Details

sample112.0ms

Algorithm

intervals

Results

24.0ms	39×	body	1280	valid
22.0ms	32×	body	2560	valid
21.0ms	172×	body	80	valid
11.0ms	20×	body	640	valid
11.0ms	95×	body	80	nan
5.0ms	4×	body	5120	valid
3.0ms	6×	body	320	valid
2.0ms	5×	body	160	valid

simplify74.0ms

Calls

1 calls:

Slowest

74.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize19.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt (fma (* a -4) c (* b b)))
1.3b	(- (sqrt (fma (* a -4) c (* b b))) b)
0.1b	(/ (- (sqrt (fma (* a -4) c (* b b))) b) (* 2 a))
0.0b	(fma (* a -4) c (* b b))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

10.0ms	(/ (- (sqrt (fma (* a -4) c (* b b))) b) (* 2 a))
10.0ms	(- (sqrt (fma (* a -4) c (* b b))) b)
1.0ms	(sqrt (fma (* a -4) c (* b b)))
0.0ms	(fma (* a -4) c (* b b))

series204.0ms

Calls

4 calls:

Slowest

76.0ms	(/ (- (sqrt (fma (* a -4) c (* b b))) b) (* 2 a))
55.0ms	(- (sqrt (fma (* a -4) c (* b b))) b)
39.0ms	(sqrt (fma (* a -4) c (* b b)))
34.0ms	(fma (* a -4) c (* b b))

simplify1.1s

Calls

34 calls:

Slowest

552.0ms	(- (* (sqrt (fma (* a -4) c (* b b))) (sqrt (fma (* a -4) c (* b b)))) (* b b))
103.0ms	(- (pow (sqrt (fma (* a -4) c (* b b))) 3) (pow b 3))
58.0ms	(/ (* (* (- (sqrt (fma (* a -4) c (* b b))) b) (- (sqrt (fma (* a -4) c (* b b))) b)) (- (sqrt (fma (* a -4) c (* b b))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
38.0ms	(- (log (- (sqrt (fma (* a -4) c (* b b))) b)) (log (* 2 a)))
27.0ms	(- (pow b 2) (* 4 (* a c)))

prune786.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.4b

localize11.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt (fma (* a -4) c (* b b)))
16.4b	(/ (* (* a -4) c) (* (* 2 a) (+ (sqrt (fma (* a -4) c (* b b))) b)))
0.9b	(+ (sqrt (fma (* a -4) c (* b b))) b)
0.1b	(* (* 2 a) (+ (sqrt (fma (* a -4) c (* b b))) b))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

11.0ms	(/ (* (* a -4) c) (* (* 2 a) (+ (sqrt (fma (* a -4) c (* b b))) b)))
8.0ms	(* (* 2 a) (+ (sqrt (fma (* a -4) c (* b b))) b))
4.0ms	(+ (sqrt (fma (* a -4) c (* b b))) b)
2.0ms	(sqrt (fma (* a -4) c (* b b)))

series299.0ms

Calls

4 calls:

Slowest

107.0ms	(/ (* (* a -4) c) (* (* 2 a) (+ (sqrt (fma (* a -4) c (* b b))) b)))
86.0ms	(* (* 2 a) (+ (sqrt (fma (* a -4) c (* b b))) b))
58.0ms	(+ (sqrt (fma (* a -4) c (* b b))) b)
47.0ms	(sqrt (fma (* a -4) c (* b b)))

simplify2.8s

Calls

41 calls:

Slowest

536.0ms	(/ (* (* (* (* a -4) c) (* (* a -4) c)) (* (* a -4) c)) (* (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* (+ (sqrt (fma (* a -4) c (* b b))) b) (+ (sqrt (fma (* a -4) c (* b b))) b)) (+ (sqrt (fma (* a -4) c (* b b))) b))))
502.0ms	(/ (* (* (* (* a -4) c) (* (* a -4) c)) (* (* a -4) c)) (* (* (* (* 2 a) (+ (sqrt (fma (* a -4) c (* b b))) b)) (* (* 2 a) (+ (sqrt (fma (* a -4) c (* b b))) b))) (* (* 2 a) (+ (sqrt (fma (* a -4) c (* b b))) b))))
468.0ms	(- (log (* (* a -4) c)) (+ (log (* 2 a)) (log (+ (sqrt (fma (* a -4) c (* b b))) b))))
310.0ms	(- (log (* (* a -4) c)) (log (* (* 2 a) (+ (sqrt (fma (* a -4) c (* b b))) b))))
209.0ms	(+ (* (sqrt (fma (* a -4) c (* b b))) (sqrt (fma (* a -4) c (* b b)))) (- (* b b) (* (sqrt (fma (* a -4) c (* b b))) b)))

prune903.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.1b

localize11.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt (fma (* a -4) c (* b b)))
0.9b	(+ (sqrt (fma (* a -4) c (* b b))) b)
0.1b	(/ c (+ (sqrt (fma (* a -4) c (* b b))) b))
0.0b	(fma (* a -4) c (* b b))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

