Details

Time bar (total: 20.6s)

sample47.0ms

Algorithm
intervals
Results
18.0ms271×body80valid

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01417
12416
24315
37515
412715
518215
621515
729115
860015
9174815
done500015

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* z (- b y))
0.0b
(* z (- t a))
1.0b
(+ (* x y) (* z (- t a)))
22.7b
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
56×*-un-lft-identity
54×prod-diff
52×add-cube-cbrt
33×distribute-rgt-in distribute-lft-in
22×associate-+r+
10×add-exp-log associate-*r* add-cbrt-cube
9×times-frac
8×pow1
6×sub-neg associate-*l* add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×flip3-+ associate-/r* flip-+ associate-/l*
2×flip3-- pow-prod-down prod-exp associate-/r/ *-commutative flip-- cbrt-unprod associate-/l/ distribute-lft-out-- difference-of-squares unswap-sqr
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 161
Calls
4 calls:
28.0ms
(* z (- b y))
25.0ms
(* z (- t a))
14.0ms
(+ (* x y) (* z (- t a)))
42.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series821.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* z (- b y))
70.0ms
(* z (- t a))
77.0ms
(+ (* x y) (* z (- t a)))
614.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify1.8s

Counts
173 → 173
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02912904
17112384
228671997
done50011922

prune599.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.8b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b
(* z (- b y))
0.8b
(fma (- t a) z (* x y))
22.7b
(/ (+ (fma (- t a) z (* x y)) (* z (fma (- a) 1 (* a 1)))) (+ y (* z (- b y))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
27×*-un-lft-identity
25×add-cube-cbrt
18×prod-diff
11×distribute-rgt-in distribute-lft-in
9×times-frac
7×add-exp-log add-cbrt-cube
5×pow1 associate-*r*
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×sub-neg flip3-+ associate-*r/ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative flip-- cbrt-unprod fma-udef div-inv distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 89
Calls
3 calls:
33.0ms
(* z (- b y))
0.0ms
(fma (- t a) z (* x y))
39.0ms
(/ (+ (fma (- t a) z (* x y)) (* z (fma (- a) 1 (* a 1)))) (+ y (* z (- b y))))

series1.7s

Counts
3 → 9
Calls
3 calls:
40.0ms
(* z (- b y))
73.0ms
(fma (- t a) z (* x y))
1.6s
(/ (+ (fma (- t a) z (* x y)) (* z (fma (- a) 1 (* a 1)))) (+ y (* z (- b y))))

simplify1.0s

Counts
98 → 98
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01892181
14461888
218271546
done50001521

prune475.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ 1 (fma (- b y) z y))
0.8b
(fma (- t a) z (* x y))
22.4b
(* (+ (fma (- t a) z (* x y)) (* z (fma (- a) 1 (* a 1)))) (/ 1 (fma (- b y) z y)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×*-un-lft-identity times-frac
19×add-cube-cbrt
16×add-exp-log
13×associate-*r*
10×add-cbrt-cube
6×pow1
4×div-exp prod-exp
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv frac-times rec-exp flip3-+ 1-exp associate-*l/ cbrt-unprod flip-+ div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative fma-udef inv-pow
Counts
3 → 85
Calls
3 calls:
10.0ms
(/ 1 (fma (- b y) z y))
1.0ms
(fma (- t a) z (* x y))
40.0ms
(* (+ (fma (- t a) z (* x y)) (* z (fma (- a) 1 (* a 1)))) (/ 1 (fma (- b y) z y)))

series1.8s

Counts
3 → 9
Calls
3 calls:
130.0ms
(/ 1 (fma (- b y) z y))
60.0ms
(fma (- t a) z (* x y))
1.6s
(* (+ (fma (- t a) z (* x y)) (* z (fma (- a) 1 (* a 1)))) (/ 1 (fma (- b y) z y)))

simplify3.4s

Counts
94 → 94
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01322102
13251860
223821544
done50001538

prune476.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.0b

localize27.0ms

Local error

Found 2 expressions with local error:

0.8b
(fma (- t a) z (* x y))
22.7b
(/ (fma (+ (- a) a) z (fma (- t a) z (* x y))) (fma (- b y) z y))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
2 → 39
Calls
2 calls:
1.0ms
(fma (- t a) z (* x y))
10.0ms
(/ (fma (+ (- a) a) z (fma (- t a) z (* x y))) (fma (- b y) z y))

series423.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(fma (- t a) z (* x y))
354.0ms
(/ (fma (+ (- a) a) z (fma (- t a) z (* x y))) (fma (- b y) z y))

simplify1.2s

Counts
45 → 45
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0781095
11301084
2320942
31378866
done5000752

prune324.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 18.0b

regimes723.0ms

Accuracy

19.2% (3.7b remaining)

Error of 21.4b against oracle of 17.7b and baseline of 22.2b

bsearch232.0ms

Steps
ItersRangePoint
7
1.4865572725398717e+297
8.707108496648727e+298
8.056516503795624e+298
9
6.752531628819403e+166
2.1847758414590318e+172
3.485182784660639e+169
8
-1.2655422099740851e+178
-3.555713338340709e+174
-8.035727998527715e+176

simplify14.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03585
14581
24781
done4781

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.4s8425×body80valid