Details

sample130.0ms

Algorithm

intervals

Results

27.0ms	89×	body	80	nan
26.0ms	197×	body	80	valid
24.0ms	29×	body	2560	valid
20.0ms	32×	body	1280	valid
6.0ms	12×	body	640	valid
5.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify119.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

118.0ms

(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.9b

localize49.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b b) (* (* 3 a) c)))
1.0b	(- (* b b) (* (* 3 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.3b	(* (* 3 a) c)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `pow1` `fma-def` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`sum-log` `flip3--` `sqrt-div` `flip--` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `associate-+l-` `flip-+`

Counts

4 → 84

Calls

4 calls:

Slowest

14.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
13.0ms	(* (* 3 a) c)
12.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
8.0ms	(- (* b b) (* (* 3 a) c))

series325.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
87.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
78.0ms	(- (* b b) (* (* 3 a) c))
36.0ms	(* (* 3 a) c)

simplify4.0s

Counts

41 → 96

Calls

41 calls:

Slowest

772.0ms	(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
505.0ms	(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
445.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
310.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
203.0ms	(- b (* 3/2 (/ (* a c) b)))

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.9b

localize43.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (- (* b b) (* (* 3 a) c)))
22.4b	(sqrt (- (* b b) (* (* 3 a) c)))
1.0b	(- (* b b) (* (* 3 a) c))
1.0b	(- (* b b) (* (* 3 a) c))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

Slowest

15.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
8.0ms	(- (* b b) (* (* 3 a) c))
8.0ms	(- (* b b) (* (* 3 a) c))

series342.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

125.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
84.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
73.0ms	(- (* b b) (* (* 3 a) c))
60.0ms	(- (* b b) (* (* 3 a) c))

simplify3.8s

Counts

32 → 82

Calls

32 calls:

Slowest

444.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
353.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
329.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
309.0ms	(/ (exp (* b b)) (exp (* (* 3 a) c)))
243.0ms	(- b (* 3/2 (/ (* a c) b)))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.9b

localize59.0ms

Local error

Found 4 expressions with local error:

23.1b	(cbrt (- (* b b) (* (* 3 a) c)))
23.1b	(cbrt (- (* b b) (* (* 3 a) c)))
23.1b	(cbrt (- (* b b) (* (* 3 a) c)))
22.4b	(sqrt (* (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (- (* b b) (* (* 3 a) c)))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 101

Calls

4 calls:

Slowest

86.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (- (* b b) (* (* 3 a) c)))))
10.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
10.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
10.0ms	(cbrt (- (* b b) (* (* 3 a) c)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
129.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
116.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
110.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (- (* b b) (* (* 3 a) c)))))

simplify10.5s

Counts

69 → 113

Calls

69 calls:

Slowest

489.0ms	(sqrt (* (* (cbrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c)))) (cbrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))) (cbrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))))
398.0ms	(cbrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
381.0ms	(cbrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
353.0ms	(sqrt (* (* (cbrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c)))) (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (- (pow (* b b) 3) (pow (* (* 3 a) c) 3)))))
351.0ms	(cbrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.9b

localize48.0ms

Local error

Found 4 expressions with local error:

23.1b	(cbrt (- (* b b) (* (* 3 a) c)))
6.9b	(+ (- b) (pow (cbrt (- (* b b) (* (* 3 a) c))) (/ 3 2)))
1.0b	(- (* b b) (* (* 3 a) c))
0.3b	(pow (cbrt (- (* b b) (* (* 3 a) c))) (/ 3 2))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`pow-unpow`
10×	`fma-def` `add-log-exp`
9×	`times-frac`
6×	`cbrt-prod` `unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in`
2×	`cbrt-div` `sum-log` `pow-pow` `flip3--` `pow1/3` `flip--` `distribute-lft-out`
1×	`neg-sub0` `pow-to-exp` `+-commutative` `neg-mul-1` `sub-neg` `flip3-+` `fma-neg` `diff-log` `prod-diff` `neg-log` `pow-exp` `associate-+l-` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 95

Calls

4 calls:

Slowest

47.0ms	(+ (- b) (pow (cbrt (- (* b b) (* (* 3 a) c))) (/ 3 2)))
14.0ms	(- (* b b) (* (* 3 a) c))
10.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
10.0ms	(pow (cbrt (- (* b b) (* (* 3 a) c))) (/ 3 2))

series453.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(pow (cbrt (- (* b b) (* (* 3 a) c))) (/ 3 2))
127.0ms	(+ (- b) (pow (cbrt (- (* b b) (* (* 3 a) c))) (/ 3 2)))
125.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
61.0ms	(- (* b b) (* (* 3 a) c))

simplify5.8s

Counts

53 → 107

Calls

53 calls:

Slowest

456.0ms	(cbrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
413.0ms	(- (pow (pow (/ -1 b) -2/3) 3/2) b)
409.0ms	(pow (* (cbrt (cbrt (- (* b b) (* (* 3 a) c)))) (cbrt (cbrt (- (* b b) (* (* 3 a) c))))) (/ 3 2))
409.0ms	(- (pow (pow (/ 1 b) -2/3) 3/2) b)
355.0ms	(pow (sqrt (cbrt (- (* b b) (* (* 3 a) c)))) (/ 3 2))

prune1.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.9b

regimes823.0ms

Accuracy

85.4% (3.4b remaining)

Error of 14.2b against oracle of 10.7b and baseline of 34.2b

bsearch143.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.2s	5894×	body	80	valid
762.0ms	1022×	body	2560	valid
611.0ms	929×	body	1280	valid
303.0ms	2822×	body	80	nan
207.0ms	460×	body	640	valid
103.0ms	239×	body	320	valid
95.0ms	103×	body	5120	valid
23.0ms	112×	body	160	valid