Details

Time bar (total: 33.7s)

sample385.0ms

Algorithm
intervals
Results
189.0ms135×body1280valid
73.0ms256×pre80true
55.0ms56×body640valid
15.0ms24×body320valid
7.0ms36×body80valid
2.0ms5×body160valid

simplify11.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09314
115314
222314
329314
435314
546314
658314
778314
893314
9126314
10178314
11270314
12330314
13360314
14370314
15386314
16408314
17424314
18440314
19457314
20471314
21487314
22505314
23520314
24534314
25556314
26572314
27587314
28607314
29623314
30639314
31656314
32670314
33686314
34704314
35719314
36733314
37755314
38771314
39786314
40806314
41822314
42838314
43855314
44869314
45885314
46903314
47918314
48932314
49952314
50968314
51983314
521001314
531017314
541033314
551050314
561064314
571080314
581098314
591113314
601127314
611147314
621163314
631178314
641198314
651214314
661230314
671247314
681261314
691277314
701295314
711310314
721324314
731346314
741362314
751377314
761395314
771411314
781427314
791444314
801458314
811474314
821492314
831507314
841521314
851543314
861559314
871574314
881594314
891610314
901626314
911643314
921657314
931673314
941691314
951706314
961720314
971740314
981756314
991771314
1001791314
1011807314
1021823314
1031840314
1041854314
1051870314
1061888314
1071903314
1081917314
1091937314
1101953314
1111968314
1121986314
1132002314
1142018314
1152035314
1162049314
1172065314
1182083314
1192098314
1202112314
1212132314
1222148314
1232163314
1242181314
1252197314
1262213314
1272230314
1282244314
1292260314
1302278314
1312293314
1322307314
1332327314
1342343314
1352358314
1362378314
1372394314
1382410314
1392427314
1402441314
1412457314
1422475314
1432490314
1442504314
1452526314
1462542314
1472557314
1482575314
1492591314
1502607314
1512624314
1522638314
1532654314
1542672314
1552687314
1562701314
1572723314
1582739314
1592754314
1602772314
1612788314
1622804314
1632821314
1642835314
1652851314
1662869314
1672884314
1682898314
1692920314
1702936314
1712951314
1722971314
1732987314
1743003314
1753020314
1763034314
1773050314
1783068314
1793083314
1803097314
1813117314
1823133314
1833148314
1843168314
1853184314
1863200314
1873217314
1883231314
1893247314
1903265314
1913280314
1923294314
1933314314
1943330314
1953345314
1963363314
1973379314
1983395314
1993412314
2003426314
2013442314
2023460314
2033475314
2043489314
2053509314
2063525314
2073540314
2083558314
2093574314
2103590314
2113607314
2123621314
2133637314
2143655314
2153670314
2163684314
2173704314
2183720314
2193735314
2203753314
2213769314
2223785314
2233802314
2243816314
2253832314
2263850314
2273865314
2283879314
2293899314
2303915314
2313930314
2323948314
2333964314
2343980314
2353997314
2364011314
2374027314
2384045314
2394060314
2404074314
2414094314
2424110314
2434125314
2444143314
2454159314
2464175314
2474192314
2484206314
2494222314
2504240314
2514255314
2524269314
2534289314
2544305314
2554320314
2564340314
2574356314
2584372314
2594389314
2604403314
2614419314
2624437314
2634452314
2644466314
2654486314
2664502314
2674517314
2684537314
2694553314
2704569314
2714586314
2724600314
2734616314
2744634314
2754649314
2764663314
2774683314
2784699314
2794714314
2804734314
2814750314
2824766314
2834783314
2844797314
2854813314
2864831314
2874846314
2884860314
2894882314
2904898314
2914913314
2924933314
2934949314
2944965314
2954982314
2964996314
done5000314

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b
(+ x (- (tan (+ y z)) (tan a)))
0.2b
(- (tan (+ y z)) (tan a))
3.6b
(tan (+ y z))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
5×add-sqr-sqrt
4×tan-quot
3×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
2×tan-sum associate-+r+ sum-log sub-neg diff-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-+ flip3-- flip-+ flip-- difference-of-squares
Counts
3 → 42
Calls
3 calls:
11.0ms
(+ x (- (tan (+ y z)) (tan a)))
13.0ms
(- (tan (+ y z)) (tan a))
5.0ms
(tan (+ y z))

series321.0ms

Counts
3 → 9
Calls
3 calls:
135.0ms
(+ x (- (tan (+ y z)) (tan a)))
125.0ms
(- (tan (+ y z)) (tan a))
61.0ms
(tan (+ y z))

simplify1.4s

Counts
51 → 51
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
09118883
119717870
246917870
3150017870
done500017870

