Details

Time bar (total: 31.5s)

sample424.0ms

Algorithm
intervals
Results
194.0ms1284×body80nan
52.0ms393×body80valid
11.0ms16×body640valid
7.0ms16×body320valid
3.0ms9×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01718
13117
26217
313517
433517
5109117
done500017

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))) x)
0.1b
(exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b))))
0.3b
(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
4.3b
(log (- 1.0 z))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity
8×add-cube-cbrt
7×pow1
6×add-exp-log add-cbrt-cube
5×log-prod add-log-exp
4×expm1-log1p-u associate-*l* log1p-expm1-u
3×exp-prod associate-*r* fma-udef
2×log-div exp-sum
1×flip3-- rem-log-exp pow-prod-down prod-exp log-pow *-commutative flip-- cbrt-unprod rem-exp-log distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 63
Calls
4 calls:
13.0ms
(* (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))) x)
2.0ms
(exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b))))
0.0ms
(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
7.0ms
(log (- 1.0 z))

series974.0ms

Counts
4 → 12
Calls
4 calls:
448.0ms
(* (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))) x)
205.0ms
(exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b))))
266.0ms
(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
54.0ms
(log (- 1.0 z))

simplify2.0s

Counts
75 → 75
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01591277
13551230
28971079
323881064
done50001058

prune502.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
0.0b
(* (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))) x)
0.1b
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
0.3b
(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

rewrite299.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
61×add-sqr-sqrt
60×prod-diff
43×add-cube-cbrt
40×associate--l+
37×distribute-rgt-in distribute-lft-in
21×pow1
17×distribute-lft-out--
13×log-pow
10×associate-*r*
8×add-cbrt-cube
7×add-exp-log associate-*l* difference-of-squares
6×log-prod
5×add-log-exp
4×expm1-log1p-u sub-neg log1p-expm1-u
3×exp-prod fma-udef
2×associate-*r/ exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- rem-exp-log
Counts
4 → 145
Calls
4 calls:
252.0ms
(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
27.0ms
(* (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))) x)
4.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
1.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

series1.1s

Counts
4 → 12
Calls
4 calls:
123.0ms
(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
377.0ms
(* (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))) x)
245.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
359.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

simplify1.2s

Counts
157 → 157
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02886764
15345392
212984429
done50003606

prune885.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
0.0b
(* (pow E (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))) x)
0.1b
(pow E (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
0.3b
(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
66×add-sqr-sqrt
60×prod-diff
45×add-cube-cbrt
40×associate--l+
37×distribute-rgt-in distribute-lft-in
20×pow1
17×distribute-lft-out--
13×add-exp-log log-pow
11×associate-*l*
10×associate-*r*
8×add-cbrt-cube
7×unpow-prod-down difference-of-squares
6×log-prod
5×prod-exp
4×expm1-log1p-u sub-neg pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×pow-unpow fma-udef sqr-pow
2×unpow-prod-up pow-to-exp e-exp-1 associate-*r/ *-commutative cbrt-unprod
1×flip3-- pow-pow pow-prod-down flip--
Counts
4 → 160
Calls
4 calls:
174.0ms
(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
14.0ms
(* (pow E (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))) x)
3.0ms
(pow E (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
0.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

series1.3s

Counts
4 → 12
Calls
4 calls:
167.0ms
(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
502.0ms
(* (pow E (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))) x)
259.0ms
(pow E (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
370.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

simplify1.4s

Counts
172 → 172
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03107455
15875958
214775035
done50014188

prune919.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (log z) t) y)
0.2b
(* (- (log z) t) y)
0.3b
(fma a (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) (* (- (log z) t) y))
0.3b
(fma a (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) (* (- (log z) t) y))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity
12×associate-*l*
10×pow1
8×add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r*
4×expm1-log1p-u associate-*l/ log1p-expm1-u distribute-lft-out-- add-log-exp
2×flip3-- pow-prod-down prod-exp log-pow *-commutative flip-- cbrt-unprod fma-udef difference-of-squares unswap-sqr
Counts
4 → 70
Calls
4 calls:
28.0ms
(* (- (log z) t) y)
43.0ms
(* (- (log z) t) y)
0.0ms
(fma a (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) (* (- (log z) t) y))
0.0ms
(fma a (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) (* (- (log z) t) y))

series1.0s

Counts
4 → 12
Calls
4 calls:
151.0ms
(* (- (log z) t) y)
142.0ms
(* (- (log z) t) y)
363.0ms
(fma a (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) (* (- (log z) t) y))
349.0ms
(fma a (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) (* (- (log z) t) y))

simplify2.1s

Counts
82 → 82
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0991234
12181206
26161064
320821042
done50011038

prune881.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes451.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02429
12929
23129
done3129

end0.0ms

sample13.9s

Algorithm
intervals
Results
7.0s41215×body80nan
2.1s12563×body80valid
271.0ms402×body640valid
155.0ms418×body320valid
80.0ms76×body1280valid
64.0ms267×body160valid