Details

Time bar (total: 27.9s)

sample423.0ms

Algorithm
intervals
Results
150.0ms1418×body80nan
77.0ms417×body80valid
9.0ms15×body640valid
6.0ms17×body320valid
5.0ms19×body160valid
3.0ms3×body1280valid

simplify992.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
01718
13117
26217
313517
437917
5136017
done500017

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.0b

localize59.0ms

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)))
4.8b
(log (- 1.0 z))

rewrite47.0ms

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:
26.0ms
(* (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)))
13.0ms
(log (- 1.0 z))

series840.0ms

Counts
4 → 12
Calls
4 calls:
385.0ms
(* (exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))) x)
153.0ms
(exp (fma y (- (log z) t) (* a (- (log (- 1.0 z)) b))))
233.0ms
(fma y (- (log z) t) (* a (- (log (- 1.0 z)) b)))
68.0ms
(log (- 1.0 z))

simplify658.0ms

Counts
75 → 75
Iterations

Useful iterations: done (651.0ms)

IterNodesCost
01591277
13601231
211451081
done50011064

prune955.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

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)))

rewrite174.0ms

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:
14.0ms
(* (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)
148.0ms
(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
2.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
428.0ms
(* (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)
134.0ms
(* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))
210.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b))))
293.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z))) b)))

simplify2.0s

Counts
157 → 157
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02886764
16385405
223564431
done50013662

prune946.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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)))
0.2b
(* (- (log z) t) y)
0.2b
(expm1 (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))))
0.3b
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))

rewrite63.0ms

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×log1p-expm1-u add-log-exp
4×expm1-log1p-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:
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)))
58.0ms
(* (- (log z) t) y)
0.0ms
(expm1 (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))))
0.0ms
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))

series1.0s

Counts
4 → 12
Calls
4 calls:
236.0ms
(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)))
96.0ms
(* (- (log z) t) y)
354.0ms
(expm1 (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))))
317.0ms
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))

simplify584.0ms

Counts
72 → 72
Iterations

Useful iterations: done (582.0ms)

IterNodesCost
01321519
12931492
29341316
done50011306

prune693.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (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))))
0.2b
(* (sqrt (expm1 (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))))) (sqrt (expm1 (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))))))
0.3b
(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 (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×pow1
18×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
8×sqrt-pow1 pow1/2 swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up log1p-expm1-u
4×expm1-log1p-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×fma-udef
1×pow2 expm1-log1p pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod expm1-udef
Counts
4 → 82
Calls
4 calls:
1.0ms
(expm1 (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))))
21.0ms
(* (sqrt (expm1 (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))))) (sqrt (expm1 (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))))))
0.0ms
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))
0.0ms
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))

series1.3s

Counts
4 → 12
Calls
4 calls:
343.0ms
(expm1 (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))))
363.0ms
(* (sqrt (expm1 (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))))) (sqrt (expm1 (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))))))
318.0ms
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))
279.0ms
(fma (- (log 1.0) (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (fma 1.0 z b))) a (* (- (log z) t) y))

simplify1.5s

Counts
94 → 94
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01074419
12403179
211372738
done50012585

prune745.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes495.0ms

Accuracy

0% (0.3b 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
02658
12858
done2858

end0.0ms

sample13.1s

Algorithm
intervals
Results
6.0s41278×body80nan
2.2s12555×body80valid
306.0ms406×body640valid
161.0ms379×body320valid
78.0ms74×body1280valid
56.0ms252×body160valid