
2	795	952
3	4883	952
done	5000	950

prune515.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.5b

regimes523.0ms

Accuracy

88% (3.5b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 34.4b

bsearch332.0ms

Steps

Iters	Range		Point
8	6412590.878131424	2116652649.122401	683389336.5992492
10	7.683585266441067e-90	6.043928490067347e-79	7.752932492055354e-90
8	-1.5489453231745737e+155	-2.021963087226922e+151	-2.2976245343188767e+152

simplify9.0ms

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	39	74
1	47	74
2	48	66
done	48	66

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.0s	5754×	body	80	valid
666.0ms	1069×	body	2560	valid
541.0ms	917×	body	1280	valid
447.0ms	91×	body	160	valid
204.0ms	2912×	body	80	nan
134.0ms	488×	body	640	valid
58.0ms	109×	body	5120	valid
52.0ms	246×	body	320	valid