Details

Time bar (total: 2.5m)

sample29.0ms

Algorithm
intervals
Results
12.0ms313×body80valid

simplify109.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01011
11511
22511
34111
46211
57911
69511
711211
812011
912311
done12311

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ t (- 1.0 z))
4.0b
(* x (- (/ y z) (/ t (- 1.0 z))))

rewrite418.0ms

Algorithm
rewrite-expression-head
Rules
791×times-frac
720×add-sqr-sqrt
717×*-un-lft-identity
546×prod-diff
542×add-cube-cbrt
275×distribute-rgt-in distribute-lft-in
86×distribute-lft-out-- difference-of-squares
69×div-inv
54×associate-/r/
28×flip3-- flip--
10×associate-*r*
6×add-exp-log add-cbrt-cube
5×associate-/r*
4×pow1
3×associate-*r/ associate-*l* associate-/l*
2×expm1-log1p-u sub-neg log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
2 → 619
Calls
2 calls:
21.0ms
(/ t (- 1.0 z))
314.0ms
(* x (- (/ y z) (/ t (- 1.0 z))))

series139.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ t (- 1.0 z))
90.0ms
(* x (- (/ y z) (/ t (- 1.0 z))))

simplify2.0s

Counts
625 → 625
Iterations

Useful iterations: done (1.9s)

IterNodesCost
099234059
1217630718
done500127332

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 z) t)
0.9b
(/ 1 (/ (- 1.0 z) t))
4.0b
(* x (- (/ y z) (/ 1 (/ (- 1.0 z) t))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
3919×times-frac
2696×add-sqr-sqrt
2672×*-un-lft-identity
2161×add-cube-cbrt
1612×prod-diff
808×distribute-rgt-in distribute-lft-in
260×difference-of-squares
253×distribute-lft-out--
235×div-inv
27×associate-/r/
22×associate-/r*
18×add-exp-log
16×associate-*r*
12×add-cbrt-cube
8×div-exp associate-/l*
6×pow1
4×cbrt-undiv
3×expm1-log1p-u associate-*r/ associate-*l* log1p-expm1-u add-log-exp
2×sub-neg rec-exp flip3-- frac-2neg 1-exp clear-num flip-- associate-/l/
1×pow-flip div-sub pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod inv-pow unswap-sqr
Counts
3 → 1794
Calls
3 calls:
31.0ms
(/ (- 1.0 z) t)
19.0ms
(/ 1 (/ (- 1.0 z) t))
568.0ms
(* x (- (/ y z) (/ 1 (/ (- 1.0 z) t))))

series154.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(/ (- 1.0 z) t)
43.0ms
(/ 1 (/ (- 1.0 z) t))
68.0ms
(* x (- (/ y z) (/ 1 (/ (- 1.0 z) t))))

simplify4.3s

Counts
1803 → 1803
Iterations

Useful iterations: done (4.1s)

IterNodesCost
02648127076
done5000118360

prune8.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

4.0b
(* x (- (/ y z) (/ 1 (/ (- 1.0 z) t))))
8.6b
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
8.6b
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
8.6b
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))

rewrite959.0ms

Algorithm
rewrite-expression-head
Rules
3787×times-frac
2599×add-sqr-sqrt
2575×*-un-lft-identity
2096×add-cube-cbrt
1612×prod-diff
808×distribute-rgt-in distribute-lft-in
244×difference-of-squares
237×distribute-lft-out--
229×div-inv
26×associate-/r/
16×associate-*r*
12×associate-*r/
9×cbrt-div
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u flip3-- frac-sub flip-- log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3 associate-*l*
2×sub-neg
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 1694
Calls
4 calls:
451.0ms
(* x (- (/ y z) (/ 1 (/ (- 1.0 z) t))))
65.0ms
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
66.0ms
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
70.0ms
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
102.0ms
(* x (- (/ y z) (/ 1 (/ (- 1.0 z) t))))
374.0ms
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
361.0ms
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
361.0ms
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))

simplify3.9s

Counts
1706 → 1706
Iterations

Useful iterations: done (3.8s)

IterNodesCost
02630126172
done5000117568

prune11.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

8.6b
(cbrt (+ (* (fma (/ (* (cbrt y) (cbrt y)) (* (cbrt z) (cbrt z))) (/ (cbrt y) (cbrt z)) (- (* (/ (cbrt 1) (/ (- 1.0 z) (cbrt t))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t))))))) x) (* (fma (- (/ (cbrt 1) (/ (- 1.0 z) (cbrt t)))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t)))) (* (/ (cbrt 1) (/ (- 1.0 z) (cbrt t))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t)))))) x)))
8.6b
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
8.6b
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
49.6b
(fma (- (/ (cbrt 1) (/ (- 1.0 z) (cbrt t)))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t)))) (* (/ (cbrt 1) (/ (- 1.0 z) (cbrt t))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t))))))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-div
6×cbrt-prod associate-*r/
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
2×flip3-- frac-sub flip--
1×distribute-rgt-out flip3-+ flip-+ fma-udef
Counts
4 → 54
Calls
4 calls:
6.0ms
(cbrt (+ (* (fma (/ (* (cbrt y) (cbrt y)) (* (cbrt z) (cbrt z))) (/ (cbrt y) (cbrt z)) (- (* (/ (cbrt 1) (/ (- 1.0 z) (cbrt t))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t))))))) x) (* (fma (- (/ (cbrt 1) (/ (- 1.0 z) (cbrt t)))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t)))) (* (/ (cbrt 1) (/ (- 1.0 z) (cbrt t))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t)))))) x)))
87.0ms
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
100.0ms
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
0.0ms
(fma (- (/ (cbrt 1) (/ (- 1.0 z) (cbrt t)))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t)))) (* (/ (cbrt 1) (/ (- 1.0 z) (cbrt t))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t))))))

series1.8m

Counts
4 → 12
Calls
4 calls:
1.8m
(cbrt (+ (* (fma (/ (* (cbrt y) (cbrt y)) (* (cbrt z) (cbrt z))) (/ (cbrt y) (cbrt z)) (- (* (/ (cbrt 1) (/ (- 1.0 z) (cbrt t))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t))))))) x) (* (fma (- (/ (cbrt 1) (/ (- 1.0 z) (cbrt t)))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t)))) (* (/ (cbrt 1) (/ (- 1.0 z) (cbrt t))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t)))))) x)))
361.0ms
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
378.0ms
(cbrt (* x (- (/ y z) (/ 1 (/ (- 1.0 z) t)))))
271.0ms
(fma (- (/ (cbrt 1) (/ (- 1.0 z) (cbrt t)))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t)))) (* (/ (cbrt 1) (/ (- 1.0 z) (cbrt t))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt t) (cbrt t))))))

simplify984.0ms

Counts
66 → 66
Iterations

Useful iterations: done (981.0ms)

IterNodesCost
02044003
15123086
217392299
done50011824

prune932.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes256.0ms

Accuracy

17.6% (3.9b remaining)

Error of 3.9b against oracle of 0.1b and baseline of 4.8b

bsearch147.0ms

Steps
ItersRangePoint
9
1575.9184687212278
116985770.3131376
475836.53912961675
7
-1.2933484220854896e-234
-1.8461846221151924e-236
-1.263127757283882e-234

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02451
13439
done3439

end0.0ms

sample1.2s

Algorithm
intervals
Results
619.0ms10108×body80valid