Details

sample135.0ms

Algorithm

intervals

Results

26.0ms	193×	body	80	valid
25.0ms	29×	body	2560	valid
20.0ms	29×	body	1280	valid
13.0ms	104×	body	80	nan
6.0ms	11×	body	640	valid
3.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	2×	body	160	valid

simplify560.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

560.0ms

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize45.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (fma (* a c) -4 (* b b)))
1.4b	(fma (* a c) -4 (* b b))
0.7b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b	(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
10×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `fma-udef` `div-inv`

Counts

4 → 167

Calls

4 calls:

Slowest

21.0ms	(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)
16.0ms	(- (- 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))

series374.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

104.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
100.0ms	(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)
98.0ms	(sqrt (fma (* a c) -4 (* b b)))
73.0ms	(fma (* a c) -4 (* b b))

simplify17.7s

Counts

205 → 179

Calls

205 calls:

Slowest

460.0ms	(/ (* (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (* (* 2 2) 2))
356.0ms	(- (* (- b) (- b)) (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))))
265.0ms	(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))))))))
256.0ms	(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))))))))
247.0ms	(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))))))))

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.8b

localize23.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (fma (* a c) -4 (* b b)))
1.4b	(fma (* a c) -4 (* b b))
0.7b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b	(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
10×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `fma-udef` `div-inv`

Counts

4 → 167

Calls

4 calls:

Slowest

21.0ms	(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)
10.0ms	(- (- 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))

series406.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(sqrt (fma (* a c) -4 (* b b)))
111.0ms	(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)
106.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
74.0ms	(fma (* a c) -4 (* b b))

simplify17.3s

Counts

205 → 179

Calls

205 calls:

Slowest

434.0ms	(/ (* (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (* (* 2 2) 2))
346.0ms	(- (* (- b) (- b)) (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))))
267.0ms	(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- 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))))))))
263.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt 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))))))))
257.0ms	(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))))))))

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.8b

localize46.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (fma (* a c) -4 (* b b)))
1.4b	(fma (* a c) -4 (* b b))
0.7b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.5b	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt 2)) (sqrt 2))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

570×	`times-frac`
460×	`add-sqr-sqrt`
459×	`*-un-lft-identity`
364×	`sqrt-prod`
287×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
64×	`distribute-rgt-neg-in`
60×	`prod-diff`
46×	`associate-/l*`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`div-inv` `add-log-exp`
7×	`neg-mul-1`
6×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp`
2×	`diff-log` `div-sub`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `neg-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 465

Calls

4 calls:

Slowest

41.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt 2)) (sqrt 2))
30.0ms	(- (- 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))

series906.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

424.0ms	(fma (* a c) -4 (* b b))
254.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt 2)) (sqrt 2))
131.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
97.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.2m

Counts

761 → 477

Calls

761 calls:

Slowest

452.0ms	(/ (/ (+ (sqrt (- b)) (sqrt (sqrt (fma (* a c) -4 (* b b))))) (sqrt 1)) (sqrt (* (cbrt 2) (cbrt 2))))
253.0ms	(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))))))))
253.0ms	(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
239.0ms	(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (sqrt 2)))
237.0ms	(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))))))))

prune7.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.8b

localize78.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (fma (* a c) -4 (* b b)))
1.4b	(fma (* a c) -4 (* b b))
1.0b	(/ (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (sqrt 2)))
1.0b	(/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
75×	`sqrt-prod`
52×	`add-sqr-sqrt`
51×	`*-un-lft-identity` `add-cube-cbrt`
34×	`add-exp-log`
15×	`pow1` `div-exp`
14×	`add-cbrt-cube` `pow1/3`
13×	`pow-flip`
12×	`div-inv`
10×	`associate-/r` `associate-/l`
7×	`cbrt-undiv`
6×	`prod-exp`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `pow-sqr` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp` `pow-div`
3×	`sqrt-pow1` `pow1/2`
2×	`clear-num` `frac-2neg` `pow-prod-down` `cbrt-unprod`
1×	`pow2` `rem-sqrt-square` `pow-plus` `fma-udef` `inv-pow` `associate-/l/`

Counts

4 → 172

Calls

4 calls:

Slowest

32.0ms	(/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
19.0ms	(/ (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (sqrt 2)))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series210.0ms

Counts

4 → 8

Calls

4 calls:

Slowest

118.0ms	(sqrt (fma (* a c) -4 (* b b)))
92.0ms	(fma (* a c) -4 (* b b))
0.0ms	(/ (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (sqrt 2)))
0.0ms	(/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

simplify8.4s

Counts

197 → 180

Calls

197 calls:

Slowest

785.0ms	(/ (* (* (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
436.0ms	(/ (* (* 1 1) 1) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
383.0ms	(/ (/ (* (* 1 1) 1) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
197.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt 2))) (sqrt (sqrt 2)))
183.0ms	(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt 2))) (sqrt (sqrt 2)))

prune3.0s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 9.8b

regimes334.0ms

Accuracy

88% (2.8b remaining)

Error of 12.3b against oracle of 9.5b and baseline of 32.9b

bsearch364.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.6s	1028×	body	2560	valid
983.0ms	5986×	body	80	valid
949.0ms	2978×	body	80	nan
794.0ms	881×	body	1280	valid
290.0ms	439×	body	640	valid
154.0ms	117×	body	5120	valid
86.0ms	212×	body	320	valid
33.0ms	119×	body	160	valid