Details

sample91.0ms

Algorithm

intervals

Results

23.0ms	203×	body	80	valid
19.0ms	31×	body	2560	valid
13.0ms	21×	body	1280	valid
10.0ms	95×	body	80	nan
9.0ms	21×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify167.0ms

Calls

1 calls:

Slowest

167.0ms

(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize36.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (fma b b (* (* a c) -4)))
1.0b	(- (sqrt (fma b b (* (* a c) -4))) b)
0.8b	(fma b b (* (* a c) -4))
0.1b	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

12.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
7.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series379.0ms

Calls

4 calls:

Slowest

113.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
108.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
97.0ms	(sqrt (fma b b (* (* a c) -4)))
61.0ms	(fma b b (* (* a c) -4))

simplify1.2s

Calls

26 calls:

Slowest

224.0ms	(- b (* 2 (/ (* a c) b)))
95.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
93.0ms	(- (* 2 (/ (* a c) b)) b)
90.0ms	(* -2 (/ (* a c) b))
77.0ms	(- (pow b 2) (* 4 (* a c)))

prune862.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (fma b b (* (* a c) -4)))
1.0b	(- (sqrt (fma b b (* (* a c) -4))) b)
0.8b	(fma b b (* (* a c) -4))
0.2b	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `fma-neg` `add-exp-log` `sqrt-prod`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`div-inv`
1×	`frac-times` `rem-sqrt-square` `sub-neg` `flip3--` `pow1/2` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `un-div-inv` `*-commutative` `cbrt-unprod` `fma-udef` `flip--`

Calls

4 calls:

Slowest

15.0ms	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
13.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series435.0ms

Calls

4 calls:

Slowest

160.0ms	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
104.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
94.0ms	(sqrt (fma b b (* (* a c) -4)))
77.0ms	(fma b b (* (* a c) -4))

simplify2.2s

Calls

34 calls:

Slowest

363.0ms	(* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ 1 a))
242.0ms	(+ (log (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (log (/ 1 a)))
230.0ms	(- b (* 2 (/ (* a c) b)))
195.0ms	(* (* (* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
173.0ms	(* (- (sqrt (fma b b (* (* a c) -4))) b) (/ 1 a))

prune980.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize2.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (fma b b (* (* a c) -4)))
1.0b	(- (sqrt (fma b b (* (* a c) -4))) b)
0.8b	(fma b b (* (* a c) -4))
0.1b	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

30.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
13.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms	(sqrt (fma b b (* (* a c) -4)))
0.0ms	(fma b b (* (* a c) -4))

series383.0ms

Calls

4 calls:

Slowest

123.0ms	(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
108.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
93.0ms	(sqrt (fma b b (* (* a c) -4)))
59.0ms	(fma b b (* (* a c) -4))

simplify1.2s

Calls

26 calls:

Slowest

215.0ms	(- b (* 2 (/ (* a c) b)))
113.0ms	(- (* 2 (/ (* a c) b)) b)
98.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
91.0ms	(* -2 (/ (* a c) b))
80.0ms	(- (pow b 2) (* 4 (* a c)))

prune909.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize20.0ms

Local error

Found 4 expressions with local error:

24.0b	(sqrt (fma b b (* (* a c) -4)))
24.0b	(sqrt (fma b b (* (* a c) -4)))
24.0b	(sqrt (fma b b (* (* a c) -4)))
1.0b	(- (sqrt (fma b b (* (* a c) -4))) b)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

6.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms	(sqrt (fma b b (* (* a c) -4)))
2.0ms	(sqrt (fma b b (* (* a c) -4)))
1.0ms	(sqrt (fma b b (* (* a c) -4)))

series418.0ms

Calls

4 calls:

Slowest

111.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
109.0ms	(sqrt (fma b b (* (* a c) -4)))
101.0ms	(sqrt (fma b b (* (* a c) -4)))
97.0ms	(sqrt (fma b b (* (* a c) -4)))

simplify1.8s

Calls

29 calls:

Slowest

236.0ms	(- b (* 2 (/ (* a c) b)))
235.0ms	(- b (* 2 (/ (* a c) b)))
223.0ms	(- b (* 2 (/ (* a c) b)))
155.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
116.0ms	(- (* 2 (/ (* a c) b)) b)

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

regimes383.0ms

Accuracy

84.9% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 33.4b

bsearch222.0ms

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.3s	885×	body	1280	valid
803.0ms	1034×	body	2560	valid
793.0ms	5888×	body	80	valid
372.0ms	2917×	body	80	nan
228.0ms	464×	body	640	valid
98.0ms	95×	body	5120	valid
95.0ms	240×	body	320	valid
47.0ms	108×	body	160	valid