Details

Time bar (total: 31.1s)

sample505.0ms

Algorithm
intervals
Results
201.0ms1400×body80nan
89.0ms412×body80valid
9.0ms12×body640valid
9.0ms18×body320valid
3.0ms10×body160valid
2.0ms1×body1280valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01718
13117
26217
313517
433517
5109117
done500017

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))) x)
0.0b
(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)))
5.0b
(log (- 1.0 z))

rewrite40.0ms

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:
21.0ms
(* (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))) x)
4.0ms
(exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b))))
1.0ms
(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
12.0ms
(log (- 1.0 z))

series1.0s

Counts
4 → 12
Calls
4 calls:
480.0ms
(* (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))) x)
200.0ms
(exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b))))
300.0ms
(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
70.0ms
(log (- 1.0 z))

simplify2.0s

Counts
75 → 75
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01591277
13551230
28971079
323881064
done50001058

prune491.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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)
0.0b
(* 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))))
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)))

rewrite567.0ms

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:
19.0ms
(* (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)
535.0ms
(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
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:
364.0ms
(* (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)
128.0ms
(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
262.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
318.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

simplify1.0s

Counts
157 → 157
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02886764
15345392
212994429
done50003606

prune823.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y)))
0.1b
(expm1 (log1p (exp (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y)))))
0.1b
(* (- (log z) t) y)
0.3b
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
7×pow1 add-cube-cbrt
6×add-exp-log associate-*l* add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×exp-prod associate-*r*
2×associate-*l/ fma-udef distribute-lft-out--
1×expm1-log1p flip3-- exp-sum pow-prod-down prod-exp log-pow *-commutative flip-- cbrt-unprod rem-exp-log expm1-udef difference-of-squares unswap-sqr
Counts
4 → 60
Calls
4 calls:
4.0ms
(exp (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y)))
1.0ms
(expm1 (log1p (exp (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y)))))
59.0ms
(* (- (log z) t) y)
1.0ms
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))

series1.2s

Counts
4 → 12
Calls
4 calls:
274.0ms
(exp (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y)))
368.0ms
(expm1 (log1p (exp (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y)))))
150.0ms
(* (- (log z) t) y)
372.0ms
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))

simplify2.0s

Counts
72 → 72
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01251520
12571471
26851302
322831289
done50011287

prune663.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
7×pow1 add-cube-cbrt
6×add-exp-log associate-*l* add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×exp-prod associate-*r* fma-udef
2×associate-*l/ distribute-lft-out--
1×flip3-- exp-sum pow-prod-down prod-exp log-pow *-commutative flip-- cbrt-unprod rem-exp-log difference-of-squares unswap-sqr
Counts
4 → 59
Calls
4 calls:
2.0ms
(exp (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y)))
34.0ms
(* (- (log z) t) y)
1.0ms
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))
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:
246.0ms
(exp (fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y)))
132.0ms
(* (- (log z) t) y)
337.0ms
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))
350.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

simplify2.1s

Counts
71 → 71
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01341463
12861438
27781257
326681239
done50001237

prune871.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes278.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02429
12629
done2629

end0.0ms

sample13.6s

Algorithm
intervals
Results
6.0s41080×body80nan
2.7s12508×body80valid
240.0ms365×body640valid
175.0ms391×body320valid
80.0ms74×body1280valid
64.0ms277×body160valid