Details

sample333.0ms

Algorithm

intervals

Results

243.0ms	1896×	body	80	nan
30.0ms	258×	body	80	valid

simplify427.0ms

Calls

1 calls:

Slowest

427.0ms

(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (log (+ x y)) (log z))
0.1b	(* (- a 0.5) (log t))
0.1b	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.0b	(- (+ (log (+ x y)) (log z)) t)

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`pow1`
7×	`fma-def`
6×	`associate-+l+` `flip3--` `add-cbrt-cube` `associate-*l/` `add-exp-log` `flip--` `add-log-exp`
5×	`fma-neg` `associate-+l-`
4×	`expm1-log1p-u` `log-div` `flip3-+` `frac-add` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
3×	`log-prod` `associate-r` `associate-l` `log-pow`
2×	`associate--l-` `+-commutative` `sum-log` `sub-neg` `associate--l+`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

117.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
33.0ms	(- (+ (log (+ x y)) (log z)) t)
10.0ms	(+ (log (+ x y)) (log z))
6.0ms	(* (- a 0.5) (log t))

series476.0ms

Calls

4 calls:

Slowest

208.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
152.0ms	(- (+ (log (+ x y)) (log z)) t)
59.0ms	(+ (log (+ x y)) (log z))
57.0ms	(* (- a 0.5) (log t))

simplify6.0s

Calls

52 calls:

Slowest

550.0ms	(+ (* (- (pow (+ (log (+ x y)) (log z)) 3) (pow t 3)) (+ (* a a) (+ (* 0.5 0.5) (* a 0.5)))) (* (+ (* (+ (log (+ x y)) (log z)) (+ (log (+ x y)) (log z))) (+ (* t t) (* (+ (log (+ x y)) (log z)) t))) (* (- (pow a 3) (pow 0.5 3)) (log t))))
457.0ms	(+ (* (- (* (+ (log (+ x y)) (log z)) (+ (log (+ x y)) (log z))) (* t t)) (+ (* a a) (+ (* 0.5 0.5) (* a 0.5)))) (* (+ (+ (log (+ x y)) (log z)) t) (* (- (pow a 3) (pow 0.5 3)) (log t))))
440.0ms	(- (+ (* 0.5 (log (/ -1 t))) (* a (log -1))) (+ (* a (log (/ -1 t))) (* 0.5 (log -1))))
358.0ms	(- (* 0.5 (log (/ 1 t))) (+ t (+ (log (/ 1 z)) (+ (log (/ 1 x)) (* a (log (/ 1 t)))))))
309.0ms	(sqrt (+ (log (+ x y)) (log z)))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ (log (+ x y)) (log z))
0.1b	(* (- a 0.5) (log t))
0.1b	(- (+ (log (+ x y)) (log z)) (- t (* (- a 0.5) (log t))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`prod-diff`
12×	`pow1` `distribute-lft-out`
7×	`log-pow`
6×	`add-log-exp`
5×	`flip3-+` `add-cbrt-cube` `fma-neg` `add-exp-log` `flip-+`
4×	`log-div` `fma-def` `flip3--` `frac-sub` `associate-+l-` `flip--`
3×	`expm1-log1p-u` `associate-+l+` `log-prod` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`associate--l-` `sum-log` `sub-neg` `diff-log` `associate-*l/` `associate--r+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `associate--r-` `difference-of-squares`

Calls

3 calls:

Slowest

60.0ms	(- (+ (log (+ x y)) (log z)) (- t (* (- a 0.5) (log t))))
6.0ms	(+ (log (+ x y)) (log z))
5.0ms	(* (- a 0.5) (log t))

series333.0ms

Calls

3 calls:

Slowest

204.0ms	(- (+ (log (+ x y)) (log z)) (- t (* (- a 0.5) (log t))))
68.0ms	(+ (log (+ x y)) (log z))
61.0ms	(* (- a 0.5) (log t))

simplify20.0s

Calls

82 calls:

Slowest

707.0ms	(* (+ (* (log (+ x y)) (log (+ x y))) (- (* (log z) (log z)) (* (log (+ x y)) (log z)))) (+ t (* (- a 0.5) (log t))))
569.0ms	(fma (- (cbrt (- t (* (- a 0.5) (log t))))) (* (cbrt (- t (* (- a 0.5) (log t)))) (cbrt (- t (* (- a 0.5) (log t))))) (* (cbrt (- t (* (- a 0.5) (log t)))) (* (cbrt (- t (* (- a 0.5) (log t)))) (cbrt (- t (* (- a 0.5) (log t)))))))
562.0ms	(fma (- (cbrt (- t (* (- a 0.5) (log t))))) (* (cbrt (- t (* (- a 0.5) (log t)))) (cbrt (- t (* (- a 0.5) (log t))))) (* (cbrt (- t (* (- a 0.5) (log t)))) (* (cbrt (- t (* (- a 0.5) (log t)))) (cbrt (- t (* (- a 0.5) (log t)))))))
544.0ms	(fma (- (cbrt (- t (* (- a 0.5) (log t))))) (* (cbrt (- t (* (- a 0.5) (log t)))) (cbrt (- t (* (- a 0.5) (log t))))) (* (cbrt (- t (* (- a 0.5) (log t)))) (* (cbrt (- t (* (- a 0.5) (log t)))) (cbrt (- t (* (- a 0.5) (log t)))))))
536.0ms	(- (* (- (* (log (+ x y)) (log (+ x y))) (* (log z) (log z))) (+ (* t t) (+ (* (* (- a 0.5) (log t)) (* (- a 0.5) (log t))) (* t (* (- a 0.5) (log t)))))) (* (- (log (+ x y)) (log z)) (- (pow t 3) (pow (* (- a 0.5) (log t)) 3))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.5b	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`pow1`
20×	`cbrt-div`
16×	`log-pow`
15×	`distribute-lft-out`
11×	`flip3-+` `flip-+`
10×	`log-div` `fma-def` `associate-+l-`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`pow1/3`
5×	`pow-prod-down` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sum-log`
2×	`associate-+r-` `associate-l/` `associate-r/` `pow-prod-up`
1×	`pow2` `+-commutative` `associate-+l+` `associate-+r+` `log-prod` `pow-plus`