7.0ms	(+ (sqrt (fma (* a -4) c (* b b))) b)
5.0ms	(/ c (+ (sqrt (fma (* a -4) c (* b b))) b))
2.0ms	(sqrt (fma (* a -4) c (* b b)))
0.0ms	(fma (* a -4) c (* b b))

series249.0ms

Calls

4 calls:

Slowest

120.0ms	(/ c (+ (sqrt (fma (* a -4) c (* b b))) b))
51.0ms	(+ (sqrt (fma (* a -4) c (* b b))) b)
46.0ms	(sqrt (fma (* a -4) c (* b b)))
32.0ms	(fma (* a -4) c (* b b))

simplify425.0ms

Calls

26 calls:

Slowest

189.0ms	(+ (* (sqrt (fma (* a -4) c (* b b))) (sqrt (fma (* a -4) c (* b b)))) (- (* b b) (* (sqrt (fma (* a -4) c (* b b))) b)))
39.0ms	(- (pow b 2) (* 4 (* a c)))
29.0ms	(- (pow b 2) (* 4 (* a c)))
27.0ms	(- (pow b 2) (* 4 (* a c)))
15.0ms	(sqrt (* (cbrt (fma (* a -4) c (* b b))) (cbrt (fma (* a -4) c (* b b)))))

prune950.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.2b

localize8.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt (fma (* a -4) c (* b b)))
0.9b	(+ (sqrt (fma (* a -4) c (* b b))) b)
0.2b	(* c (/ 1 (+ (sqrt (fma (* a -4) c (* b b))) b)))
0.1b	(/ 1 (+ (sqrt (fma (* a -4) c (* b b))) b))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
9×	`*-un-lft-identity`
6×	`sqrt-prod`
6×	`associate-r`
6×	`fma-def`
5×	`add-exp-log`
5×	`pow1`
4×	`add-log-exp`
4×	`log1p-expm1-u`
4×	`associate-/r/`
4×	`add-cbrt-cube`
4×	`expm1-log1p-u`
3×	`flip-+`
3×	`flip3-+`
3×	`associate-/r*`
2×	`div-inv`
1×	`inv-pow`
1×	`pow-flip`
1×	`*-commutative`
1×	`un-div-inv`
1×	`associate-*r/`
1×	`pow1/2`
1×	`frac-2neg`
1×	`clear-num`
1×	`rec-exp`
1×	`rem-sqrt-square`
1×	`+-commutative`

Calls

4 calls:

Slowest

4.0ms	(+ (sqrt (fma (* a -4) c (* b b))) b)
3.0ms	(/ 1 (+ (sqrt (fma (* a -4) c (* b b))) b))
2.0ms	(* c (/ 1 (+ (sqrt (fma (* a -4) c (* b b))) b)))
1.0ms	(sqrt (fma (* a -4) c (* b b)))

series327.0ms

Calls

4 calls:

Slowest

123.0ms	(* c (/ 1 (+ (sqrt (fma (* a -4) c (* b b))) b)))
100.0ms	(/ 1 (+ (sqrt (fma (* a -4) c (* b b))) b))
55.0ms	(+ (sqrt (fma (* a -4) c (* b b))) b)
48.0ms	(sqrt (fma (* a -4) c (* b b)))

simplify695.0ms

Calls

35 calls:

Slowest

191.0ms	(+ (* (sqrt (fma (* a -4) c (* b b))) (sqrt (fma (* a -4) c (* b b)))) (- (* b b) (* (sqrt (fma (* a -4) c (* b b))) b)))
179.0ms	(+ (* (sqrt (fma (* a -4) c (* b b))) (sqrt (fma (* a -4) c (* b b)))) (- (* b b) (* (sqrt (fma (* a -4) c (* b b))) b)))
26.0ms	(sqrt (* (cbrt (fma (* a -4) c (* b b))) (cbrt (fma (* a -4) c (* b b)))))
24.0ms	(sqrt (sqrt (fma (* a -4) c (* b b))))
23.0ms	(sqrt (sqrt (fma (* a -4) c (* b b))))

prune719.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.2b

regimes235.0ms

Accuracy

96.7% (0.6b remaining)

Error of 13.2b against oracle of 12.6b and baseline of 29.6b

bsearch259.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

834.0ms	1026×	body	2560	valid
776.0ms	946×	body	1280	valid
742.0ms	5795×	body	80	valid
402.0ms	2915×	body	80	nan
377.0ms	121×	body	160	valid
273.0ms	477×	body	640	valid
117.0ms	118×	body	5120	valid
102.0ms	230×	body	320	valid