prune266.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan y) (tan z))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.3b
(* (tan y) (tan z))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt add-log-exp
7×tan-quot
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
3×sum-log associate-*r* associate-*l* distribute-lft-out
2×+-commutative associate-+r+ sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- times-frac flip3-- pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod flip-- unswap-sqr
Counts
4 → 67
Calls
4 calls:
6.0ms
(+ (tan y) (tan z))
61.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
109.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
11.0ms
(* (tan y) (tan z))

series1.0s

Counts
4 → 12
Calls
4 calls:
100.0ms
(+ (tan y) (tan z))
421.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
387.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
100.0ms
(* (tan y) (tan z))

simplify2.1s

Counts
79 → 79
Iterations

Useful iterations: 3 (937.0ms)

IterNodesCost
015538687
137536931
2102436891
3329136691
done500136691

prune441.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b
(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b
(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))
0.3b
(* (tan y) (tan z))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt *-un-lft-identity
11×add-cbrt-cube add-exp-log add-log-exp
8×add-cube-cbrt
6×pow1
5×tan-quot
4×times-frac
3×associate-*r* associate-*l* associate-/l*
2×cbrt-undiv associate-+r+ sum-log sub-neg flip3-+ diff-log div-exp prod-exp cbrt-unprod flip-+ distribute-lft-out distribute-lft-out-- difference-of-squares associate-/l/
1×frac-times +-commutative clear-num associate-+r- associate-/r* frac-2neg flip3-- pow-prod-down associate-*l/ associate-*r/ associate-/r/ cos-mult *-commutative frac-sub div-inv flip-- unswap-sqr
Counts
4 → 78
Calls
4 calls:
95.0ms
(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
163.0ms
(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
33.0ms
(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))
11.0ms
(* (tan y) (tan z))

series1.1s

Counts
4 → 12
Calls
4 calls:
439.0ms
(- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
396.0ms
(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
161.0ms
(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))
101.0ms
(* (tan y) (tan z))

simplify1.9s

Counts
90 → 90
Iterations

Useful iterations: done (1.9s)

IterNodesCost
019561693
149360098
2162359738
done500659578

prune674.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (tan z))
0.3b
(* (* (sin y) (cos z)) (* (sin y) (cos z)))
0.3b
(* (* (cos y) (sin z)) (* (cos y) (sin z)))
3.5b
(/ (- (* (* (sin y) (cos z)) (* (sin y) (cos z))) (* (* (cos y) (sin z)) (* (cos y) (sin z)))) (* (* (cos y) (cos z)) (- (* (sin y) (cos z)) (* (cos y) (sin z)))))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
39×add-cbrt-cube add-exp-log
35×pow-prod-down
20×prod-exp cbrt-unprod
10×add-sqr-sqrt
8×*-un-lft-identity pow-sqr pow-prod-up add-cube-cbrt
5×associate-*r* associate-*l* associate-/r/
4×frac-times times-frac pow-plus tan-quot associate-*r/ sin-cos-mult associate-/l* add-log-exp
3×cbrt-undiv flip3-- div-exp associate-*l/ cos-mult *-commutative flip--
2×pow2 swap-sqr difference-of-squares associate-/l/
1×clear-num associate-/r* frac-2neg div-sub div-inv unswap-sqr
Counts
4 → 125
Calls
4 calls:
11.0ms
(* (tan y) (tan z))
32.0ms
(* (* (sin y) (cos z)) (* (sin y) (cos z)))
31.0ms
(* (* (cos y) (sin z)) (* (cos y) (sin z)))
129.0ms
(/ (- (* (* (sin y) (cos z)) (* (sin y) (cos z))) (* (* (cos y) (sin z)) (* (cos y) (sin z)))) (* (* (cos y) (cos z)) (- (* (sin y) (cos z)) (* (cos y) (sin z)))))

series544.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (tan y) (tan z))
63.0ms
(* (* (sin y) (cos z)) (* (sin y) (cos z)))
57.0ms
(* (* (cos y) (sin z)) (* (cos y) (sin z)))
319.0ms
(/ (- (* (* (sin y) (cos z)) (* (sin y) (cos z))) (* (* (cos y) (sin z)) (* (cos y) (sin z)))) (* (* (cos y) (cos z)) (- (* (sin y) (cos z)) (* (cos y) (sin z)))))

simplify2.4s

Counts
137 → 137
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
023054924
168746741
2384643660
done502043660

prune770.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes528.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
018690
122690
done22690

end0.0ms

sample7.9s

Algorithm
intervals
Results
4.9s3909×body1280valid
1.2s1990×body640valid
826.0ms8000×pre80true
319.0ms1112×body80valid
236.0ms690×body320valid
105.0ms299×body160valid