Calls

4 calls:

Slowest

53.0ms	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))
1.0ms	(cbrt (+ x y))
1.0ms	(cbrt (+ x y))
1.0ms	(cbrt (+ x y))

series1.1s

Calls

4 calls:

Slowest

516.0ms	(cbrt (+ x y))
266.0ms	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))
171.0ms	(cbrt (+ x y))
145.0ms	(cbrt (+ x y))

simplify4.4s

Calls

55 calls:

Slowest

472.0ms	(- (+ (log (* (pow (pow x 2) 1/3) (pow (cbrt -1) 2))) (+ (log (* (pow (* x -1) 1/3) (cbrt -1))) (log -1))) (log (/ -1 z)))
420.0ms	(- (+ (log (pow (/ 1 x) -2/3)) (log (pow (/ 1 x) -1/3))) (log (/ 1 z)))
388.0ms	(- (+ (pow y 1/3) (* 1/3 (* x (pow (/ 1 (pow y 2)) 1/3)))) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 5)) 1/3))))
375.0ms	(- (+ (pow y 1/3) (* 1/3 (* x (pow (/ 1 (pow y 2)) 1/3)))) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 5)) 1/3))))
360.0ms	(- (+ (pow y 1/3) (* 1/3 (* x (pow (/ 1 (pow y 2)) 1/3)))) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 5)) 1/3))))

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.4b	(+ (log (cbrt (+ x y))) (+ (log (cbrt (+ x y))) (+ (log (cbrt (+ x y))) (log z))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`distribute-lft-out`
22×	`pow1`
19×	`log-pow`
12×	`cbrt-prod` `cbrt-div`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`flip3-+` `flip-+`
6×	`log-div` `associate-+l+` `log-prod` `associate-+r-` `sum-log` `associate-+l-` `add-log-exp`
5×	`fma-def`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `associate-+r+`

Calls

4 calls:

Slowest

79.0ms	(+ (log (cbrt (+ x y))) (+ (log (cbrt (+ x y))) (+ (log (cbrt (+ x y))) (log z))))
2.0ms	(cbrt (+ x y))
1.0ms	(cbrt (+ x y))
1.0ms	(cbrt (+ x y))

series564.0ms

Calls

4 calls:

Slowest

152.0ms	(+ (log (cbrt (+ x y))) (+ (log (cbrt (+ x y))) (+ (log (cbrt (+ x y))) (log z))))
142.0ms	(cbrt (+ x y))
136.0ms	(cbrt (+ x y))
135.0ms	(cbrt (+ x y))

simplify4.0s

Calls

59 calls:

Slowest

504.0ms	(- (* 3 (log (pow (/ 1 x) -1/3))) (log (/ 1 z)))
438.0ms	(- (+ (* 3 (log (* (pow (* x -1) 1/3) (cbrt -1)))) (log -1)) (log (/ -1 z)))
407.0ms	(- (+ (pow y 1/3) (* 1/3 (* x (pow (/ 1 (pow y 2)) 1/3)))) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 5)) 1/3))))
381.0ms	(- (+ (pow y 1/3) (* 1/3 (* x (pow (/ 1 (pow y 2)) 1/3)))) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 5)) 1/3))))
327.0ms	(- (+ (pow y 1/3) (* 1/3 (* x (pow (/ 1 (pow y 2)) 1/3)))) (* 1/9 (* (pow x 2) (pow (/ 1 (pow y 5)) 1/3))))

prune2.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

Details

sample333.0ms

simplify427.0ms

prune25.0ms

localize45.0ms

rewrite167.0ms

series476.0ms

simplify6.0s

prune1.4s

localize5.0ms

rewrite73.0ms

series333.0ms

simplify20.0s

prune1.6s

localize20.0ms

rewrite56.0ms

series1.1s

simplify4.4s

prune2.2s

localize20.0ms

rewrite85.0ms

series564.0ms

simplify4.0s

prune2.0s

regimes1.6s

bsearch3.0ms

end0.0ms