Details

Time bar (total: 5.5s)

sample27.0ms

Algorithm
intervals
Results
7.0ms250×body80valid
2.0ms17×body640valid
1.0ms10×body1280valid
1.0ms13×body320valid
0.0ms9×body160valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0236
1465
21285
33625
410245
522965
650015
done50015

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
16.1b
(fma (- y z) (/ (- t x) (- a z)) x)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
23.0ms
(/ (- t x) (- a z))
0.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

series155.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(/ (- t x) (- a z))
101.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

simplify57.0ms

Counts
70 → 70
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0268450
1733425
22490423
35001421
done5001421

prune194.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
4.2b
(+ x (* (- y z) (/ (- t x) (- a z))))
6.2b
(* (- y z) (/ (- t x) (- a z)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
74×*-un-lft-identity
51×times-frac
31×associate-*r*
28×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
3×expm1-log1p-u fma-def log1p-expm1-u
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 128
Calls
3 calls:
25.0ms
(/ (- t x) (- a z))
8.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
59.0ms
(* (- y z) (/ (- t x) (- a z)))

series370.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(/ (- t x) (- a z))
174.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
141.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify53.0ms

Counts
137 → 137
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0488901
12066849
25001847
done5001847

prune344.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- t x))
0.5b
(cbrt (- t x))
0.5b
(* (cbrt (- t x)) (cbrt (- t x)))
15.9b
(fma (- y z) (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (cbrt (- t x)) (- a z))) x)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
38×cbrt-prod
34×add-sqr-sqrt
32×*-un-lft-identity
16×cbrt-div
14×add-cube-cbrt
11×pow1
10×swap-sqr
8×flip3-- pow1/3 associate-*r* associate-*l* flip-- distribute-lft-out--
6×add-exp-log difference-of-squares
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 102
Calls
4 calls:
4.0ms
(cbrt (- t x))
4.0ms
(cbrt (- t x))
38.0ms
(* (cbrt (- t x)) (cbrt (- t x)))
0.0ms
(fma (- y z) (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (cbrt (- t x)) (- a z))) x)

series537.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(cbrt (- t x))
151.0ms
(cbrt (- t x))
130.0ms
(* (cbrt (- t x)) (cbrt (- t x)))
104.0ms
(fma (- y z) (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (cbrt (- t x)) (- a z))) x)

simplify40.0ms

Counts
114 → 114
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0315857
11088795
25002740
done5002740

prune381.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- y z))
3.0b
(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
3.4b
(* (cbrt (- y z)) (/ (- t x) (- a z)))
9.6b
(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
114×cbrt-div
84×frac-times
58×flip3-- flip--
53×add-sqr-sqrt
43×*-un-lft-identity
40×associate-*l/
32×associate-*r*
30×add-exp-log
27×times-frac associate-*r/
19×add-cube-cbrt
18×pow1 add-cbrt-cube
15×prod-exp cbrt-unprod
12×cbrt-prod distribute-lft-out-- difference-of-squares
9×associate-*l* pow-prod-down
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×cbrt-undiv fma-def div-exp
2×associate-/r/ *-commutative
1×+-commutative flip3-+ pow1/3 sum-log flip-+ div-inv
Counts
4 → 177
Calls
4 calls:
4.0ms
(cbrt (- y z))
116.0ms
(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
61.0ms
(* (cbrt (- y z)) (/ (- t x) (- a z)))
9.0ms
(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
148.0ms
(cbrt (- y z))
147.0ms
(* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z))))
628.0ms
(* (cbrt (- y z)) (/ (- t x) (- a z)))
174.0ms
(+ x (* (* (cbrt (- y z)) (cbrt (- y z))) (* (cbrt (- y z)) (/ (- t x) (- a z)))))

simplify89.0ms

Counts
189 → 189
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
09112598
133742346
250022273
done50022273

prune465.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.0b

regimes358.0ms

Accuracy

31.1% (8.2b remaining)

Error of 11.9b against oracle of 3.7b and baseline of 15.6b

bsearch81.0ms

Steps
ItersRangePoint
9
1.2893535391803096e+185
1.3650528676108602e+190
1.0813640309665593e+189
7
-2.7815652200329975e+115
-2.4524093287392163e+113
-2.729091847189307e+115

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02716
12716
done2716

end0.0ms

sample747.0ms

Algorithm
intervals
Results
228.0ms7766×body80valid
60.0ms491×body640valid
36.0ms283×body1280valid
33.0ms427×body320valid
15.0ms280×body160valid
3.0ms16×body2560valid