Details

sample152.0ms

Algorithm

intervals

Results

47.0ms	35×	body	2560	valid
31.0ms	182×	body	80	valid
25.0ms	29×	body	1280	valid
15.0ms	97×	body	80	nan
8.0ms	12×	body	640	valid
3.0ms	6×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	2×	body	160	valid

simplify247.0ms

Calls

1 calls:

Slowest

246.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize37.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (fma (* a c) -4 (* b b)))
0.8b	(fma (* a c) -4 (* b b))
0.5b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.1b	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`prod-diff`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
16×	`sqrt-prod`
7×	`neg-mul-1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`div-sub` `div-inv` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `flip3--` `pow1/2` `diff-log` `fma-udef` `flip--` `distribute-lft-out--` `associate-/l/`

Calls

4 calls:

Slowest

17.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
5.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series444.0ms

Calls

4 calls:

Slowest

127.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
117.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
104.0ms	(sqrt (fma (* a c) -4 (* b b)))
96.0ms	(fma (* a c) -4 (* b b))

simplify5.3s

Calls

77 calls:

Slowest

136.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))))))
135.0ms	(- (* 2 (/ (* a c) b)) (* 2 b))
118.0ms	(fma 1 (- b) (- (* (sqrt (cbrt (fma (* a c) -4 (* b b)))) (sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b))))))))
116.0ms	(fma -1 b (- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt 1))))
113.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))))))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (fma (* a c) -4 (* b b)))
0.8b	(fma (* a c) -4 (* b b))
0.5b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b	(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `prod-diff`
22×	`add-cube-cbrt`
16×	`sqrt-prod`
7×	`neg-mul-1`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u`
2×	`div-inv` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `sub-neg` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `un-div-inv` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `distribute-lft-out--`

Calls

4 calls:

Slowest

25.0ms	(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
11.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series456.0ms

Calls

4 calls:

Slowest

154.0ms	(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
122.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
100.0ms	(sqrt (fma (* a c) -4 (* b b)))
80.0ms	(fma (* a c) -4 (* b b))

simplify6.5s

Calls

85 calls:

Slowest

469.0ms	(fma (- (cbrt (sqrt (fma (* a c) -4 (* b b))))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b)))))))
309.0ms	(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
225.0ms	(* (* (* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
225.0ms	(* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (/ 1 a))
219.0ms	(+ (log (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (log (/ 1 a)))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.8b

localize11.0ms

Local error

Found 4 expressions with local error:

25.7b	(sqrt (fma (* a c) -4 (* b b)))
0.8b	(fma (* a c) -4 (* b b))
0.5b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`prod-diff`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
16×	`sqrt-prod`
7×	`neg-mul-1`
6×	`add-log-exp`
5×	`pow1` `associate-/r*` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `insert-posit16` `log1p-expm1-u`
2×	`associate-/r/` `div-inv` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `pow1/2` `diff-log` `fma-udef` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow`

Calls

4 calls:

Slowest

16.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
0.0ms	(fma (* a c) -4 (* b b))

series447.0ms

Calls

4 calls:

Slowest

144.0ms	(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
117.0ms	(sqrt (fma (* a c) -4 (* b b)))
106.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
80.0ms	(fma (* a c) -4 (* b b))

simplify5.4s

Calls

78 calls:

Slowest

126.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
122.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt 1))))
119.0ms	(* -2 (/ (* a c) b))
119.0ms	(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))))))
114.0ms	(fma 1 (- b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.8b

localize26.0ms

Local error

Found 4 expressions with local error:

26.6b	(cbrt (fma (* a c) -4 (* b b)))
26.6b	(cbrt (fma (* a c) -4 (* b b)))
26.6b	(cbrt (fma (* a c) -4 (* b b)))
11.5b	(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`rem-sqrt-square` `pow1/2` `sqrt-prod`

Calls

4 calls:

Slowest

3.0ms	(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
1.0ms	(cbrt (fma (* a c) -4 (* b b)))
1.0ms	(cbrt (fma (* a c) -4 (* b b)))
1.0ms	(cbrt (fma (* a c) -4 (* b b)))

series980.0ms

Calls

4 calls:

Slowest

261.0ms	(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
246.0ms	(cbrt (fma (* a c) -4 (* b b)))
241.0ms	(cbrt (fma (* a c) -4 (* b b)))
232.0ms	(cbrt (fma (* a c) -4 (* b b)))

simplify3.7s

Calls

23 calls:

Slowest

399.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
374.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
344.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
307.0ms	(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
297.0ms	(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))

prune1.1s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.8b

regimes461.0ms

Accuracy

82.4% (5.0b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 33.8b

bsearch192.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.3s	1089×	body	2560	valid
824.0ms	5837×	body	80	valid
759.0ms	923×	body	1280	valid
643.0ms	427×	body	640	valid
362.0ms	2942×	body	80	nan
117.0ms	105×	body	5120	valid
81.0ms	233×	body	320	valid
29.0ms	121×	body	160	valid