Details

sample392.0ms

Algorithm

intervals

Results

62.0ms	39×	body	640	valid
61.0ms	298×	body	80	nan
29.0ms	145×	body	80	valid
29.0ms	29×	body	1280	valid
17.0ms	22×	body	640	nan
16.0ms	19×	body	1280	nan
14.0ms	24×	body	320	valid
7.0ms	19×	body	160	valid
6.0ms	10×	body	320	nan
2.0ms	5×	body	160	nan

simplify271.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

271.0ms

(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.2b

localize43.0ms

Local error

Found 4 expressions with local error:

18.4b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
14.0b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b	(* (sqrt 2) t)
0.1b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 94

Calls

4 calls:

Slowest

57.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
43.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
25.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
7.0ms	(* (sqrt 2) t)

series2.8s

Counts

4 → 12

Calls

4 calls:

Slowest

1.9s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
510.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
232.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
78.0ms	(* (sqrt 2) t)

simplify8.8s

Counts

64 → 106

Calls

64 calls:

Slowest

380.0ms	(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
362.0ms	(/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) t)) (* (* (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
359.0ms	(sqrt (+ (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (+ (* (* l l) (* l l)) (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
312.0ms	(- (+ (* 2 (pow t 2)) (+ (* 2 (* x (pow l 2))) (* 2 (pow l 2)))))
311.0ms	(* (* l l) (/ (+ x 1) (- x 1)))

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.1b

localize43.0ms

Local error

Found 4 expressions with local error:

26.5b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
7.8b	(/ (* (* t t) 4) x)
3.4b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b	(* (sqrt 2) t)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `times-frac` `div-exp` `associate-r*`
2×	`unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

4 → 78

Calls

4 calls:

Slowest

16.0ms	(/ (* (* t t) 4) x)
7.0ms	(* (sqrt 2) t)
1.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series677.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

473.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
91.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
64.0ms	(* (sqrt 2) t)
49.0ms	(/ (* (* t t) 4) x)

simplify2.8s

Counts

46 → 90

Calls

46 calls:

Slowest

277.0ms	(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
238.0ms	(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
231.0ms	(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
209.0ms	(* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* t t) t))
200.0ms	(sqrt (* (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize40.0ms

Local error

Found 4 expressions with local error:

26.5b	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
7.8b	(/ (* (* t t) 4) x)
3.4b	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

Slowest

27.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
21.0ms	(/ (* (* t t) 4) x)
1.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series718.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

488.0ms	(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
108.0ms	(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
73.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
49.0ms	(/ (* (* t t) 4) x)

simplify3.2s

Counts

46 → 92

Calls

46 calls:

Slowest

293.0ms	(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))
279.0ms	(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* t t) t)))
239.0ms	(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
226.0ms	(sqrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
223.0ms	(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

localize68.0ms

Local error

Found 4 expressions with local error:

27.3b	(cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
27.3b	(cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
27.3b	(cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
11.5b	(sqrt (* (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`cbrt-prod` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 64

Calls

4 calls:

Slowest

10.0ms	(sqrt (* (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
2.0ms	(cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
1.0ms	(cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
1.0ms	(cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

258.0ms	(cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
257.0ms	(sqrt (* (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
253.0ms	(cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
236.0ms	(cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))

simplify5.7s

Counts

32 → 76

Calls

32 calls:

Slowest

657.0ms	(- (+ (exp (* 1/3 (- (+ (log 4) (* 2 (log t))) (log x)))) (* 1/6 (* x (exp (* 1/3 (- (+ (log 4) (* 2 (log t))) (log x))))))) (* 2/9 (* (exp (* 1/3 (- (+ (log 1/16) (* 2 (log x))) (* 4 (log t))))) (pow l 2))))
238.0ms	(cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
230.0ms	(exp (* 1/3 (- (+ (log -2) (log (/ -1 x))) (* 2 (log (/ -1 l))))))
227.0ms	(exp (* 1/3 (- (+ (log -2) (log (/ -1 x))) (* 2 (log (/ -1 l))))))
222.0ms	(* (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))

prune1.3s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.0b

regimes553.0ms

Accuracy

77% (5.4b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 27.1b

bsearch1.9s

end0.0ms

sample9.0s

Algorithm

intervals

Results

2.1s	5155×	body	80	valid
2.1s	10177×	body	80	nan
933.0ms	1017×	body	640	valid
909.0ms	619×	body	640	nan
833.0ms	832×	body	1280	valid
656.0ms	627×	body	1280	nan
449.0ms	617×	body	320	valid
201.0ms	323×	body	320	nan
163.0ms	379×	body	160	valid
63.0ms	182×	body	160	nan